// Numbas version: finer_feedback_settings
{"name": "Test Yourself", "feedback": {"showtotalmark": true, "advicethreshold": 0, "showanswerstate": true, "showactualmark": true, "allowrevealanswer": true, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "duration": 0, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "metadata": {"description": "<p>This test has a mixture of fundamentals questions. &nbsp;You can use this to see which areas you need to practice.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Fractions - Four Operations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "j", "m", "p", "r", "t", "v", "x", "z", "bb", "dd", "ff", "hh", "jj", "ll", "nn", "pp", "rr", "tt", "h", "k", "l", "n", "o", "q", "s", "u", "w", "y", "aa", "cc", "ee", "gg", "ii", "kk", "mm", "oo", "qq", "ss"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>What is the answer to $\\frac{\\var{a}}{\\var{b}} \\times \\frac{\\var{c}}{\\var{b}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(a*c)/(b*b)", "minValue": "(a*c)/(b*b)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Multiply the numerators</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "a*c", "minValue": "a*c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply the denominators</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "b*b", "minValue": "b*b", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Put into a fration</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(a*c)/(b*b)", "minValue": "(a*c)/(b*b)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>What is the answer to $\\frac{\\var{d}}{\\var{f}} \\div \\frac{\\var{g}}{\\var{f}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "d/g", "minValue": "d/g", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Filp the second fraction</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "f/g", "minValue": "f/g", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply the fractions as above</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(d*f)/(g*f)", "minValue": "(d*f)/(g*f)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>What is the answer to $\\frac{\\var{h}}{\\var{j}} + \\frac{\\var{k}}{\\var{j}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(h+k)/j", "minValue": "(h+k)/j", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Check to see if the denominators are the same</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}, {"prompt": "<p>Add the numerators</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "h+k", "minValue": "h+k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Write as a fraction over the similar denominator; cancel down if you can.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(h+k)/j", "minValue": "(h+k)/j", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>What is the answer to $\\frac{\\var{l}}{\\var{m}} - \\frac{\\var{n}}{\\var{m}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(l-n)/m", "minValue": "(l-n)/m", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Check to see if the denominators are the same</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}, {"prompt": "<p>Subtract the numerators</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "abs((l-n))", "minValue": "abs((l-n))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Create a fraction with the original denominator; cancel down if you can.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(abs((l-n)))/m", "minValue": "(abs((l-n)))/m", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "1", "prompt": "<p>What is the answer to $\\frac{\\var{o}}{\\var{p}} \\times \\frac{\\var{q}}{\\var{r}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(o*q)/(p*r)", "minValue": "(o*q)/(p*r)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Multiply the numerators to make the top of the fraction</p>\n<p>Multiply the denominators to make the bottom of the fraction</p>\n<p>Cancel down if you can</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "1", "prompt": "<p>What is the answer to $\\frac{\\var{s}}{\\var{t}} \\div \\frac{\\var{u}}{\\var{v}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(s*v)/(u*t)", "minValue": "(s*v)/(u*t)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Flip the second fraction</p>\n<p>Multiply through as before</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "1", "prompt": "<p>What is the answer to $\\frac{\\var{w}}{\\var{x}} + \\frac{\\var{y}}{\\var{z}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "((w*z)+(y*x))/(x*z)", "minValue": "((w*z)+(y*x))/(x*z)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Check to see if the denominators are the same</p>\n<p>If they are not - multiply each fraction up to equivalent fractions with equal denominators</p>\n<p>Once they are equal add the numerators and put over the equal denominator</p>\n<p>Cancel down if needed</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "1", "prompt": "<p>What is the answer to $\\frac{\\var{aa}}{\\var{bb}} - \\frac{\\var{cc}}{\\var{dd}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "((aa*dd)-(cc*bb))/(bb*dd)", "minValue": "((aa*dd)-(cc*bb))/(bb*dd)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Check to see if the denominators are the same</p>\n<p>If they are not - multiply each fraction up to equivalent fractions with equal denominators</p>\n<p>Once they are equal subtract&nbsp;the numerators and put over the equal denominator</p>\n<p>Cancel down if needed</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "3", "prompt": "<p>What is the answer to $\\frac{\\var{ee}}{\\var{ff}} \\times&nbsp;\\frac{\\var{gg}}{\\var{hh}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(ee*gg)/(ff*hh)", "minValue": "(ee*gg)/(ff*hh)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Follow through the steps from the first and fifth questions</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "3", "prompt": "<p>What is the answer to $\\frac{\\var{ii}}{\\var{jj}} \\div \\frac{\\var{kk}}{\\var{ll}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(ii*ll)/(jj*kk)", "minValue": "(ii*ll)/(jj*kk)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Follow the steps from the second and sixth questions</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "3", "prompt": "<p>What is the answer to $\\frac{\\var{mm}}{\\var{nn}} + \\frac{\\var{oo}}{\\var{pp}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "((mm*pp)+(nn*oo))/(nn*pp)", "minValue": "((mm*pp)+(nn*oo))/(nn*pp)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Follow the steps from the third &nbsp;and seventh questions</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "3", "prompt": "<p>What is the answer to $\\frac{\\var{qq}}{\\var{rr}} - \\frac{\\var{ss}}{\\var{tt}}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "((qq*tt)-(rr*ss))/(rr*tt)", "minValue": "((qq*tt)-(rr*ss))/(rr*tt)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Follow the steps from the fourth and eighth questions</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>These are basic questions to help you practice adding, subtracting, multiplying and dividing fractions.</p>\n<p>You should be able to do these without a calculator.</p>\n<p>You can show steps to help you with the methods. &nbsp;You will lose marks for continuously veiwing steps.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"aa": {"definition": "random(1..bb-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "aa", "description": ""}, "jj": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "jj", "description": ""}, "cc": {"definition": "random(1..dd-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "gg": {"definition": "random(1..hh-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "gg", "description": ""}, "pp": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "pp", "description": ""}, "nn": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "nn", "description": ""}, "ll": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ll", "description": ""}, "ee": {"definition": "random(1..ff-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ee", "description": ""}, "qq": {"definition": "random(1..rr-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "qq", "description": ""}, "bb": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "bb", "description": ""}, "dd": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "dd", "description": ""}, "hh": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "hh", "description": ""}, "a": {"definition": "random(1..b-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "ff": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ff", "description": ""}, "ss": {"definition": "random(1..tt-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ss", "description": ""}, "d": {"definition": "random(1..f-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "oo": {"definition": "random(1..pp-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "oo", "description": ""}, "ii": {"definition": "random(1..jj-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ii", "description": ""}, "c": {"definition": "random(1..b-a) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "rr": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "rr", "description": ""}, "g": {"definition": "random(1..f-d) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "kk": {"definition": "random(1..ll-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "kk", "description": ""}, "h": {"definition": "random(1..j-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(1..j-h) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(1..m-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "o": {"definition": "random(1..p-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "o", "description": ""}, "n": {"definition": "random(1..m-l) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "random(1..r-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random(1..t-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(1..v-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "random(1..x-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "v": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "y": {"definition": "random(1..x-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "z": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}, "tt": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "tt", "description": ""}, "mm": {"definition": "random(1..nn-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "mm", "description": ""}}, "metadata": {"description": "<p>This is a set of questions designed to help you praction adding, subtracting, multiplying and dividing fractions.</p>\n<p>All of these can be done without a calculator</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Fractions - Equivalent Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"maxAnswers": 0, "prompt": "<p>Tick&nbsp;all the equivalent fractions.</p>\n<p>You should have no empty options.