// Numbas version: finer_feedback_settings
{"name": "Fractions 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": [], "name": "Fractions 2", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Learn from your mistakes and have another attempt by clicking on 'Try another question like this one' until you get full marks.</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"], "": []}, "parts": [{"stepsPenalty": "0", "prompt": "<p>Calculate</p>\n<p>$\\displaystyle\\simplify{(x+{a})/({b}x)-({c}x-{d})/({ee}x)}=$[[0]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><em>Expand the fractions to get a common denominator. Then add and subract.<br/></em></p>\n<hr/>\n<p>(Simplify if possible.)</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({ee-b*c}x+{ee*a+b*d})/({b*ee}x)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "0", "prompt": "<p>Calculate</p>\n<p>$\\displaystyle{\\frac{\\frac{x}{\\var{j}}+\\frac{1}{\\var{l}}}{\\frac{\\var{g}x}{\\var{j*l}}+\\frac{1}{\\var{j}}}} =$[[0]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Find the common denominator for all the small fractions. Then multiply by this on both sides of the main fraction line.</p>\n<hr/>\n<p>Example:&nbsp;</p>\n<p style=\"text-align: center;\">\\[\\frac{\\frac{2x}{3}+\\frac{1}{5}}{\\frac{4x}{15}-\\frac{1}{3}}=\\frac{(\\frac{2x}{3}+\\frac{1}{5})\\cdot 15}{(\\frac{4x}{15}-\\frac{1}{3})\\cdot 15}=\\frac{2x\\cdot 5+1\\cdot3}{4x-1\\cdot 5}=\\frac{10x+3}{4x-5}\\]</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\"></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({l}x+{j})/({g}x+{l})", "marks": "1", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Calculate and give your answer as a fraction or an algebra expression. Use &nbsp;/ &nbsp;as the fraction line, for example&nbsp;$\\frac{x-2}{3}$ is written as&nbsp;(x-2)/3 and&nbsp;$\\frac{(x+1)}{(x-4)}$ as&nbsp;(x+1)/(x-4)</p>", "variable_groups": [{"variables": ["a", "b", "c", "d", "ee", "g", "j", "l"], "name": "numerical fractions"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..3)", "templateType": "anything", "group": "numerical fractions", "name": "a", "description": ""}, "c": {"definition": "random(2..5)", "templateType": "anything", "group": "numerical fractions", "name": "c", "description": ""}, "b": {"definition": "random(2..6 except a)", "templateType": "anything", "group": "numerical fractions", "name": "b", "description": ""}, "d": {"definition": "random(2..5)", "templateType": "anything", "group": "numerical fractions", "name": "d", "description": ""}, "g": {"definition": "random(3..7)", "templateType": "anything", "group": "numerical fractions", "name": "g", "description": ""}, "ee": {"definition": "random(2..5 except b)", "templateType": "anything", "group": "numerical fractions", "name": "ee", "description": ""}, "j": {"definition": "random(2..5)", "templateType": "anything", "group": "numerical fractions", "name": "j", "description": ""}, "l": {"definition": "random(2..5 except j)", "templateType": "anything", "group": "numerical fractions", "name": "l", "description": ""}}, "metadata": {"description": "<p>Add, subtract, multiply and divide algebraic 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": "Robert F\u00f8rland", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/827/"}]}]}], "contributors": [{"name": "Robert F\u00f8rland", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/827/"}]}