// Numbas version: finer_feedback_settings
{"name": "Compute more complicated combinations of 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": {"u2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "name": "u2"}, "x21": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s2*v2*x2/(r2*v2-s2*u2)", "description": "", "name": "x21"}, "e2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "x2/z2", "description": "", "name": "e2"}, "s2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..11 except r2)", "description": "", "name": "s2"}, "r2": {"templateType": "anything", "group": "Ungrouped variables", "definition": 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"definition": "o2/q2", "description": "", "name": "g2"}, "k2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "gcd(a2*d2*f2-b2*c2*f2-b2*d2*e2,b2*d2*f2)", "description": "", "name": "k2"}}, "ungrouped_variables": ["f2", "h2", "j2", "w2", "b2", "y2", "d2", "q2", "s2", "u2", "k2", "m2", "x21", "o2", "x22", "g2", "i2", "v2", "a2", "x2", "c2", "z2", "e2", "p2", "r2", "t2", "l2", "u21"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Compute more complicated combinations of fractions and reduce to lowest terms", "functions": {}, "showQuestionGroupNames": false, "parts": [{"prompt": "<p>$\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} + \\dfrac{\\var{e2}}{\\var{f2}}$</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": "{(a2*d2*f2+b2*c2*f2+b2*d2*e2)/i2}", "minValue": "{(a2*d2*f2+b2*c2*f2+b2*d2*e2)/i2}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}, {"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{(b2*d2*f2)/i2}", "minValue": "{(b2*d2*f2)/i2}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"prompt": "\n      <p>$\\dfrac{\\var{a2}}{\\var{b2}} - \\dfrac{\\var{c2}}{\\var{d2}} + \\dfrac{\\var{e2}}{\\var{f2}}$</p> <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>\n       \n        ", "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{(a2*d2*f2-b2*c2*f2+b2*d2*e2)/j2}", "minValue": "{(a2*d2*f2-b2*c2*f2+b2*d2*e2)/j2}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}, {"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{(b2*d2*f2)/j2}", "minValue": "{(b2*d2*f2)/j2}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"prompt": "\n      <p>$\\dfrac{\\var{a2}}{\\var{b2}} - \\dfrac{\\var{c2}}{\\var{d2}} - \\dfrac{\\var{e2}}{\\var{f2}}$</p> <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>\n       \n        ", "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{(a2*d2*f2-b2*c2*f2-b2*d2*e2)/k2}", "minValue": "{(a2*d2*f2-b2*c2*f2-b2*d2*e2)/k2}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}, {"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{(b2*d2*f2)/k2}", "minValue": "{(b2*d2*f2)/k2}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"prompt": "<p>$\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} \\times \\dfrac{\\var{e2}}{\\var{f2}}$</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": "{(a2*d2*f2+b2*c2*e2)/l2}", "minValue": "{(a2*d2*f2+b2*c2*e2)/l2}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}, {"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{(b2*d2*f2)/l2}", "minValue": "{(b2*d2*f2)/l2}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"prompt": "<p>$\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} \\times \\dfrac{\\var{g2}}{\\var{h2}}+\\dfrac{\\var{e2}}{\\var{f2}}$</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": "{(a2*d2*f2*h2+b2*c2*f2*g2+b2*d2*e2*h2)/m2}", "minValue": "{(a2*d2*f2*h2+b2*c2*f2*g2+b2*d2*e2*h2)/m2}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}, {"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{(b2*d2*f2*h2)/m2}", "minValue": "{(b2*d2*f2*h2)/m2}", "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": ["checked2015", "Fractions", "fractions", "Lowest terms", "SFY0001"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Harder questions testing addition, subtraction, multiplication and division of numerical fractions and reduction to lowest terms. They also test BIDMAS in the context of fractions.