</p>", "matrix": [["1", "1", "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, "0", 0, "1", "1", "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, "1", "1", "1", 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, "0", 0, "1", "1", "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, "1", "1", "1", 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, "1", "1", "1"]], "shuffleAnswers": true, "minAnswers": 0, "variableReplacements": [], "answers": ["<p>$\\frac{\\var{a*o}}{\\var{b*o}}$</p>", "<p>$\\frac{\\var{a*p}}{\\var{b*p}}$</p>", "<p>$\\frac{\\var{a*q}}{\\var{b*q}}$</p>", "<p>$\\frac{\\var{c*r}}{\\var{d*r}}$</p>", "<p>$\\frac{\\var{c*s}}{\\var{d*s}}$</p>", "<p>$\\frac{\\var{c*t}}{\\var{d*t}}$</p>", "<p>$\\frac{\\var{f*u}}{\\var{g*u}}$</p>", "<p>$\\frac{\\var{f*v}}{\\var{g*v}}$</p>", "<p>$\\frac{\\var{f*w}}{\\var{g*w}}$</p>", "<p>$\\frac{\\var{h*x}}{\\var{j*x}}$</p>", "<p>$\\frac{\\var{h*y}}{\\var{j*y}}$</p>", "<p>$\\frac{\\var{h*z}}{\\var{j*z}}$</p>", "<p>$\\frac{\\var{k*aa}}{\\var{l*aa}}$</p>", "<p>$\\frac{\\var{k*bb}}{\\var{l*bb}}$</p>", "<p>$\\frac{\\var{k*cc}}{\\var{l*cc}}$</p>", "<p>$\\frac{\\var{m*dd}}{\\var{n*dd}}$</p>", "<p>$\\frac{\\var{m*ee}}{\\var{n*ee}}$</p>", "<p>$\\frac{\\var{m*ff}}{\\var{n*ff}}$</p>"], "choices": ["<p>$\\frac{\\var{a}}{\\var{b}}$</p>", "<p>$\\frac{\\var{c}}{\\var{d}}$</p>", "<p>$\\frac{\\var{f}}{\\var{g}}$</p>", "<p>$\\frac{\\var{h}}{\\var{j}}$</p>", "<p>$\\frac{\\var{k}}{\\var{l}}$</p>", "<p>$\\frac{\\var{m}}{\\var{n}}$</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "checkbox", "maxMarks": 0, "scripts": {}, "warningType": "none", "marks": 0, "showCorrectAnswer": true, "type": "m_n_x", "shuffleChoices": true, "minMarks": 0, "layout": {"expression": "", "type": "all"}}, {"maxAnswers": 0, "prompt": "<p>Reading across each row check the fraction which&nbsp;is the simplest form of the fraction for that row.</p>", "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "shuffleAnswers": true, "minAnswers": 0, "variableReplacements": [], "answers": ["<p>$\\frac{\\var{gg}}{\\var{hh}}$</p>", "<p>$\\frac{\\var{ii}}{\\var{jj}}$</p>", "<p>$\\frac{\\var{jj}}{\\var{kk}}$</p>", "<p>$\\frac{\\var{hh}}{\\var{ll}}$</p>", "<p>$\\frac{\\var{kk}}{\\var{mm}}$</p>", "<p>$\\frac{\\var{gg}}{\\var{nn}}$</p>", "<p>$\\frac{\\var{gg*oo}}{\\var{hh*oo}}$</p>", "<p>$\\frac{\\var{gg*pp}}{\\var{hh*pp}}$</p>", "<p>$\\frac{\\var{ii*qq}}{\\var{jj*qq}}$</p>", "<p>$\\frac{\\var{ii*rr}}{\\var{jj*rr}}$</p>", "<p>$\\frac{\\var{jj*ss}}{\\var{kk*ss}}$</p>", "<p>$\\frac{\\var{jj*tt}}{\\var{kk*tt}}$</p>", "<p>$\\frac{\\var{hh*uu}}{\\var{ll*uu}}$</p>", "<p>$\\frac{\\var{hh*vv}}{\\var{ll*vv}}$</p>", "<p>$\\frac{\\var{kk*ww}}{\\var{mm*ww}}$</p>", "<p>$\\frac{\\var{kk*xx}}{\\var{mm*xx}}$</p>", "<p>$\\frac{\\var{gg*yy}}{\\var{nn*yy}}$</p>", "<p>$\\frac{\\var{gg*zz}}{\\var{nn*zz}}$</p>"], "choices": ["<p>$\\frac{\\var{gg*aaa}}{\\var{hh*aaa}}$</p>", "<p>$\\frac{\\var{ii*bbb}}{\\var{jj*bbb}}$</p>", "<p>$\\frac{\\var{jj*ccc}}{\\var{kk*ccc}}$</p>", "<p>$\\frac{\\var{hh*ddd}}{\\var{ll*ddd}}$</p>", "<p>$\\frac{\\var{kk*eee}}{\\var{mm*eee}}$</p>", "<p>$\\frac{\\var{gg*fff}}{\\var{nn*fff}}$</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "0", "scripts": {}, "warningType": "none", "marks": 0, "showCorrectAnswer": true, "type": "m_n_x", "shuffleChoices": true, "minMarks": 0, "layout": {"expression": "", "type": "all"}}], "statement": "<p>These two questions check that you can match equivalent fractions and find the simplest form of different fractions.</p>\n<p>You should be able to do these without a calculator. &nbsp;</p>", "variable_groups": [{"variables": ["a", "c", "f", "h", "k", "m"], "name": "Numerators"}, {"variables": ["b", "d", "g", "j", "l", "n"], "name": "Denominators"}, {"variables": ["o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", "aa", "bb", "cc", "dd", "ee", "ff", "oo", "pp", "qq", "rr", "ss", "tt", "uu", "vv", "ww", "xx", "yy", "zz", "aaa", "bbb", "ccc", "ddd", "eee", "fff"], "name": "Multipliers"}, {"variables": ["gg", "hh", "ii", "jj", "kk", "ll", "mm", "nn"], "name": "Set Values"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"aa": {"definition": "random(2..12 except [bb,cc]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "aa", "description": ""}, "jj": {"definition": "4", "templateType": "anything", "group": "Set Values", "name": "jj", "description": ""}, "cc": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "cc", "description": ""}, "ww": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "ww", "description": ""}, "gg": {"definition": "2", "templateType": "anything", "group": "Set Values", "name": "gg", "description": ""}, "xx": {"definition": "random(2..12 except ww) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "xx", "description": ""}, "vv": {"definition": "random(2..12 except uu) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "vv", "description": ""}, "fff": {"definition": "random(10..20 except [yy,zz]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "fff", "description": ""}, "pp": {"definition": "random(2..12 except oo) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "pp", "description": ""}, "rr": {"definition": "random(2..12 except qq) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "rr", "description": ""}, "p": {"definition": "random(2..12 except [o,q]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "p", "description": ""}, "ll": {"definition": "8", "templateType": "anything", "group": "Set Values", "name": "ll", "description": ""}, "z": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "z", "description": ""}, "bbb": {"definition": "random(10..20 except [qq,rr]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "bbb", "description": ""}, "ee": {"definition": "random(2..12 except ff) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "ee", "description": ""}, "oo": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "oo", "description": ""}, "ddd": {"definition": "random(10..20 except [uu,vv]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "ddd", "description": ""}, "a": {"definition": "random(1..b-1) //random numerator less than the variable for the denominator", "templateType": "anything", "group": "Numerators", "name": "a", "description": ""}, "bb": {"definition": "random(2..12 except cc) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "bb", "description": ""}, "dd": {"definition": "random(2..12 except [ee,ff]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "dd", "description": ""}, "yy": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "yy", "description": ""}, "y": {"definition": "random(2..12 except z) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "y", "description": ""}, "hh": {"definition": "3", "templateType": "anything", "group": "Set Values", "name": "hh", "description": ""}, "ff": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "ff", "description": ""}, "ss": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "ss", "description": ""}, "zz": {"definition": "random(2..12 except yy) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "zz", "description": ""}, "d": {"definition": "random(2..15) //random number for denominator", "templateType": "anything", "group": "Denominators", "name": "d", "description": ""}, "qq": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "qq", "description": ""}, "ii": {"definition": "1", "templateType": "anything", "group": "Set Values", "name": "ii", "description": ""}, "c": {"definition": "random(1..d-1) //random numerator less than the variable for the denominator", "templateType": "anything", "group": "Numerators", "name": "c", "description": ""}, "b": {"definition": "random(2..15) //random number for denominator", "templateType": "anything", "group": "Denominators", "name": "b", "description": ""}, "aaa": {"definition": "random(10..20 except [oo,pp]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "aaa", "description": ""}, "nn": {"definition": "7", "templateType": "anything", "group": "Set Values", "name": "nn", "description": ""}, "g": {"definition": "random(2..15) //random number for denominator", "templateType": "anything", "group": "Denominators", "name": "g", "description": ""}, "f": {"definition": "random(1..g-1) //random numerator less than the variable for the denominator", "templateType": "anything", "group": "Numerators", "name": "f", "description": ""}, "mm": {"definition": "9", "templateType": "anything", "group": "Set Values", "name": "mm", "description": ""}, "h": {"definition": "random(1..j-1) //random numerator less than the variable for the denominator", "templateType": "anything", "group": "Numerators", "name": "h", "description": ""}, "k": {"definition": "random(1..l-1) //random numerator less than the variable for the denominator", "templateType": "anything", "group": "Numerators", "name": "k", "description": ""}, "j": {"definition": "random(2..15) //random number for denominator", "templateType": "anything", "group": "Denominators", "name": "j", "description": ""}, "m": {"definition": "random(1..n-1) //random numerator less than the variable for the denominator", "templateType": "anything", "group": "Numerators", "name": "m", "description": ""}, "l": {"definition": "random(2..15) //random number for denominator", "templateType": "anything", "group": "Denominators", "name": "l", "description": ""}, "o": {"definition": "random(2..12 except q) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "o", "description": ""}, "n": {"definition": "random(2..15) //random number for denominator", "templateType": "anything", "group": "Denominators", "name": "n", "description": ""}, "q": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "q", "description": ""}, "kk": {"definition": "5", "templateType": "anything", "group": "Set Values", "name": "kk", "description": ""}, "s": {"definition": "random(2..12 except t) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "s", "description": ""}, "r": {"definition": "random(2..12 except [s,t]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "r", "description": ""}, "u": {"definition": "random(2..12 except [v,w]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "u", "description": ""}, "t": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "t", "description": ""}, "w": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "w", "description": ""}, "v": {"definition": "random(2..12 except w) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "v", "description": ""}, "eee": {"definition": "random(10..20 except [ww,xx]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "eee", "description": ""}, "x": {"definition": "random(2..12 except [y,z]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "x", "description": ""}, "uu": {"definition": "random(2..12) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "uu", "description": ""}, "tt": {"definition": "random(2..12 except ss) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "tt", "description": ""}, "ccc": {"definition": "random(10..20 except [ss,tt]) //randomly generated multipler for equivalent fractions", "templateType": "anything", "group": "Multipliers", "name": "ccc", "description": ""}}, "metadata": {"description": "<p>This question is designed to give you some practice with cancelling down and multiplying up fractions.</p>\n<p>You do not need a calculator for these.