// Numbas version: exam_results_page_options
{"name": "Harry's copy of MA1002 using fractions (simple operations)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "advice": "<p>When<strong> adding/subtracting</strong> fractions, you must first find a <em>common denominator</em> between the fractions. If they already have the same denominator then you only need to worry about adding/subtracting the numerators and dividing the result by the common denominator.</p>\n<p>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 $\\frac{6}{15}$. This is known as 'scaling up'.<br/>Now you can add the two fractions together (by adding the numerators) because they have the same denominator:<br/>$\\frac{6}{15}+\\frac{7}{15}=\\frac{13}{15}$.</p>\n<p>The same applies with&nbsp;subtraction as well as addition.</p>\n<p></p>\n<p>When <strong>multiplying</strong> fractions, you can simply multiply the two numerators and divide this by the multiplication of the two denominators.</p>\n<p>For example:<br/>$\\frac{a}{b}\\times\\frac{c}{d}$ = $\\frac{a\\times{c}}{b\\times{d}}$</p>\n<p></p>\n<p>When <strong>dividing</strong> fractions, you firstly need to reciprocate (flip) <i>the second fraction</i>, then multiply the numerators and denominators as you would a normal multiplication question.</p>\n<p>For example:<br/>$\\frac{a}{b} \\div \\frac{c}{d}$ would be flipped to become&nbsp;$\\frac{a}{b} \\div \\frac{d}{c}$ and then treated as a normal multiplication question (as explained above).</p>", "parts": [{"prompt": "<p>Calculate the following and simplify where appropriate:</p>\n<p>$\\frac{\\var{a}}{\\var{b}} \\times \\frac{\\var{c}}{\\var{b}}$?</p>\n<p>&nbsp;[[0]]</p>", "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"scripts": {}, "type": "patternmatch", "displayAnswer": "{answer1}", "variableReplacementStrategy": "originalfirst", "matchMode": "regex", "marks": 1, "showFeedbackIcon": true, "variableReplacements": [], "answer": "{answer1}", "showCorrectAnswer": true}], "marks": 0, "showFeedbackIcon": true, "variableReplacements": [], "showCorrectAnswer": true}, {"allowFractions": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "correctAnswerFraction": true, "prompt": "<p>What is the answer to $\\frac{\\var{d}}{\\var{f}} \\div \\frac{\\var{g}}{\\var{f}}$?</p>", "scripts": {}, "type": "numberentry", "showCorrectAnswer": true, "minValue": "d/g", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "marks": "1", "showFeedbackIcon": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "d/g"}, {"allowFractions": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "correctAnswerFraction": true, "prompt": "<p>What is the answer to $\\frac{\\var{h}}{\\var{j}} + \\frac{\\var{k}}{\\var{j}}$?</p>", "scripts": {}, "type": "numberentry", "showCorrectAnswer": true, "minValue": "(h+k)/j", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "marks": "1", "showFeedbackIcon": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "(h+k)/j"}, {"allowFractions": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "correctAnswerFraction": true, "prompt": "<p>What is the answer to $\\frac{\\var{l}}{\\var{m}} - \\frac{\\var{n}}{\\var{m}}$?</p>", "scripts": {}, "type": "numberentry", "showCorrectAnswer": true, "minValue": "(l-n)/m", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "marks": "1", "showFeedbackIcon": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "(l-n)/m"}, {"allowFractions": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "correctAnswerFraction": true, "prompt": "<p>What is the answer to $\\frac{\\var{o}}{\\var{p}} \\times \\frac{\\var{q}}{\\var{r}}$?</p>", "scripts": {}, "type": "numberentry", "showCorrectAnswer": true, "minValue": "(o*q)/(p*r)", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "marks": "1", "showFeedbackIcon": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "(o*q)/(p*r)"}, {"allowFractions": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "correctAnswerFraction": true, "prompt": "<p>What is the answer to $\\frac{\\var{s}}{\\var{t}} \\div \\frac{\\var{u}}{\\var{v}}$?</p>", "scripts": {}, "type": "numberentry", "showCorrectAnswer": true, "minValue": "(s*v)/(u*t)", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "marks": "1", "showFeedbackIcon": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "(s*v)/(u*t)"}, {"allowFractions": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "correctAnswerFraction": true, "prompt": "<p>What is the answer to $\\frac{\\var{w}}{\\var{x}} + \\frac{\\var{y}}{\\var{z}}$?