// Numbas version: exam_results_page_options
{"name": "Lucy's copy of Adding, subtracting, multiplying, dividing fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"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"], "name": "Lucy's copy of Adding, subtracting, multiplying, dividing fractions", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>When adding/subtracting fractions, you must first find a common denominator between the fractions.&nbsp;<br/>For example:<br/>To find a common denominator of $\\frac{2}{5} + \\frac{7}{15}$, the most obvious would be $15$, because $5\\times3=15$. Therefore, you must multiply both sides of the fraction&nbsp;$\\frac{2}{5}$ by $3$ to obtain a new fraction $\\frac{6}{15}$.&nbsp;<br/>Now you can add the two fractions together (by adding the numerators) because they have the same denominator by simply:<br/>$\\frac{6}{15}+\\frac{7}{15}=\\frac{13}{15}$.</p>\n<p></p>\n<p>When multiplying fractions, you can simply multiply the two numerators and divide this by the multiplication of the two denominators.</p>\n<p></p>\n<p>When diving fractions, you firstly need to recipricate (flip) <em>one</em> of the fractions, then multiply the numerators and denominators as you would a normal multiplication question. For example:<br/>$\\frac{a}{b} \\div \\frac{c}{d}$ woud be flipped to become&nbsp;$\\frac{a}{b} \\div \\frac{d}{c}$ and then treated as a normal multiplication question.</p>", "rulesets": {}, "parts": [{"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", "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}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "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", "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}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "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", "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"}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "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", "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"}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "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", "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"}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "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", "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"}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "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", "steps": [{"prompt": "<p>Follow through the steps from the first and fifth questions</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "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", "steps": [{"prompt": "<p>Follow the steps from the second and sixth questions</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "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", "steps": [{"prompt": "<p>Follow the steps from the third &nbsp;and seventh questions</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "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", "steps": [{"prompt": "<p>Follow the steps from the fourth and eighth questions</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "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": []}], "contributors": [{"name": "Lucy Hadfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/110/"}]}]}], "contributors": [{"name": "Lucy Hadfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/110/"}]}