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Fractions - Fraction of an Amount", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "aa", "b", "bb", "c", "cc", "d", "dd", "f", "ff", "g", "gg", "h", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>What is $\\frac{\\var{a}}{\\var{b}}$ of $\\var{c}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(c/b)*a", "minValue": "(c/b)*a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\frac{\\var{d}}{\\var{f}}$ of $\\var{g}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(g/f)*d", "minValue": "(g/f)*d", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\frac{\\var{h}}{\\var{j}}$ of $\\var{k}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(k/j)*h", "minValue": "(k/j)*h", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\frac{\\var{l}}{\\var{m}}$ of $\\var{n}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(n/m)*l", "minValue": "(n/m)*l", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\frac{\\var{o}}{\\var{p}}$ of $\\var{q}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(q/p)*o", "minValue": "(q/p)*o", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\frac{\\var{r}}{\\var{s}}$ of $\\var{t}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(t/s)*r", "minValue": "(t/s)*r", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\frac{\\var{u}}{\\var{v}}$ of $\\var{w}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(w/v)*u", "minValue": "(w/v)*u", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\frac{\\var{x}}{\\var{y}}$ of $\\var{z}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(z/y)*x", "minValue": "(z/y)*x", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\frac{\\var{aa}}{\\var{bb}}$ of $\\var{cc}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(cc/bb)*aa", "minValue": "(cc/bb)*aa", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\frac{\\var{dd}}{\\var{ff}}$ of $\\var{gg}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(gg/ff)*dd", "minValue": "(gg/ff)*dd", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>These questions should help you practice working out a fraction of an amount.</p>\n<p>Remember to divide by the denominator and then multiply by the numerator.</p>\n<p>You should be able to do these without a calculator</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"aa": {"definition": "random(1..bb-1) //random number for numerator less than the denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "aa", "description": ""}, "cc": {"definition": "random(0..200#bb except 0) //random total value checking it divides by the numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "gg": {"definition": "random(0..200#ff except 0) //random total value checking it divides by the numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "gg", "description": ""}, "bb": {"definition": "random(2..25) //random number for denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "bb", "description": ""}, "dd": {"definition": "random(1..ff-1) //random number for numerator less than the denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "dd", "description": ""}, "ff": {"definition": "random(2..25) //random number for denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ff", "description": ""}, "a": {"definition": "random(1..b-1) //random number for numerator less than the denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(0..200#b except 0) //random total value checking it divides by the numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..25) //random number for denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..f-1) //random number for numerator less than the denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(0..200#f except 0) //random total value checking it divides by the numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(2..25) //random number for denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(1..j-1) //random number for numerator less than the denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(0..200#j except 0) //random total value checking it divides by the numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(2..25) //random number for denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(2..25) //random number for denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(1..m-1) //random number for numerator less than the denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "o": {"definition": "random(1..p-1) //random number for numerator less than the denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "o", "description": ""}, "n": {"definition": "random(0..200#m except 0) //random total value checking it divides by the numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "random(0..200#p except 0) //random total value checking it divides by the numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random(2..25) //random number for denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random(2..25) //random number for denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(1..s-1) //random number for numerator less than the denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(1..v-1) //random number for numerator less than the denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random(0..200#s except 0) //random total value checking it divides by the numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "random(0..200#v except 0) //random total value checking it divides by the numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "v": {"definition": "random(2..25) //random number for denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "y": {"definition": "random(2..25) //random number for denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "random(1..y-1) //random number for numerator less than the denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "z": {"definition": "random(0..200#y except 0) //random total value checking it divides by the numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}}, "metadata": {"description": "<p>This question allows you to practice working out a fraction of an amount.</p>\n<p>It is designed for you to complete without a calculator.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Fractions - Worded Questions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", "aa", "bb", "cc", "dd", "ee", "ff", "gg", "hh", "ii", "jj", "kk", "ll", "mm", "nn", "oo", "pp", "qq", "rr", "ss", "tt", "uu", "vv", "ww", "xx", "yy", "zz"], "tags": [], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "2", "prompt": "<p>Person A is $\\var{a}$ cm tall and Person B is $\\frac{\\var{b}}{\\var{c}}$ as tall. &nbsp;How tall is Person B?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "a+((b/c)*a)", "minValue": "a+((b/c)*a)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Work out the fraction increase.</p>\n<p>Add to Person A's height.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>In a sale a TV is reduced by $\\frac{\\var{f}}{\\var{g}}$ from&nbsp;$&pound;\\var{d}$. &nbsp;How much does it cost now?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "d-((f/g)*d)", "minValue": "d-((f/g)*d)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Work out the fraction reduction.</p>\n<p>Subtract from starting value.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>A rectangle measures $\\frac{\\var{h}}{\\var{j}}$ by $\\frac{\\var{k}}{\\var{l}}$ what is its area?</p>\n<p>Give your answer as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(h*k)/(j*l)", "minValue": "(h*k)/(j*l)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Area of rectangle = length x width.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>To get to work you need to ride your bike for&nbsp;$\\frac{\\var{m}}{\\var{n}}$ of a mile followed by walking $\\frac{\\var{o}}{\\var{p}}$. &nbsp;How far do you travel in total?</p>\n<p>Give your answer as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(m*p+o*n)/(n*p)", "minValue": "(m*p+o*n)/(n*p)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>To find out how far you travel, add together how far you ride your bike for with how far you walk.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>You and your friend order two medium pizzas (8 slices). &nbsp;If you eat $\\var{q}$ slices and your friend eats $\\var{r}$ slices, how much pizza is left over?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(16-q-r)/16", "minValue": "(16-q-r)/16", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Work out how many slices you have in total.</p>\n<p>Work out how many slices have been eaten.</p>\n<p>Use the remaining slices to make a fraction.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>Work out&nbsp;the greater value $\\frac{\\var{s}}{\\var{t}}$ or $\\frac{\\var{u}}{\\var{v}}$ of $&pound;\\var{w}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "max((s*w)/t,(u*w)/v)", "minValue": "max((s*w)/t,(u*w)/v)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Work out the two fractions of the amount and insert the larger value.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>You buy a packet of $\\var{x}$ bicuits. &nbsp;If you eat $\\frac{\\var{y}}{\\var{z}}$ on Monday and $\\frac{\\var{aa}}{\\var{bb}}$ of the remaining on Tuesday, how many do you have left for Wednesday?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(x-((x*y)/z))-((x-((x*y)/z))*(aa/bb))", "minValue": "(x-((x*y)/z))-((x-((x*y)/z))*(aa/bb))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Work out how many you eat on Monday.</p>\n<p>From what is left work out how many you eat on Tuesday.</p>\n<p>What is left is for Wednesday.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>If $\\frac{\\var{cc}}{\\var{dd}}$ inches of snow fall on one day and then $\\frac{\\var{ee}}{\\var{ff}}$ inches fall on the following day how much snow has fallen in total?</p>\n<p>Give your answer as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(cc*ff+dd*ee)/(dd*ff)", "minValue": "(cc*ff+dd*ee)/(dd*ff)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Total amount of snowfall is the sum of the two depths.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>Out of $\\var{gg}$ families surveyed $\\frac{\\var{hh}}{\\var{ii}}$ owned pets. &nbsp;If $\\var{jj}$ said they own dogs and $\\var{kk}$ own cats, how many families owned pets of a other varieties?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "((gg*hh)/ii)-jj-kk", "minValue": "((gg*hh)/ii)-jj-kk", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Work out how many families owned pets.</p>\n<p>Work out how many families are left once you have excluded the families that own dogs and cats.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>A train has $\\var{ll}$ passengers, if $\\frac{\\var{mm}}{\\var{nn}}$ get off at Nottingham Station and $\\var{oo}$ people get on the train how many people are on the train when it leaves Nottingham Station?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "ll+oo-(mm*ll)/nn", "minValue": "ll+oo-(mm*ll)/nn", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Work out the fraction that get off.</p>\n<p>Subtract from the total.</p>\n<p>Then add how many peple get on.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>If $\\var{pp}$ shelves have $\\var{qq}$ books on each shelf and $\\frac{\\var{rr}}{\\var{ss}}$ of these books are non-fiction, how many fiction books are there on the shelves?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(pp*qq)-((pp*qq*rr)/ss)", "minValue": "(pp*qq)-((pp*qq*rr)/ss)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Find out how many book there are in total.</p>\n<p>Work out how many are fiction books.</p>\n<p>Subtract from the total to work out how many are non fiction.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>A shop sells milkshakes in two sizes. &nbsp;The small size is $\\var{tt}$ ml and the large size is $\\frac{\\var{uu}}{\\var{vv}}$ of this amount bigger. &nbsp;Work out the larger amount $\\frac{\\var{ww}}{\\var{xx}}$ of the small drink or $\\frac{\\var{yy}}{\\var{zz}}$ of the large?