// Numbas version: exam_results_page_options
{"name": "Numerical fractions 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Numerical fractions 3", "tags": ["Arithmetic", "Fractions", "Lowest terms", "arithmetic", "fractions"], "advice": "\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)} * \\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.</p>\n    ", "rulesets": {}, "parts": [{"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>\n         \n      \n        ", "gaps": [{"minvalue": "{(a1*d1+b1*c1)/f1}", "type": "numberentry", "maxvalue": "{(a1*d1+b1*c1)/f1}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{b1*d1/f1}", "type": "numberentry", "maxvalue": "{b1*d1/f1}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"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      \n        ", "gaps": [{"minvalue": "{(a1*d1-b1*c1)/g1}", "type": "numberentry", "maxvalue": "{(a1*d1-b1*c1)/g1}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{b1*d1/g1}", "type": "numberentry", "maxvalue": "{b1*d1/g1}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"prompt": "\n        <p>$\\dfrac{\\var{a1}}{\\var{b1}} \\times \\dfrac{\\var{c1}}{\\var{d1}}$</p> <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>\t\t      \n      \n        ", "gaps": [{"minvalue": "{a1*c1/h1}", "type": "numberentry", "maxvalue": "{a1*c1/h1}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{b1*d1/h1}", "type": "numberentry", "maxvalue": "{b1*d1/h1}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"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      \n        ", "gaps": [{"minvalue": "{a1*d1/j1}", "type": "numberentry", "maxvalue": "{a1*d1/j1}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{b1*c1/j1}", "type": "numberentry", "maxvalue": "{b1*c1/j1}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "extensions": [], "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>", "variable_groups": [], "progress": "testing", "type": "question", "variables": {"f1": {"definition": "gcd(a1*d1+b1*c1,b1*d1)", "name": "f1"}, "r1": {"definition": "random(1..11)", "name": "r1"}, "g1": {"definition": "gcd(a1*d1-b1*c1,b1*d1)", "name": "g1"}, "s1": {"definition": "random(2..13 except r1)", "name": "s1"}, "h1": {"definition": "gcd(a1*c1,b1*d1)", "name": "h1"}, "u1": {"definition": "random(1..11)", "name": "u1"}, "j1": {"definition": "gcd(a1*d1,b1*c1)", "name": "j1"}, "t1": {"definition": "gcd(r1,s1)", "name": "t1"}, "a1": {"definition": "r1/t1", "name": "a1"}, "v1": {"definition": "random(2..13 except [u1,s1,u11])", "name": "v1"}, "b1": {"definition": "s1/t1", "name": "b1"}, "w1": {"definition": "gcd(u1,v1)", "name": "w1"}, "u11": {"definition": "s1*u1/r1", "name": "u11"}, "c1": {"definition": "u1/w1", "name": "c1"}, "d1": {"definition": "v1/w1", "name": "d1"}}, "metadata": {"notes": "", "description": "<p>Questions testing understanding of numerators and denominators of numerical fractions, and reduction to lowest terms.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}