// Numbas version: exam_results_page_options
{"name": "Numbers II: using fractions (advanced operations)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "j", "m", "p", "q", "r", "t", "v", "x", "z", "bb", "dd", "ff", "hh", "jj", "ll", "nn", "pp", "rr", "tt", "h", "k", "l", "n", "o", "s", "u", "w", "y", "aa", "cc", "ee", "gg", "ii", "kk", "mm", "oo", "qq", "ss", "int", "pow", "ddd", "fff", "pow3"], "name": "Numbers II: using fractions (advanced operations)", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p><span style=\"text-decoration: underline;\"><strong>Mixed fractions:</strong></span></p>\n<p>When converting a mixed fraction into a top heavy fraction it will help to see the integer as a fraction of the denominator. Any integer can first be converted into a fraction by dividing by one. Then scale up to have a common denominator.</p>\n<p>E.g. $3\\frac{2}{4} = \\frac{3}{1}+\\frac{2}{4}$</p>\n<p>Now you have a simple addition question where you need to scale up to find a common denominator: $\\frac{12}{4}+\\frac{2}{4} = \\frac{14}{4}$</p>\n<p>You can now convert $\\frac{14}{4}$ into a mixed fraction by deducing how many times&nbsp;4 goes into 14. 4 goes into 14 3 times with a remainder of 2. This equates to $3\\frac{2}{4}$ which further cancels to $3\\frac{1}{2}$.</p>\n<p></p>\n<p><span style=\"text-decoration: underline;\"><strong>Powers/roots:</strong></span></p>\n<p>It is useful to know that $(\\frac{a}{b})^c = \\frac{a^c}{b^c}$</p>\n<p>and $\\sqrt[c]\\frac{a}{b}$ is the same&nbsp;as $\\frac{\\sqrt[c]{a}}{\\sqrt[c]{b}}$</p>\n<p><span style=\"text-decoration: underline;\"><strong>BODMAS:</strong></span></p>\n<p>BODMAS tells us the order which we carry out operations. B stands for brackets, O for orders, D for division, M for multiplication, A for addition and S for subtraction.&nbsp;</p>\n<p>Therefore calculating a question with BODMAS laws in mind gives a mathematically accurate answer as the operations are carried out in the correct order.</p>\n<p>Start from B and working in order of priority of order until S.</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>What is the answer to $\\var{int}\\frac{\\var{a}}{\\var{b}} \\times \\frac{\\var{c}}{\\var{b}}$?</p>\n<p>Give your answer as a <strong>fraction</strong>.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "((({int}*b)+a)*c)/(b*b)", "minValue": "((({int}*b)+a)*c)/(b*b)", "variableReplacementStrategy": "originalfirst", "steps": [{"vsetrangepoints": 5, "prompt": "<p>What does the first equation $\\var{int}\\frac{\\var{a}}{\\var{b}}$ equate to as a top heavy fraction?</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": false, "answersimplification": "all", "scripts": {}, "answer": "(({int}*{b})+{a})/{b}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"prompt": "<p>Multiply the two numerators as you would with&nbsp;the original question, using the new numerator calculated above. Then divide this by the sum of the multiplication of the two denominators.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "((({int}*b)+a)*c)/(b*b)", "minValue": "((({int}*b)+a)*c)/(b*b)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "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>\n<p>Give your answer as a <strong>fraction</strong>.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "d/g", "minValue": "d/g", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Flip 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 to give the overall answer.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(d*f)/(g*f)", "minValue": "(d*f)/(g*f)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "vsetrangepoints": 5, "prompt": "<p>What is the answer to $(\\frac{\\var{ddd}}{\\var{fff}})^{\\var{pow3}}$?</p>\n<p>Give your answer as a <strong>fraction&nbsp;</strong>in its simplest form.</p>\n<p></p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><em>Please note:</em></p>\n<p>Rather than typing the above question straight into your calculator, you can alternatively think of the question as $\\frac{\\var{ddd}^{\\var{pow3}}}{\\var{fff}^{\\var{pow3}}}$</p>\n<p>Similarly, with roots, instead of typing $\\sqrt[\\var{pow3}]\\frac{\\var{ddd}}{\\var{fff}}$ straight into your calculator, you can think of the question as $\\frac{\\sqrt[\\var{pow3}]{\\var{ddd}}}{\\sqrt[\\var{pow3}]{\\var{fff}}}$</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({ddd}/{fff})^{pow3}", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"stepsPenalty": 0, "precisionType": "dp", "prompt": "<p>Using principles of BODMAS, what is the answer to $\\frac{\\var{q}}{\\var{r}} \\times \\frac{\\var{kk}}{\\var{ll}}-\\frac{\\var{ii}}{\\var{jj}}\\div\\frac{\\var{ee}}{\\var{ff}}+\\frac{\\var{nn}}{\\var{mm}}$?</p>\n<p>Give your answer to <strong>2 decimal places</strong>.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": true, "variableReplacements": [], "maxValue": "(q/r)*(kk/ll)-(ii/jj)/(ee/ff)+(nn/mm)", "strictPrecision": false, "minValue": "(q/r)*(kk/ll)-(ii/jj)/(ee/ff)+(nn/mm)", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>BODMAS tells us the order which we carry out operations. B stands for brackets, O stands for Powers, D stands for Division, M stands for Multiplication, A stands for Addition and S stands for subtraction.&nbsp;</p>\n<p>Therefore calculating a question with BODMAS laws in mind, gives a mathematically accurate answer as the operations are carried out in the correct order.</p>\n<p>Start from B and working in order of priority of order until S.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>These are slightly more complex&nbsp;questions to follow up on your simple operations of fraction knowledge.</p>\n<p>The questions include: mixed fractions, powers and the rules of BODMAS.</p>\n<p>To get the most out of the questions, please attempt without a calculator.</p>\n<p>Give your answer as a&nbsp;<em><strong>fraction</strong></em> unless asked otherwise.</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": ""}, "ff": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ff", "description": ""}, "ee": {"definition": "random(1..ff-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ee", "description": ""}, "pow": {"definition": "random(2..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "pow", "description": ""}, "rr": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "rr", "description": ""}, "ii": {"definition": "random(1..jj-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ii", "description": ""}, "fff": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "fff", "description": ""}, "pp": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "pp", "description": ""}, "kk": {"definition": "random(1..ll-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "kk", "description": ""}, "nn": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "nn", "description": ""}, "pow3": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "pow3", "description": ""}, "tt": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "tt", "description": ""}, "int": {"definition": "random(1..11#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "int", "description": ""}, "ddd": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "ddd", "description": ""}, "oo": {"definition": "random(1..pp-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "oo", "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": ""}, "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": ""}, "qq": {"definition": "random(1..rr-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "qq", "description": ""}, "gg": {"definition": "random(1..hh-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "gg", "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": ""}, "d": {"definition": "random(1..f-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "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": ""}, "ss": {"definition": "random(1..tt-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ss", "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": ""}, "ll": {"definition": "random(2..20) //random denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "ll", "description": ""}, "mm": {"definition": "random(1..nn-1) //random numerator less than denominator", "templateType": "anything", "group": "Ungrouped variables", "name": "mm", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}]}]}], "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}]}