</p>", "scripts": {}, "type": "numberentry", "showCorrectAnswer": true, "minValue": "((w*z)+(y*x))/(x*z)", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "marks": "1", "showFeedbackIcon": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "((w*z)+(y*x))/(x*z)"}, {"allowFractions": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "correctAnswerFraction": true, "prompt": "<p>What is the answer to $\\frac{\\var{aa}}{\\var{bb}} - \\frac{\\var{cc}}{\\var{dd}}$?</p>", "scripts": {}, "type": "numberentry", "showCorrectAnswer": true, "minValue": "((aa*dd)-(cc*bb))/(bb*dd)", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "marks": "1", "showFeedbackIcon": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "((aa*dd)-(cc*bb))/(bb*dd)"}], "variable_groups": [], "name": "Harry's copy of MA1002 using fractions (simple operations)", "statement": "<h2>Attempt the questions&nbsp;without a calculator.</h2>\n<h2>Give your answer as a fraction <strong>in its simplest form</strong>.</h2>", "variables": {"n": {"description": "", "group": "Ungrouped variables", "name": "n", "templateType": "anything", "definition": "random(1..m-l) //random numerator less than denominator"}, "ee": {"description": "", "group": "Ungrouped variables", "name": "ee", "templateType": "anything", "definition": "random(1..ff-1) //random numerator less than denominator"}, "g": {"description": "", "group": "Ungrouped variables", "name": "g", "templateType": "anything", "definition": "random(1..f-d) //random numerator less than denominator"}, "nn": {"description": "", "group": "Ungrouped variables", "name": "nn", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "num1": {"description": "", "group": "Ungrouped variables", "name": "num1", "templateType": "anything", "definition": "{a}{c}"}, "x": {"description": "", "group": "Ungrouped variables", "name": "x", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "dd": {"description": "", "group": "Ungrouped variables", "name": "dd", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "r": {"description": "", "group": "Ungrouped variables", "name": "r", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "f": {"description": "", "group": "Ungrouped variables", "name": "f", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "den1": {"description": "<p>den1</p>", "group": "Ungrouped variables", "name": "den1", "templateType": "anything", "definition": "{b}{b}"}, "pp": {"description": "", "group": "Ungrouped variables", "name": "pp", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "b": {"description": "", "group": "Ungrouped variables", "name": "b", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "c": {"description": "", "group": "Ungrouped variables", "name": "c", "templateType": "anything", "definition": "random(1..b-a) //random numerator less than denominator"}, "u": {"description": "", "group": "Ungrouped variables", "name": "u", "templateType": "anything", "definition": "random(1..v-1) //random numerator less than denominator"}, "ll": {"description": "", "group": "Ungrouped variables", "name": "ll", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "gg": {"description": "", "group": "Ungrouped variables", "name": "gg", "templateType": "anything", "definition": "random(1..hh-1) //random numerator less than denominator"}, "mm": {"description": "", "group": "Ungrouped variables", "name": "mm", "templateType": "anything", "definition": "random(1..nn-1) //random numerator less than denominator"}, "q": {"description": "", "group": "Ungrouped variables", "name": "q", "templateType": "anything", "definition": "random(1..r-1) //random numerator less than denominator"}, "tt": {"description": "", "group": "Ungrouped variables", "name": "tt", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "h": {"description": "", "group": "Ungrouped variables", "name": "h", "templateType": "anything", "definition": "random(1..j-1) //random numerator less than denominator"}, "k": {"description": "", "group": "Ungrouped variables", "name": "k", "templateType": "anything", "definition": "random(1..j-h) //random numerator less than denominator"}, "aa": {"description": "", "group": "Ungrouped variables", "name": "aa", "templateType": "anything", "definition": "random(1..bb-1) //random numerator less than denominator"}, "rr": {"description": "", "group": "Ungrouped