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "max((tt*ww)/xx, (tt+((tt*uu)/vv))*(yy/zz))", "minValue": "max((tt*ww)/xx, (tt+((tt*uu)/vv))*(yy/zz))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>Work out the size of the larger drink.</p>\n<p>Work out the fraction of each drink.</p>\n<p>Insert the larger value.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Below are a selection of worded fraction questions.</p>\n<p>You may press show steps in order to be given clues about how to answer the questions. &nbsp;You will lose marks for doing this.</p>\n<p>These questions are designed to be done without a calculator.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"aa": {"definition": "random(1..bb-1) //random numerator value", "templateType": "anything", "group": "Ungrouped variables", "name": "aa", "description": ""}, "zz": {"definition": "random(2..6) //random value of denominator for value of large drink drunk", "templateType": "anything", "group": "Ungrouped variables", "name": "zz", "description": ""}, "ee": {"definition": "random(1..ff-1) //random numerator value", "templateType": "anything", "group": "Ungrouped variables", "name": "ee", "description": ""}, "gg": {"definition": "random(5*ii..12*ii#ii)  //random number of families that divides by ii", "templateType": "anything", "group": "Ungrouped variables", "name": "gg", "description": ""}, "xx": {"definition": "random(2..6) //random value of denominator for value of small drink drunk", "templateType": "anything", "group": "Ungrouped variables", "name": "xx", "description": ""}, "vv": {"definition": "random(2..6) //random value of denominator for the increase to a larger size drink", "templateType": "anything", "group": "Ungrouped variables", "name": "vv", "description": ""}, "pp": {"definition": "random(5..15)  //random number of shelves", "templateType": "anything", "group": "Ungrouped variables", "name": "pp", "description": ""}, "rr": {"definition": "random(1..ss-1) //random numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "rr", "description": ""}, "p": {"definition": "random(2..15) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "ll": {"definition": "random(10*nn..15*nn#nn) //random number of passengers", "templateType": "anything", "group": "Ungrouped variables", "name": "ll", "description": ""}, "z": {"definition": "random(2..15) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}, "cc": {"definition": "random(1..dd-1) //random numerator value", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "jj": {"definition": "random(2..((gg*hh)/ii)/2) //random value of dogs", "templateType": "anything", "group": "Ungrouped variables", "name": "jj", "description": ""}, "oo": {"definition": "random(10..12*nn) //random number of passengers on", "templateType": "anything", "group": "Ungrouped variables", "name": "oo", "description": ""}, "bb": {"definition": "random(2..15) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "bb", "description": ""}, "dd": {"definition": "random(2..15) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "dd", "description": ""}, "ww": {"definition": "random(1..xx-1)  //random numerator for the value of small drink drunk", "templateType": "anything", "group": "Ungrouped variables", "name": "ww", "description": ""}, "y": {"definition": "random(1..z-1) //random numerator value", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "hh": {"definition": "random(1..ii-1) //random numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "hh", "description": ""}, "a": {"definition": "random(c*10..c*15#c) //a random hieght in cm that can be divided by the denominator of the fraction", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "ff": {"definition": "random(2..15) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ff", "description": ""}, "d": {"definition": "random(g*20..g*50#g) // random value for TV divisible by the denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "qq": {"definition": "random(6*ss..10*ss#ss) //random number of books on a shelf", "templateType": "anything", "group": "Ungrouped variables", "name": "qq", "description": ""}, "ii": {"definition": "random(2..15) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ii", "description": ""}, "c": {"definition": "random(15..20) //random value for denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..5) //random value of the numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "nn": {"definition": "random(2..15) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "nn", "description": ""}, "g": {"definition": "random(3..5) //random value for denominator of sale reduction", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(1..g-2) // random value for numerator in sale reduction", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "ss": {"definition": "random(2..9) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ss", "description": ""}, "h": {"definition": "random(1..j-1) //random numerator value", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(1..l-1) //random numerator value", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(2..15) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(1..n-1) //random numerator value", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(2..15) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "o": {"definition": "random(1..p-1) //random numerator value", "templateType": "anything", "group": "Ungrouped variables", "name": "o", "description": ""}, "n": {"definition": "random(2..15) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "random(3..7) //random number of pizza slices", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "kk": {"definition": "random(2..((gg*hh)/ii)/2) //random value of cats", "templateType": "anything", "group": "Ungrouped variables", "name": "kk", "description": ""}, "s": {"definition": "random(1..t-1) //random numerator value", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(3..7) //random number of pizza slices", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(1..v-1) //random numerator", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random(2..15) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "random(2*t*v..10*t*v#t*v) //random monetary value that is divisible by t and v", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "v": {"definition": "random(2..15 except t) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "yy": {"definition": "random(1..zz-1)  //random numerator for the value of large drink drunk", "templateType": "anything", "group": "Ungrouped variables", "name": "yy", "description": ""}, "x": {"definition": "random(2*z*bb..4*z*bb#bb*z) // random number of biscuits in a packet", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "uu": {"definition": "random(1..vv-1)  //random numerator for increase to the larger size", "templateType": "anything", "group": "Ungrouped variables", "name": "uu", "description": ""}, "tt": {"definition": "random(10*xx*vv*zz..15*xx*vv*zz#xx*vv*zz)  //random volume of small drink", "templateType": "anything", "group": "Ungrouped variables", "name": "tt", "description": ""}, "mm": {"definition": "random(1..nn-1) //random numerator value", "templateType": "anything", "group": "Ungrouped variables", "name": "mm", "description": ""}}, "metadata": {"description": "<p>A variety of non-calculator worded fraction questions.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Percentages - Quick Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "g", "f", "h", "j", "k", "l", "m", "n"], "tags": [], "advice": "<p>Work out your quick percentages first: &nbsp;50%, 25%, 10%, 5% and 1%</p>\n<p>Add or subtract combinations of these to get the required amount.</p>", "rulesets": {}, "parts": [{"prompt": "<p>What is $\\var{a}\\text{%}$ of $\\var{b}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(a/100)*b", "minValue": "(a/100)*b", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\var{c}\\text{%}$ of $\\var{d}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(c/100)*d", "minValue": "(c/100)*d", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\var{g}\\text{%}$ of $\\var{f}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(g/100)*f", "minValue": "(g/100)*f", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\var{h}\\text{%}$ of $\\var{j}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(h/100)*j", "minValue": "(h/100)*j", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\var{k}\\text{%}$ of $\\var{l}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(k/100)*l", "minValue": "(k/100)*l", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\var{m}\\text{%}$ of $\\var{n}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(m/100)*n", "minValue": "(m/100)*n", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>These questions are asking you to use a non-calculator method to work out a percentage amount of a value.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(0..100#5 except 0) //a multiple of 5%", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(0..100#5 except 0) //a multiple of 5%", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(100..1000#20) //a multiple of 20 betwen 100 and 1000", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(100..1000#20) //a multiple of 20 betwen 100 and 1000", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(0..100#5 except 0) //a multiple of 5%", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(100..1000#20) //a multiple of 20 betwen 100 and 1000", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(1..99) //select a random percentage", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(1..99) //select a random percentage", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(100..1000#20)", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(1..99) //select a random percentage", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(100..1000#20)", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random(100..1000)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"notes": "<p>They are to be done without a calculator, and increase in difficulty.</p>", "description": "<p>These questions are asking you to use a non-calculator method to work out a percentage amount of a value.