// Numbas version: finer_feedback_settings
{"name": "Fractions: improper and mixed fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a1", "b1", "c1", "a2", "b2", "c2", "a3", "b3", "c3", "ans3", "a4", "b4", "c4", "ans4"], "name": "Fractions: improper and mixed fractions", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>Convert the following improper fractions to mixed numerals (also known as mixed numbers):</p>\n<p><em>Note: Write the whole number part in the first box&nbsp;and the fraction&nbsp;part&nbsp;in the second&nbsp;</em></p>\n<p>$\\displaystyle\\frac{\\var{a1*c1+b1}}{\\var{c1}}=$[[0]][[1]]</p>\n<p>$\\displaystyle\\frac{\\var{a2*c2+b2}}{\\var{c2}}=$[[2]][[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><em>Do the division and write your remainder over the original denominator. Simplify the fraction if possible.</em>&nbsp;</p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example,&nbsp;converting&nbsp;$\\frac{21}{9}$ into a mixed numeral, you ask yourself \"how many times does 9&nbsp;go into 21?\", it goes in twice&nbsp;(since $2\\times 9=18$ but $3\\times 9=27$), with a remainder of 3&nbsp;(since $21-18=3$). So we can write our answer as $2\\frac{3}{9}$ (which actually means $2+\\frac{3}{9}$). But notice we can simplify the fraction, so we should rewrite our answer as $2\\frac{1}{3}$.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Note: we could have cancelled common factors at the beginning.&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "a1", "minValue": "a1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "b1/c1", "minValue": "b1/c1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "a2", "minValue": "a2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "b2/c2", "minValue": "b2/c2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Convert the following mixed numerals to improper fractions:</p>\n<p>$\\var{a3}\\frac{\\var{b3}}{\\var{c3}}=$[[0]]</p>\n<p>$\\var{a4}\\frac{\\var{b4}}{\\var{c4}}=$[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><em>Multiply the whole number and the denominator, add the numerator, and put it all over the denominator.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example $2\\frac{3}{4}$ can be written as $\\frac{2\\times 4+3}{4}$ that is, $\\frac{11}{4}$.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>To understand why, realise that $2\\frac{3}{4}$ is shorthand for $2+\\frac{3}{4}$&nbsp;and&nbsp;if we want to add these numbers we need to&nbsp;have a common denominator (recall the denominator of a whole number is 1). Our working could look like this:</p>\n<p>\\[2\\tfrac{3}{4}=2+\\frac{3}{4}=\\frac{2\\times 4}{4}+\\frac{3}{4}=\\frac{2\\times 4+3}{4}=\\frac{11}{4}\\]</p>\n<p>but in practice we normally don't write anything more than \\[2\\tfrac{3}{4}=\\frac{2\\times 4+3}{4}=\\frac{11}{4}\\]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "ans3", "minValue": "ans3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "ans4", "minValue": "ans4", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Remember to enter fractions in the following format:</p>\n<p>$\\frac{3}{4}$ = 3/4</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"b4": {"definition": "random(1..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "ans3": {"definition": "(a3*c3+b3)/c3", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "(a4*c4+b4)/c4", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "a1": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a4": {"definition": "random(1..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "b2": {"definition": "random(1..11)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "c3": {"definition": "b3+random(1..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "c2": {"definition": "b2+random(1..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "c1": {"definition": "b1+random(1..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "c4": {"definition": "b4+random(1..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}, "b1": {"definition": "random(1..11)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}}, "metadata": {"description": "<p>Questions on converting between improper and mixed fractions</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": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}]}], "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}