// Numbas version: exam_results_page_options
{"name": "Simplifying fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Simplifying fractions", "tags": ["fractions", "lowest form", "simplifying fractions"], "advice": "<p>We have:<br/>\\[\\simplify[std]{{g} / ({a} + {s1} * ({b * g} / {f})) = {g} / (({a} * {f} + {s1} * {b * g}) / {f}) ={g} / (({a * f + s1 * b * g}) / {f})= ({f}*{g}) / ({a * f + s1 * b * g}) = ({g * f} / {(a * f + s1 * b * g)})}\\]<br/>Here we use the result that dividing by a fraction $\\frac{a}{b}$ is the same as multiplying by $\\frac{b}{a}$.<br/>The resulting fraction is in lowest form i.e. the top and bottom do not have a common factor.</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"]}, "parts": [{"prompt": "\n      <p>\\[\\simplify{{g} / ({a} + {s1} * ({b * g} / {f}))}\\]<br/>Input your answer here: [[0]]</p>\n      <p>Your answer must be of the form a/b for suitable integers a and b. No decimal numbers allowed.</p>\n      <p>Do not include brackets in your answer.</p>\n      ", "gaps": [{"musthave": {"message": "<p>You must write your answer in the form p/q for integers p and q</p>", "showstrings": false, "strings": ["/"], "partialcredit": 0.0}, "checkingaccuracy": 0.0001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 1.0, "answer": "{g*f}/{a*f+s1*b*g}", "type": "jme", "notallowed": {"message": "<p>You must write your answer in the form p/q for integers p and q</p>", "showstrings": false, "strings": ["+", ".", "(", ")", "1-", "2-", "3-", "4-", "5-", "6-", "7-", "8-", "9-"], "partialcredit": 0.0}, "maxlength": {"length": 7.0, "message": "<p>answer too long</p>", "partialcredit": 0.0}}], "type": "gapfill", "marks": 0.0}], "extensions": [], "statement": "<p>Write the following expression as a single fraction in its lowest form:</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(1..11)", "name": "a"}, "b": {"definition": "switch(f=2,1,f=3,random(1,2),f=4,random(1,3),f=5, random(1..4),f=6,random(1,5),f=7,random(1..6),f=8,random(1,3,5,7),f=9,random(1,2,4,5,7,8),f=10,random(1,3,7,9),f=11,random(1..10))", "name": "b"}, "g": {"definition": "switch(a=1, random(2..11),a=2,random(3..11#2),a=3,random(4,5,7,8,10,11),a=4,random(5,7,9,11),a=5, random(6,7,8,9,11),a=6,random(7,11),a=7,random(8,9,10,11),a=8,random(9,11),a=9,random(10,11),a=10,11,a=11,12)", "name": "g"}, "f": {"definition": "switch(g=2,random(3..11#2),g=3,random(2,4,5,7,8,10,11),g=4,random(3,5,7,9,11),g=5, random(2,3,4,6,7,8,9,11),g=6,random(5,7,11),g=7,random(2,3,4,5,6,8,9,10,11),g=8,random(3,5,7,9,11),g=9,random(2,4,5,7,8,10,11),g=10,random(3,7,9),g=11,random(2..10),g=12,random(5,7,11))", "name": "f"}, "s1": {"definition": "if(a*f+s*b*g=1,-s,s)", "name": "s1"}, "s": {"definition": "random(1,-1)", "name": "s"}}, "metadata": {"notes": "\n    \t\t<p><strong>5/08/2012:</strong></p>\n    \t\t        <p>Added description.</p>\n    \t\t", "description": "<p>Find $\\displaystyle \\frac{a} {b + \\frac{c}{d}}$ as a single fraction in the form $\\displaystyle \\frac{p}{q}$ for integers $p$ and $q$.</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/"}]}