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Percentages- Percentage Increases and Decreases", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n"], "tags": [], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Increase $\\var{a}$ by $\\var{b}\\text{%}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1+b/100)*a", "minValue": "(1+b/100)*a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out $\\var{b}\\text{%}$ of $\\var{a}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(b/100)*a", "minValue": "(b/100)*a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Add your previous answer to $\\var{a}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1+b/100)*a", "minValue": "(1+b/100)*a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "2", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>Increase $\\var{c}$ by $\\var{d}\\text{%}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1+d/100)*c", "minValue": "(1+d/100)*c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out $\\var{d}\\text{%}$ of $\\var{c}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(d/100)*c", "minValue": "(d/100)*c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Add your previous answer to $\\var{c}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1+d/100)*c", "minValue": "(1+d/100)*c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "2", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>Decrease $\\var{f}$ by $\\var{g}\\text{%}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1-g/100)*f", "minValue": "(1-g/100)*f", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out $\\var{g}\\text{%}$ of $\\var{f}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(g/100)*f", "minValue": "(g/100)*f", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Subtract your previous answer from $\\var{f}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1-g/100)*f", "minValue": "(1-g/100)*f", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "2", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>Decrease $\\var{h}$ by $\\var{j}\\text{%}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1-j/100)*h", "minValue": "(1-j/100)*h", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out $\\var{j}\\text{%}$ of $\\var{h}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(j/100)*h", "minValue": "(j/100)*h", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Subtract your previous answer from $\\var{h}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1-j/100)*h", "minValue": "(1-j/100)*h", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "2", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>Increase&nbsp;$\\var{k}$ by $\\var{l}\\text{%}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1+l/100)*k", "minValue": "(1+l/100)*k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out $\\var{l}\\text{%}$ of $\\var{k}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(l/100)*k", "minValue": "(l/100)*k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Add&nbsp;your previous answer to&nbsp;$\\var{k}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1-l/100)*k", "minValue": "(1-l/100)*k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "2", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>Decrease $\\var{m}$ by $\\var{n}\\text{%}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1-n/100)*m", "minValue": "(1-n/100)*m", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out $\\var{n}\\text{%}$ of $\\var{m}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(n/100)*m", "minValue": "(n/100)*m", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Subtract your previous answer from $\\var{m}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1-n/100)*m", "minValue": "(1-n/100)*m", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "2", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Here you need to work out percentage increases and decreases using non-calculator methods.</p>\n<p>If you get stuck you can select \"Show Steps\" which will take you through how to answer the question.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(100..1000#20)  //random number between 100 and 1000 that is divisible by 20", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(100..1000#20)  //random number between 100 and 1000 that is divisible by 20", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(0..100#5) //A random percentage between 0 and 100 that is divisble by 5", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(0..100#5) //A random percentage between 0 and 100 that is divisble by 5", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(0..100#5) //A random percentage between 0 and 100 that is divisble by 5", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(100..1000#20)  //random number between 100 and 1000 that is divisible by 20", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(100..1000#20)  //random number between 100 and 1000 that is divisible by 20", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(100..1000#10) // random number between 100 and 1000 that is divisble by 10", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(0..100#5) //A random percentage between 0 and 100 that is divisble by 5", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(100..1000#10) // random number between 100 and 1000 that is divisble by 10", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(0..100) //random number between 1 and 100", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random(0..100) //random number between 1 and 100", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"notes": "", "description": "<p>Non-calculator percentage increase and decrease calculations.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Percentages - One Amount as a Percentage of Another", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n"], "tags": [], "advice": "<p>Write it as a fraction - the small amount over the larger amount.</p>\n<p>If the denominator is not a factor of 100 then cancel the fraction down till it is a factor of 100.</p>\n<p>Once the denominator is a factor of 100 multiply the fraction up so that the denominator is 100.</p>\n<p>The percentage is the value of the numerator.</p>", "rulesets": {}, "parts": [{"stepsPenalty": "2", "prompt": "<p>What percentage of $\\var{a}$ is $\\var{b}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(b/a)*100", "minValue": "(b/a)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by writing it as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "b/a", "minValue": "b/a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply the fraction up so that the denominator is equal to 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(b/a)*((100/a)/(100/a))", "minValue": "(b/a)*((100/a)/(100/a))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The value of the numerator is the percentage.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(b/a)*100", "minValue": "(b/a)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>What percentage of $\\var{c}$ is $\\var{d}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(d/c)*100", "minValue": "(d/c)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by writing it as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "d/c", "minValue": "d/c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply the fraction up so that the denominator is equal to 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(d/c)*((100/c)/(100/c))", "minValue": "(d/c)*((100/c)/(100/c))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The value of the numerator is the percentage.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(d/c)*100", "minValue": "(d/c)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{j}$ is what percengage of $\\var{h}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(j/h)*100", "minValue": "(j/h)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by writing it as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "j/h", "minValue": "j/h", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply the fraction up so that the denominator is equal to 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(j/h)*((100/h)/(100/h))", "minValue": "(j/h)*((100/h)/(100/h))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The value of the numerator is the percentage.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(j/h)*100", "minValue": "(j/h)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{f}$ is what percentage of $\\var{g}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(f/g)*100", "minValue": "(f/g)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by making it a fraction</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "f/g", "minValue": "f/g", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Then cancel the fraction&nbsp;down so that the denominator is a factor of 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(f/4)/(g/4)", "minValue": "(f/4)/(g/4)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply up the fraction so that the denominator is 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(f*(100/g))/(g*(100/g))", "minValue": "(f*(100/g))/(g*(100/g))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The percentage is the value of the numerator.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(f/g)*100", "minValue": "(f/g)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{k}$ is what percentage of $\\var{l}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(k/l)*100", "minValue": "(k/l)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by making it a fraction</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "k/l", "minValue": "k/l", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Then cancel the fraction&nbsp;down so that the denominator is a factor of 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(k/3)/(l/3)", "minValue": "(k/3)/(l/3)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply up the fraction so that the denominator is 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(k*(100/l))/(l*(100/l))", "minValue": "(k*(100/l))/(l*(100/l))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The percentage is the value of the numerator.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(k/l)*100", "minValue": "(k/l)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{m}$ is what percentage of $\\var{n}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(m/n)*100", "minValue": "(m/n)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by making it a fraction</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "m/n", "minValue": "m/n", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Then cancel the fraction&nbsp;down so that the denominator is a factor of 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(m/7)/(n/7)", "minValue": "(m/7)/(n/7)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply up the fraction so that the denominator is 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(m*(100/n))/(m*(100/n))", "minValue": "(m*(100/n))/(n*(100/n))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The percentage is the value of the numerator.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(m/n)*100", "minValue": "(m/n)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>For each of the following questions work out one value as a percentage of the other. You are&nbsp;expected to do this without the help of a calculator.</p>\n<p>You can click reveal steps to show you how to solve each question. You will lose marks for revealing steps.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random([5,10,20,25,50,100]) //random value that is a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random([5,10,20,25,50,100]) //random value that is a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..a-1) //random number that is less than the value of a", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..c-1) //random number that is less than the value of c", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(20,40,80) //random number from list", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(4..g-1#4) // a random number less than f that is divisible by 4", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random([5,10,20,25,50,100,200]) //random value that is a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(3..l-1#3)  //random number less than l that is divisible by 3", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(1..h-1) //random number that is less than the value of h", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(7..n-1#7)  //random number that is divisble by 7 and less than n", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(15,30,60,75,150)  //a random number that divides by 3 to give a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random(35,70,140,175,350)  //random number that when divided by 7 gives a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"notes": "", "description": "<p>This question asks you to work out one value as a percentage of another. &nbsp;You are expected to do these without the help of a calculator.