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>Perform the various operations required in the order dictated by BIDMAS.</p>\n<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 \\simplify{(c/d)=(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. In some of the following there might be slightly simpler approaches possible.&nbsp;</p>\n<p>a) $\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} + \\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2*d2}+ \\var{b2*c2}}{\\var{b2*d2}} + \\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2*d2+ b2*c2}}{\\var{b2*d2}} + \\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2*d2+ b2*c2} \\times \\var{f2}+\\var{b2*d2} \\times \\var{e2}}{\\var{b2*d2} \\times \\var{f2}}=\\dfrac{\\var{(a2*d2+ b2*c2)*f2}+\\var{b2*d2*e2}}{\\var{b2*d2*f2}}=\\dfrac{\\var{(a2*d2+ b2*c2)*f2+b2*d2*e2}}{\\var{b2*d2*f2}}$.</p>\n<p>In lowest terms, this is $\\dfrac{\\var{(a2*d2*f2+b2*c2*f2+b2*d2*e2)/i2}}{\\var{(b2*d2*f2)/i2}}$.</p>\n<p></p>\n<p>b) $\\dfrac{\\var{a2}}{\\var{b2}} - \\dfrac{\\var{c2}}{\\var{d2}} + \\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2*d2}- \\var{b2*c2}}{\\var{b2*d2}} + \\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2*d2- b2*c2}}{\\var{b2*d2}} + \\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2*d2- b2*c2} \\times \\var{f2}+\\var{b2*d2} \\times \\var{e2}}{\\var{b2*d2} \\times \\var{f2}}=\\dfrac{\\var{(a2*d2- b2*c2)*f2}+\\var{b2*d2*e2}}{\\var{b2*d2*f2}}=\\dfrac{\\var{(a2*d2- b2*c2)*f2+b2*d2*e2}}{\\var{b2*d2*f2}}$.</p>\n<p>In lowest terms, this is $\\dfrac{\\var{(a2*d2*f2-b2*c2*f2+b2*d2*e2)/j2}}{\\var{(b2*d2*f2)/j2}}$.</p>\n<p></p>\n<p>c) $\\dfrac{\\var{a2}}{\\var{b2}} - \\dfrac{\\var{c2}}{\\var{d2}} - \\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2*d2}- \\var{b2*c2}}{\\var{b2*d2}} - \\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2*d2- b2*c2}}{\\var{b2*d2}} - \\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2*d2- b2*c2}\\times \\var{f2}-\\var{b2*d2} \\times \\var{e2}}{\\var{b2*d2} \\times \\var{f2}}=\\dfrac{\\var{(a2*d2- b2*c2)*f2}-\\var{b2*d2*e2}}{\\var{b2*d2*f2}}=\\dfrac{\\var{(a2*d2- b2*c2)*f2-b2*d2*e2}}{\\var{b2*d2*f2}}$.</p>\n<p>In lowest terms, this is $\\dfrac{\\var{(a2*d2*f2-b2*c2*f2-b2*d2*e2)/k2}}{\\var{(b2*d2*f2)/k2}}$.</p>\n<p></p>\n<p>d) $\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} \\times \\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}\\times \\var{e2}}{\\var{d2} \\times \\var{f2}}=\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2*e2}}{\\var{d2*f2}} =\\dfrac{\\var{a2} \\times \\var{d2*f2}}{\\var{b2} \\times \\var{d2*f2}} + \\dfrac{\\var{b2} \\times \\var{c2*e2}}{\\var{b2}\\times \\var{d2*f2}}=\\dfrac{\\var{a2*d2*f2}+\\var{b2*c2*e2}}{\\var{b2*d2*f2}}=\\dfrac{\\var{a2*d2*f2+b2*c2*e2}}{\\var{b2*d2*f2}} $.</p>\n<p>In lowest terms this is $\\dfrac{\\var{(a2*d2*f2+b2*c2*e2)/l2}}{\\var{(b2*d2*f2)/l2}} $</p>\n<p></p>\n<p>e) $\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} \\times \\dfrac{\\var{g2}}{\\var{h2}}+\\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2}}{\\var{b2}} +\\left[ \\dfrac{\\var{c2}}{\\var{d2}} \\times \\dfrac{\\var{g2}}{\\var{h2}}\\right]+\\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2}}{\\var{b2}} +\\left[ \\dfrac{\\var{c2} \\times \\var{g2} }{\\var{d2} \\times \\var{h2}} \\right]+\\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2*g2} }{\\var{d2*h2}} +\\dfrac{\\var{e2}}{\\var{f2}}$</p>\n<p>$=\\left[\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2*g2} }{\\var{d2*h2}} \\right]+\\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2} \\times \\var{d2*h2}+\\var{b2} \\times \\var{c2*g2}}{\\var{b2} \\times \\var{d2*h2}} &nbsp;+\\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2*d2*h2+b2*c2*g2}}{\\var{b2*d2*h2}} &nbsp;+\\dfrac{\\var{e2}}{\\var{f2}}=\\dfrac{\\var{a2*d2*h2+b2*c2*g2} \\times \\var{f2}+\\var{b2*d2*h2} \\times \\var{e2}}{\\var{b2*d2*h2} \\times \\var{f2}}=\\dfrac{\\var{(a2*d2*h2+b2*c2*g2)*f2+b2*d2*h2*e2}}{\\var{b2*d2*h2*f2}}$.</p>\n<p>In lowest terms this is $\\dfrac{\\var{((a2*d2*h2+b2*c2*g2)*f2+b2*d2*h2*e2)/m2}}{\\var{b2*d2*h2*f2/m2}}$.</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/"}]}