variables", "name": "rr", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "s": {"description": "", "group": "Ungrouped variables", "name": "s", "templateType": "anything", "definition": "random(1..t-1) //random numerator less than denominator"}, "o": {"description": "", "group": "Ungrouped variables", "name": "o", "templateType": "anything", "definition": "random(1..p-1) //random numerator less than denominator"}, "ii": {"description": "", "group": "Ungrouped variables", "name": "ii", "templateType": "anything", "definition": "random(1..jj-1) //random numerator less than denominator"}, "p": {"description": "", "group": "Ungrouped variables", "name": "p", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "ff": {"description": "", "group": "Ungrouped variables", "name": "ff", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "qq": {"description": "", "group": "Ungrouped variables", "name": "qq", "templateType": "anything", "definition": "random(1..rr-1) //random numerator less than denominator"}, "oo": {"description": "", "group": "Ungrouped variables", "name": "oo", "templateType": "anything", "definition": "random(1..pp-1) //random numerator less than denominator"}, "z": {"description": "", "group": "Ungrouped variables", "name": "z", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "bb": {"description": "", "group": "Ungrouped variables", "name": "bb", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "a": {"description": "", "group": "Ungrouped variables", "name": "a", "templateType": "anything", "definition": "random(1..b-1) //random numerator less than denominator"}, "l": {"description": "", "group": "Ungrouped variables", "name": "l", "templateType": "anything", "definition": "random(1..m-1) //random numerator less than denominator"}, "m": {"description": "", "group": "Ungrouped variables", "name": "m", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "j": {"description": "", "group": "Ungrouped variables", "name": "j", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "jj": {"description": "", "group": "Ungrouped variables", "name": "jj", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "hh": {"description": "", "group": "Ungrouped variables", "name": "hh", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "simpleden1": {"description": "", "group": "Ungrouped variables", "name": "simpleden1", "templateType": "anything", "definition": "den1/gcd(num1,den1)"}, "y": {"description": "", "group": "Ungrouped variables", "name": "y", "templateType": "anything", "definition": "random(1..x-1) //random numerator less than denominator"}, "t": {"description": "", "group": "Ungrouped variables", "name": "t", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "cc": {"description": "", "group": "Ungrouped variables", "name": "cc", "templateType": "anything", "definition": "random(1..dd-1) //random numerator less than denominator"}, "v": {"description": "", "group": "Ungrouped variables", "name": "v", "templateType": "anything", "definition": "random(2..20) //random denominator"}, "answer1": {"description": "", "group": "Ungrouped variables", "name": "answer1", "templateType": "anything", "definition": "simplenum1+\"/\"+simpleden1"}, "w": {"description": "", "group": "Ungrouped variables", "name": "w", "templateType": "anything", "definition": "random(1..x-1) //random numerator less than denominator"}, "d": {"description": "", "group": "Ungrouped variables", "name": "d", "templateType": "anything", "definition": "random(1..f-1) //random numerator less than denominator"}, "kk": {"description": "", "group": "Ungrouped variables", "name": "kk", "templateType": "anything", "definition": "random(1..ll-1) //random numerator less than denominator"}, "ss": {"description": "", "group": "Ungrouped variables", "name": "ss", "templateType": "anything", "definition": "random(1..tt-1) //random numerator less than denominator"}, "simplenum1": {"description": "", "group": "Ungrouped variables", "name": "simplenum1", "templateType": "anything", "definition": "num1/gcd(num1,den1)"}}, "tags": [], "extensions": [], "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", "num1", "den1", "simplenum1", "simpleden1", "answer1"], "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "metadata": {"description": "<p>This is a set of questions designed to help you practice 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", "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}]}], "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}