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Percentages - Non-Calculator Worded Questions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", "aa", "bb", "cc", "dd", "ee", "ff", "gg", "hh", "ii", "jj"], "tags": [], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "4", "prompt": "<p>The monthly budget for front of house is $\\var{a}$. &nbsp;If $\\var{b}\\text{%}$ is spent on flowers, how much is spent on flowers?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(b/100)*a", "minValue": "(b/100)*a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>First find 10%, 5% and 1%.</p>\n<p>Add together what you need to make up the required percentage.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>Out of $\\var{c}$ people $\\var{d}\\text{%}$ have have brown hair. &nbsp;How many people do not have brown hair?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((100-d)/100)*c", "minValue": "((100-d)/100)*c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out what percentage of people do not have brown hair.</p>\n<p>Work out 50%, 25%, 10%, 5% and 1%.</p>\n<p>Combine together to get the correct percentage.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A jumper is priced at &pound;$\\var{f}$ in a sale there there is $\\var{g}\\text{%}$ off. &nbsp;What is the sale price of the jumper?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "f*(1-(g/100))", "minValue": "f*(1-(g/100))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out 50%, 25%, 10%, 5%, 1%.</p>\n<p>Find out the amount of money to be removed.</p>\n<p>Subtract to find the sale price.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>Pupils spend $\\var{l}$ hours a week in lessons. $\\var{m}$ hours a week are allocated to English, what percentage of the lessons&nbsp;is this?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(m/l)*100", "minValue": "(m/l)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Write it as a fraction of&nbsp;what you want over the total amount.</p>\n<p>If you need to: cancel the fraction down so the denominator goes into 100.</p>\n<p>Multiply your fraction up so that the denominator is equal to 100.</p>\n<p>The percentage is the value of the numerator.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A television is reduced in price from $\\var{cc}$ by $\\var{dd}\\text{%}$. &nbsp;What is the new price of the television?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(cc)*(1-((dd)/100))", "minValue": "(cc)*(1-((dd)/100))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out the quick percentages.</p>\n<p>Combine to give the amount of the decrease.</p>\n<p>Take this value from the starting value.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A market researcher wants to take a sample of $\\var{v}\\text{%}$ out of a group of applicants. &nbsp;If there are $\\var{w}$ in the group what is the minimum number of people they need in the sample?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "ceil((v/100)*w)", "minValue": "ceil((v/100)*w)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out the quick percentages.</p>\n<p>Combine till you have the percentage amount.</p>\n<p>Round up to the nearest person (you cannot have point something of a person).</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>In a small village $\\var{gg}$ people turn up to vote in the local election. &nbsp;If there are $\\var{hh}$ residents in the village what percentage of the village turned up to vote?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((gg)/(hh))*100", "minValue": "((gg)/(hh))*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Make a fraction of those that turned up over total number of people.</p>\n<p>If you need to: cancel down the fraction of that the denominator goes into 100.</p>\n<p>Multiplty up the fraction so that the denominator is equal to 100.</p>\n<p>The percentage is the value of the numerator.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A theatre sells ice ceam during the intervals of its show. &nbsp;Last night $\\var{x}$ ice creams were sold of which $\\var{y}\\text{%}$ of them were strawberry flavour. &nbsp;How many strawberry ice creams were sold?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(y/100)*x", "minValue": "(y/100)*x", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out the quick percentages.</p>\n<p>Combine to give the total number of strawberry ice creams sold.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>House prices are expected to increase next year by $\\var{z}\\text{%}$. &nbsp;If your house is currently worth &pound;$\\var{aa}$ how much will it be worth this time next year?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(aa)*(1+(z/100))", "minValue": "(aa)*(1+(z/100))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out the quick percentages.</p>\n<p>Combine to work out the amount to increase it by.</p>\n<p>Add to the starting value.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A pupil scored $\\var{n}\\text{%}$ in a test. &nbsp;Later they scored $\\var{o}$ out of $\\var{p}$ in a second test. &nbsp;What is the difference in the percentage scores?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "abs(n-((o/p)*100))", "minValue": "abs(n-((o/p)*100))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Take the second score and turn it into a fraction.</p>\n<p>Cancel down if needed so the denominator divides into 100.</p>\n<p>Multiply up so that the denominator is 100.</p>\n<p>The numerator is the percentage value.</p>\n<p>Work out the difference between the two percentages.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>If there are currently 7 billion people on the planet and the population is expected to rise by $\\var{bb}\\text{%}$ over the next year, how many people will there be next year?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(7000000000)*(1+((bb)/100))", "minValue": "(7000000000)*(1+((bb)/100))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out the quick percentages.</p>\n<p>Combine to give the amount of the increase.</p>\n<p>Add to the starting value.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A resturant has two specials on its menu. &nbsp;Last night it sold $\\var{ee}$ specials in total of which $\\var{ff}$ were steak. &nbsp;What percentage of the specials were steak?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((ff)/(ee))*100", "minValue": "((ff)/(ee))*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Write as a fraction of steaks over total amount of specials.</p>\n<p>If you need to: cancel down so that 100 can be divided by the denominator.</p>\n<p>Mutilply the fraction up so that the denominator is 100.</p>\n<p>The percentage is the value of the numerator.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>Red, green and yellow balls are in a bag; of which $\\var{h}\\text{%}$ of the balls are red and&nbsp;$\\var{j}\\text{%}$ green. &nbsp;If there are $\\var{k}$ balls in the bag how many are yellow?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((100-h-j)/100)*k", "minValue": "((100-h-j)/100)*k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out what percentage of the balls are yellow.</p>\n<p>Find the quick percentages.</p>\n<p>Combine to give the number of yellow balls.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>The area of a circle is $\\var{ii}\\pi$. If a sector is cut out of the circle with area $\\var{jj}\\pi$ what percentage of the circle is the sector?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((jj)/(ii))*100", "minValue": "((jj)/(ii))*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Write a fraction of the area of the sector over the total area.</p>\n<p>If you need to: cancel the fraction down so that the denominator goes into 100.</p>\n<p>Multiply up so that the denominator is equal to 100.</p>\n<p>The percentage is the value of the numerator.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": false, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Each of the questions below check your understanding of the methods in the previous questions.</p>\n<p>You should be able to do these without a calculator.</p>\n<p>You can click show steps but you will lose all your marks for doing so.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"aa": {"definition": "random(80000..350000#1000)  // random price for house", "templateType": "anything", "group": "Ungrouped variables", "name": "aa", "description": ""}, "jj": {"definition": "random(6..ii-1#6) // random area of sector of circle", "templateType": "anything", "group": "Ungrouped variables", "name": "jj", "description": ""}, "cc": {"definition": "random(240..450#5) // random price of television", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "ii": {"definition": "random(12..144#12 except 84) // random number for total area of circle", "templateType": "anything", "group": "Ungrouped variables", "name": "ii", "description": ""}, "ee": {"definition": "random([5,10,20,25,50,200,100]) // random number of steak sales", "templateType": "anything", "group": "Ungrouped variables", "name": "ee", "description": ""}, "bb": {"definition": "random(1..10) // random percentage increase of population", "templateType": "anything", "group": "Ungrouped variables", "name": "bb", "description": ""}, "dd": {"definition": "random(5..30)  // random percentage decrease in cost of TV", "templateType": "anything", "group": "Ungrouped variables", "name": "dd", "description": ""}, "hh": {"definition": "random(300..1000#50)  // random number of residents in village", "templateType": "anything", "group": "Ungrouped variables", "name": "hh", "description": ""}, "ff": {"definition": "random(1..ee-1)  // random number of specials that were steak", "templateType": "anything", "group": "Ungrouped variables", "name": "ff", "description": ""}, "a": {"definition": "random(1000..15000#1000)  // random number of thousands between 1000 and 10000 for front of house takings", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "gg": {"definition": "random(0..hh-1#5) // random number of people who turned up to vote", "templateType": "anything", "group": "Ungrouped variables", "name": "gg", "description": ""}, "c": {"definition": "random(100..1000#50) // random number of students between 100 and 1000", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(5..15)  // random percentage of 5 to 15 spent on flowers", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(30..60) // random percentage between 30 and 60 of those that passed", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(5..35) // random percentage off the jumper", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(35..65#5) // random price of jumper", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(10..40) // random percentage less than 40 for red balls", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(100..50#50) // random number divisible by 50 total number of balls", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(10..40) // random percentage less than 40 for green