// Numbas version: finer_feedback_settings
{"name": "Combine fractions and reduce to lowest terms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"g1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "gcd(a1*d1-b1*c1,b1*d1)", "description": "", "name": "g1"}, "s1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..13 except r1)", "description": "", "name": "s1"}, "r1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..11)", "description": "", "name": "r1"}, "u11": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s1*u1/r1", "description": "", "name": "u11"}, "f1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "gcd(a1*d1+b1*c1,b1*d1)", "description": "", "name": "f1"}, "b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s1/t1", "description": "", "name": "b1"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "r1/t1", "description": "", "name": "a1"}, "d1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "v1/w1", "description": "", "name": "d1"}, "t1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "gcd(r1,s1)", "description": "", "name": "t1"}, "c1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "u1/w1", "description": "", "name": "c1"}, "j1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "gcd(a1*d1,b1*c1)", "description": "", "name": "j1"}, "v1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..13 except [u1,s1,u11])", "description": "", "name": "v1"}, "u1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..11)", "description": "", "name": "u1"}, "h1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "gcd(a1*c1,b1*d1)", "description": "", "name": "h1"}, "w1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "gcd(u1,v1)", "description": "", "name": "w1"}}, "ungrouped_variables": ["f1", "r1", "g1", "s1", "h1", "u1", "j1", "t1", "a1", "v1", "b1", "w1", "u11", "c1", "d1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Combine fractions and reduce to lowest terms", "functions": {}, "showQuestionGroupNames": false, "parts": [{"prompt": "<p>$\\dfrac{\\var{a1}}{\\var{b1}} + \\dfrac{\\var{c1}}{\\var{d1}}$</p>\n      <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>", "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{(a1*d1+b1*c1)/f1}", "minValue": "{(a1*d1+b1*c1)/f1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}, {"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{b1*d1/f1}", "minValue": "{b1*d1/f1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"prompt": "\n      <p>$\\dfrac{\\var{a1}}{\\var{b1}} - \\dfrac{\\var{c1}}{\\var{d1}}$</p> <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>\t\t      \n        ", "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{(a1*d1-b1*c1)/g1}", "minValue": "{(a1*d1-b1*c1)/g1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}, {"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{b1*d1/g1}", "minValue": "{b1*d1/g1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"prompt": "<p>$\\dfrac{\\var{a1}}{\\var{b1}} \\times \\dfrac{\\var{c1}}{\\var{d1}}$</p>\n      <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>", "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{a1*c1/h1}", "minValue": "{a1*c1/h1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}, {"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{b1*d1/h1}", "minValue": "{b1*d1/h1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"prompt": "\n      <p>$\\dfrac{\\var{a1}}{\\var{b1}} \\div \\dfrac{\\var{c1}}{\\var{d1}}$</p> <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>\t\t      \n        ", "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{a1*d1/j1}", "minValue": "{a1*d1/j1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}, {"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{b1*c1/j1}", "minValue": "{b1*c1/j1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}], "statement": "<p>Evaluate the following as fractions in lowest terms. Write the numerator and denominator of the lowest term fraction in the boxes provided.</p>", "tags": ["Arithmetic", "arithmetic", "checked2015", "Fractions", "fractions", "Lowest terms", "SFY0001"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Questions testing understanding of numerators and denominators of numerical fractions, and reduction to lowest terms.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>For addition and subtraction, write fractions so that they have a common denominator and then perform addition or subtraction on the numerators. One method of doing this is 'cross-multiplication'. The rules are :</p>\n<p>\\[\\simplify{a/b+ c/d=(a*d+b*c)/(b*d)}.\\]<br/>\\[\\simplify{a/b- c/d=(a*d-b*c)/(b*d)}.\\]</p>\n<p>For multiplication and division the rules are simpler:</p>\n<p>\\[\\simplify{(a/b)} \\times&nbsp;\\simplify{(c/d)}=\\simplify{(a*c)/(b*d)}.\\]<br/>\\[\\simplify{(a/b)} / \\simplify{(c/d)}=\\simplify{(a*d)/(b*c)}.\\]</p>\n<p>Having applied these rules, it will be necessary to reduce the resulting fractions to lowest terms. We get:</p>\n<p></p>\n<p>a) $\\dfrac{\\var{a1}}{\\var{b1}} + \\dfrac{\\var{c1}}{\\var{d1}}=\\dfrac{\\var{a1} \\times \\var{d1} + \\var{b1} \\times \\var{c1}}{\\var{b1} \\times \\var{d1}}=\\dfrac{\\var{a1*d1 + b1*c1}}{\\var{b1*d1}}$. In lowest terms this is $\\dfrac{\\var{(a1*d1 + b1*c1)/f1}}{\\var{b1*d1/f1}}$.</p>\n<p></p>\n<p>b) $\\dfrac{\\var{a1}}{\\var{b1}} - \\dfrac{\\var{c1}}{\\var{d1}}=\\dfrac{\\var{a1} \\times \\var{d1} - \\var{b1} \\times \\var{c1}}{\\var{b1} \\times \\var{d1}}=\\dfrac{\\var{a1*d1 - b1*c1}}{\\var{b1*d1}}$. In lowest terms this is $\\dfrac{\\var{(a1*d1 - b1*c1)/g1}}{\\var{b1*d1/g1}}$.</p>\n<p></p>\n<p>c) $\\dfrac{\\var{a1}}{\\var{b1}} \\times \\dfrac{\\var{c1}}{\\var{d1}}=\\dfrac{\\var{a1} \\times \\var{c1}}{\\var{b1} \\times \\var{d1}}=\\dfrac{\\var{a1*c1}}{\\var{b1*d1}}$. In lowest terms this is $\\dfrac{\\var{a1*c1/h1}}{\\var{b1*d1/h1}}$</p>\n<p></p>\n<p>d) $\\dfrac{\\var{a1}}{\\var{b1}} \\div \\dfrac{\\var{c1}}{\\var{d1}}=\\dfrac{\\var{a1}}{\\var{b1}} \\times \\dfrac{\\var{d1}}{\\var{c1}}=\\dfrac{\\var{a1} \\times \\var{d1}}{\\var{b1} \\times \\var{c1}}=\\dfrac{\\var{a1*d1}}{\\var{b1*c1}}$. In lowest terms this is $\\dfrac{\\var{a1*d1/j1}}{\\var{b1*c1/j1}}$</p>\n<p></p>\n<p></p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}