// Numbas version: finer_feedback_settings
{"name": "Fractions - Worded Questions", "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", "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"], "name": "Fractions - Worded Questions", "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}], "extensions": [], "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/"}]}]}], "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}]}