balls", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random([5,6,8,10,12])  // random number of hours allocated to English", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random([20,25])  // random number from list for number of hours in lessons", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "o": {"definition": "random(18..p-1#6)  // random number for score", "templateType": "anything", "group": "Ungrouped variables", "name": "o", "description": ""}, "n": {"definition": "random(60..80)  // random percentage test score", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "random([0,1]) // random numbr of hours for a test to take", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random([20,24,25,30,50,60,75,120,150])  // random total of marks in a test", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random(10..30#5)  // random percentage of extra time granted in the test", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(10..50#10) // random number of minutes for a test to take", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(10..50#10)  // random starting time for test - minutes", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random(9,10)  // random starting time for test - hour", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "random(60..600#10)  // random number of people in the group", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "v": {"definition": "random(30..45)  // random percentage for sample size", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "y": {"definition": "random(20..80)  // random percentage of ice creams that were strawberry", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "random(20..300#10) // random number of ice creams sold", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "z": {"definition": "random(1..12) // random percentage increase for house prices", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}}, "metadata": {"notes": "", "description": "<p>These are worded questions on percentages. &nbsp;They can be done without a calculator.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Decimals - Four Operations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", "aa", "bb", "cc", "dd", "ee", "ff", "gg", "hh"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Solve the following:</p>\n<p>$\\var{a} + \\var{b}$ =&nbsp;[[0]]</p>\n<p>$\\var{c} + \\var{d}$ = [[1]]</p>\n<p>$\\var{f} + \\var{g}$ = [[2]]</p>\n<p>$\\var{h} + \\var{j}$ = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "a+b", "minValue": "a+b", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "c+d", "minValue": "c+d", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "f+g", "minValue": "f+g", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "h+j", "minValue": "h+j", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Solve the following:</p>\n<p>$\\var{k} - \\var{l}$ = [[0]]</p>\n<p>$\\var{m} - \\var{n}$ = [[1]]</p>\n<p>$\\var{o} - \\var{p}$ = [[2]]</p>\n<p>$\\var{q} - \\var{r}$ = [[3]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "k-l", "minValue": "k-l", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "m-n", "minValue": "m-n", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "o-p", "minValue": "o-p", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "q-r", "minValue": "q-r", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Solve the following:</p>\n<p>$\\var{s} \\times \\var{t}$ = [[0]]</p>\n<p>$\\var{u} \\times \\var{v}$ = [[1]]</p>\n<p>$\\var{w} \\times \\var{x}$ = [[2]]</p>\n<p>$\\var{y} \\times \\var{z}$ = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "s*t", "minValue": "s*t", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "u*v", "minValue": "u*v", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "w*x", "minValue": "w*x", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "y*z", "minValue": "y*z", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Solve the following:</p>\n<p>$\\var{aa} \\div \\var{bb}$ = [[0]]</p>\n<p>$\\var{cc} \\div \\var{dd}$ = [[1]]</p>\n<p>$\\var{ee} \\div \\var{ff}$ = [[2]]</p>\n<p>$\\var{gg} \\div \\var{hh}$ = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "aa/bb", "minValue": "aa/bb", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "cc/dd", "minValue": "cc/dd", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "ee/ff", "minValue": "ee/ff", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "gg/hh", "minValue": "gg/hh", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>This quick question allows you to practice adding, subtracting, multiplying and dividing decimals.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"aa": {"definition": "random(3..20)*bb //random number divisible by bb", "templateType": "anything", "group": "Ungrouped variables", "name": "aa", "description": ""}, "cc": {"definition": "random(3..20)*dd //random number divisible by dd", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "gg": {"definition": "random(3..20)*hh //random number divisible by hh", "templateType": "anything", "group": "Ungrouped variables", "name": "gg", "description": ""}, "ee": {"definition": "random(3..20)*ff //random number divisible by ff", "templateType": "anything", "group": "Ungrouped variables", "name": "ee", "description": ""}, "bb": {"definition": "random(0..5#0.1 except 0) //random one decimal number", "templateType": "anything", "group": "Ungrouped variables", "name": "bb", "description": ""}, "dd": {"definition": "random(0..20#0.01 except 0) //random two decimal number", "templateType": "anything", "group": "Ungrouped variables", "name": "dd", "description": ""}, "hh": {"definition": "random(0..1#0.001 except 0) //random one decimal number", "templateType": "anything", "group": "Ungrouped variables", "name": "hh", "description": ""}, "ff": {"definition": "random(0..20#0.001 except 0) //random one decimal number", "templateType": "anything", "group": "Ungrouped variables", "name": "ff", "description": ""}, "a": {"definition": "random(0..1#0.001 except 0)  //random decimal between 0 and 1", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(0..5#0.001 except 0) //random 2 digit decimal between 0 and 5", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(0..1#0.001 except 0)  //random decimal between 0 and 1", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(0..5#0.001 except 0) //random 3 digit decimal between 0 and 5", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(0..20#0.001 except 0)\n", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(0..20#0.01 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(10..50#0.001 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(0..1#0.001 except 0)  //random decimal between 0 and 1", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(10..50#0.01 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(0..5#0.001 except 0) //random 2 digit decimal between 0 and 5", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(0..k#0.001 except [0,k])   //random decimal between 0 and 1", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "o": {"definition": "random(0..20#0.01 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "o", "description": ""}, "n": {"definition": "random(0..m#0.001 except [0,m]) //random 3 digit decimal between 0 and 5", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "random(10..50#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random(0..o#0.001 except [0,o])", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random(0..20#0.1 except 0) //random one decimal value between 0 and 20", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(10..q#0.001 except q)", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(0..20#0.1 except 0) //random one decimal value between 0 and 20", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random(0..20#0.1 except 0) //random one decimal value between 0 and 20", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "random(0..20#0.01 except 0) //random two decimal value between 0 and 20", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "v": {"definition": "random(0..20#0.01 except 0) //random two decimal value between 0 and 20", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "y": {"definition": "random(0..20#0.01 except 0) //random two decimal value between 0 and 20", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "random(0..20#0.01 except 0) //random two decimal value between 0 and 20", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "z": {"definition": "random(0..20#0.001 except 0) //random three decimal value between 0 and 20", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}}, "metadata": {"description": "<p>This is a non-calculator questions on adding, subtracting, multiplying and dividing decimals.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Conversions - Decimals and Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", "aa", "bb", "cc", "dd", "ee", "ff", "gg", "hh", "ii", "jj", "kk", "ll"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"distractors": ["", "", "", "", "", "", "", ""], "prompt": "<p>Select the answer that is equal to $\\var{a}$%</p>", "matrix": ["1", 0, 0, 0, 0, 0, 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["<p>$\\var{b}$</p>", "<p>$\\var{c}$</p>", "<p>$\\var{d}$</p>", "<p>$\\var{f}$</p>", "<p>$\\var{g}$</p>", "<p>$\\var{h}$</p>", "<p>$\\var{j}$</p>", "<p>$\\var{k}$</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "1", "scripts": {}, "marks": 0, "displayColumns": "0", "showCorrectAnswer": true, "type": "1_n_2", "minMarks": "1"}, {"distractors": ["", "", "", "", "", "", "", ""], "prompt": "<p>Select the answer that is equal to $\\var{l}$%</p>", "matrix": ["1", 0, 0, 0, 0, 0, 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["<p>$\\var{m}$</p>", "<p>$\\var{n}$</p>", "<p>$\\var{o}$</p>", "<p>$\\var{p}$</p>", "<p>$\\var{q}$</p>", "<p>$\\var{r}$</p>", "<p>$\\var{s}$</p>", "<p>$\\var{t}$</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "1", "scripts": {}, "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": "1"}, {"distractors": ["", "", "", "", "", "", "", ""], "prompt": "<p>Select the answer that is equal to $\\var{u}$</p>", "matrix": ["1", 0, 0, 0, 0, 0, 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["<p>$\\var{v}$ %</p>", "<p>$\\var{w}$ %</p>", "<p>$\\var{x}$ %</p>", "<p>$\\var{y}$ %</p>", "<p>$\\var{z}$ %</p>", "<p>$\\var{aa}$ %</p>", "<p>$\\var{bb}$ %</p>", "<p>$\\var{cc}$ %</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "1", "scripts": {}, "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": "1"}, {"distractors": ["", "", "", "", "", "", "", ""], "prompt": "<p>Select the answer that is equal to $\\var{dd}$</p>", "matrix": ["1", 0, 0, 0, 0, 0, 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["<p>$\\var{ee}$ %</p>", "<p>$\\var{ff}$ %</p>", "<p>$\\var{gg}$ %</p>", "<p>$\\var{hh}$ %</p>", "<p>$\\var{ii}$ %</p>", "<p>$\\var{jj}$ %</p>", "<p>$\\var{kk}$ %</p>", "<p>$\\var{ll}$ %</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "1", "scripts": {}, "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": "1"}, {"maxAnswers": 0, "prompt": "<p>Match up the equivalent decimals and percentages</p>", "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "shuffleAnswers": false, "minAnswers": 0, "variableReplacements": [], "answers": ["<p>$50$ %</p>", "<p>$25$ %</p>", "<p>$20$ %</p>", "<p>$10$ %</p>", "<p>$12.5$ %</p>", "<p>$5$ %</p>", "<p>$4$ %</p>", "<p>$1$ %</p>", "<p>$33.\\dot{3}$ %</p>", "<p>$11.