// Numbas version: finer_feedback_settings
{"name": "Fractions - Test Yourself", "feedback": {"allowrevealanswer": true, "showtotalmark": true, "advicethreshold": 0, "intro": "", "feedbackmessages": [], "showanswerstate": true, "showactualmark": 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 activity has a variety of fraction&nbsp;questions all designed to be done without a calculator.</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 - 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 - 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 - 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 - 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": []}]}]}], "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "extensions": [], "custom_part_types": [], "resources": []}