\\dot{1}$ %</p>", "<p>$60$ %</p>", "<p>$30$ %</p>", "<p>$85$ %</p>", "<p>$66.\\dot{6}$ %</p>", "<p>$45$ %</p>"], "choices": ["<p>$0.5$</p>", "<p>$0.25$</p>", "<p>$0.2$</p>", "<p>$0.1$</p>", "<p>$0.125$</p>", "<p>$0.05$</p>", "<p>$0.04$</p>", "<p>$0.01$</p>", "<p>$0.3\\dot{3}$</p>", "<p>$0.1\\dot{1}$</p>", "<p>$0.6$</p>", "<p>$0.3$</p>", "<p>$0.85$</p>", "<p>$0.6\\dot{6}$</p>", "<p>$0.45$</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "marks": 0, "warningType": "none", "showCorrectAnswer": true, "type": "m_n_x", "shuffleChoices": false, "minMarks": 0, "layout": {"expression": "", "type": "all"}}], "statement": "<p>Here you just need to pick out the solution that is equivalent to the value in the question.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"aa": {"definition": "u*2", "templateType": "anything", "group": "Ungrouped variables", "name": "aa", "description": ""}, "jj": {"definition": "dd*2", "templateType": "anything", "group": "Ungrouped variables", "name": "jj", "description": ""}, "cc": {"definition": "u*20", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "gg": {"definition": "dd/100", "templateType": "anything", "group": "Ungrouped variables", "name": "gg", "description": ""}, "ll": {"definition": "dd*20", "templateType": "anything", "group": "Ungrouped variables", "name": "ll", "description": ""}, "ee": {"definition": "dd*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ee", "description": ""}, "bb": {"definition": "u*200", "templateType": "anything", "group": "Ungrouped variables", "name": "bb", "description": ""}, "dd": {"definition": "random(0..1#0.001)", "templateType": "anything", "group": "Ungrouped variables", "name": "dd", "description": ""}, "hh": {"definition": "dd*1000\n", "templateType": "anything", "group": "Ungrouped variables", "name": "hh", "description": ""}, "ff": {"definition": "dd*10", "templateType": "anything", "group": "Ungrouped variables", "name": "ff", "description": ""}, "a": {"definition": "random(1..100) //random percentage between 1 and 100", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "ii": {"definition": "dd/10", "templateType": "anything", "group": "Ungrouped variables", "name": "ii", "description": ""}, "c": {"definition": "a/10", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "a/100", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "a*100", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "a*10", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "a/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "kk": {"definition": "dd*200", "templateType": "anything", "group": "Ungrouped variables", "name": "kk", "description": ""}, "h": {"definition": "a/2", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "a/20", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "a/200", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "l/100", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(1..100#0.1) //random decimal percentage", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "o": {"definition": "l*100", "templateType": "anything", "group": "Ungrouped variables", "name": "o", "description": ""}, "n": {"definition": "l/10", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "l*10", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "l/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "l/200", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "l/2", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(0..1#0.01) //random decimal to become a percentage", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "l/20", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "u*10", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "v": {"definition": "u*100", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "y": {"definition": "u*1000", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "u/100", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "z": {"definition": "u/10", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}}, "metadata": {"description": "<p>This question concentrates on converting between decimals and percentages</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Conversions - Fractions and Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Insert a fraction that has the same value as the following percentages:</p>\n<p>$\\var{a}$ % = [[0]]</p>\n<p>$\\var{b}$ % = [[1]]</p>\n<p>$\\var{c}$ % = [[2]]</p>\n<p>$\\var{d}$ % = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "a/100", "minValue": "a/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "b/100", "minValue": "b/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "c/100", "minValue": "c/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "d/100", "minValue": "d/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Insert the correct percentage for each of these fractions</p>\n<p>$\\frac{\\var{f}}{\\var{g}}$ = [[0]]</p>\n<p>$\\frac{\\var{h}}{\\var{j}}$ = [[1]]</p>\n<p>$\\frac{\\var{k}}{\\var{l}}$ = [[2]]</p>\n<p>$\\frac{\\var{m}}{\\var{n}}$ = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "(f/g)*100", "minValue": "(f/g)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "(h/j)*100", "minValue": "(h/j)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "(k/l)*100", "minValue": "(k/l)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "(m/n)*100", "minValue": "(m/n)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"maxAnswers": "15", "prompt": "<p>Match up commonly used fractions and percentages</p>", "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "shuffleAnswers": true, "minAnswers": "10", "variableReplacements": [], "answers": ["<p>$\\frac{1}{2}$</p>", "<p>$\\frac{1}{4}$</p>", "<p>$\\frac{1}{5}$</p>", "<p>$\\frac{1}{10}$</p>", "<p>$\\frac{1}{8}$</p>", "<p>$\\frac{1}{20}$</p>", "<p>$\\frac{1}{25}$</p>", "<p>$\\frac{1}{100}$</p>", "<p>$\\frac{1}{3}$</p>", "<p>$\\frac{1}{9}$</p>", "<p>$\\frac{3}{4}$</p>", "<p>$\\frac{2}{5}$</p>", "<p>$\\frac{1}{11}$</p>", "<p>$\\frac{1}{6}$</p>", "<p>$\\frac{1}{45}$</p>"], "choices": ["<p>$50$ %</p>", "<p>$25$ %</p>", "<p>$20$ %</p>", "<p>$10$ %</p>", "<p>$12.5$ %</p>", "<p>$5$ %</p>", "<p>$4$ %</p>", "<p>$1$ %</p>", "<p>$33.\\dot{3}$ %</p>", "<p>$11.\\dot{1}$ %</p>", "<p>$60$ %</p>", "<p>$30$ %</p>", "<p>$85$ %</p>", "<p>$66.\\dot{6}$ %</p>", "<p>$45$ %</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "10", "scripts": {}, "marks": 0, "warningType": "none", "showCorrectAnswer": true, "type": "m_n_x", "shuffleChoices": true, "minMarks": "10", "layout": {"expression": "", "type": "all"}}], "statement": "<p>This question allows you to practice converting between fractions and percentages.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(0..100#10 except [0,100])", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(0..100 except [0,100])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(0..100#5 except [0,100])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..200)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random([2,4,5,10,20,25,50,100])", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(1..g-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(0..j-1#2 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(0..l-1#4 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random([4,5,10,20,25,40,50,100,200])", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(1..n)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random([8,16,20,40,80,100,200,400])", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random([3,6,9])", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"description": "<p>This question will help you practice converting between fractions and percentages</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Conversions - Decimals and Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n"], "tags": [], "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Give a fraction which is equivalent to these decimals:</p>\n<p>$\\var{a}$ = [[0]]</p>\n<p>$\\var{b}$ = [[1]]</p>\n<p>$\\var{c}$ = [[2]]</p>\n<p>$\\var{d}$ = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "(a*10)/10", "minValue": "(a*10)/10", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "(b*100)/100", "minValue": "(b*100)/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "(c*1000)/1000", "minValue": "(c*1000)/1000", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "(d*100)/100", "minValue": "(d*100)/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Give the decimal that is equivalent to these fractions:</p>\n<p>$\\frac{\\var{f}}{\\var{g}}$ = [[0]]</p>\n<p>$\\frac{\\var{h}}{\\var{j}}$ = [[1]]</p>\n<p>$\\frac{\\var{k}}{\\var{l}}$ = [[2]]</p>\n<p>$\\frac{\\var{m}}{\\var{n}}$ = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "f/g", "minValue": "f/g", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "h/j", "minValue": "h/j", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "k/l", "minValue": "k/l", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "m/n", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "m/n", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"maxAnswers": 0, "prompt": "<p>Match any pairs of fractions and decimals (you might not use all of the&nbsp;options).</p>", "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "shuffleAnswers": true, "minAnswers": "0", "variableReplacements": [], "answers": ["<p>$\\frac{1}{2}$</p>", "<p>$\\frac{1}{4}$</p>", "<p>$\\frac{1}{5}$</p>", "<p>$\\frac{1}{10}$</p>", "<p>$\\frac{1}{8}$</p>", "<p>$\\frac{1}{20}$</p>", "<p>$\\frac{1}{25}$</p>", "<p>$\\frac{1}{100}$</p>", "<p>$\\frac{1}{3}$</p>", "<p>$\\frac{1}{9}$</p>", "<p>$\\frac{3}{4}$</p>", "<p>$\\frac{2}{5}$</p>", "<p>$\\frac{1}{11}$</p>", "<p>$\\frac{1}{33}$</p>", "<p>$\\frac{1}{01}$</p>"], "choices": ["<p>$0.5$</p>", "<p>$0.25$</p>", "<p>$0.2$</p>", "<p>$0.1$</p>", "<p>$0.125$</p>", "<p>$0.05$</p>", "<p>$0.04$</p>", "<p>$0.01$</p>", "<p>$0.3\\dot{3}$</p>", "<p>$0.1\\dot{1}$</p>", "<p>$0.6$</p>", "<p>$0.3$</p>", "<p>$0.85$</p>", "<p>$0.6\\dot{6}$</p>", "<p>$0.45$</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "10", "scripts": {}, "warningType": "none", "marks": 0, "showCorrectAnswer": true, "type": "m_n_x", "shuffleChoices": true, "minMarks": "10", "layout": {"type": "all", "expression": ""}}], "statement": "<p>This question allows you to practice converting between decimals and fractions</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(0..1#0.1 except[0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(0..1#0.001 except [0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(0..1#0.01 except[0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..2#0.01 except [1,2])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random([2,4,5,10,20,25,50,100,200,1000])", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(1..g-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(1..j-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(1..l-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random([2,4,5,8,10,20,25,40,50,100,200,400,1000] except g)", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(1..n-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random([2,4,5,8,10,20,25,40,50,100,200,400,1000] except j)", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random([3,6,9])", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"description": "<p>This question allows you to practice converting between decimals and fractions</p>", "licence": "Creative Commons 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