// Numbas version: exam_results_page_options
{"name": "Maria's copy of Manipulation of formula 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"c": {"definition": "random(2..10#1)", "templateType": "randrange", "name": "c", "description": "", "group": "Ungrouped variables"}, "a": {"definition": "random(6..15#1)", "templateType": "randrange", "name": "a", "description": "", "group": "Ungrouped variables"}, "b": {"definition": "random(2..10#1)", "templateType": "randrange", "name": "b", "description": "", "group": "Ungrouped variables"}, "d": {"definition": "random(8..16#1)", "templateType": "randrange", "name": "d", "description": "", "group": "Ungrouped variables"}}, "parts": [{"marks": 0, "prompt": "<p>Express your answer as a fraction:</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;\\(V =\\)&nbsp;[[0]]</p>", "gaps": [{"showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacements": [], "type": "jme", "showpreview": true, "scripts": {}, "checkvariablenames": false, "checkingaccuracy": 0.001, "marks": "2", "answer": "((5*{b}-{d})R+8)/(({a}*{d}-{b}*{c})R+7*{a}-3*{c})", "vsetrangepoints": 5, "checkingtype": "absdiff", "vsetrange": [0, 1], "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst"}], "variableReplacements": [], "type": "gapfill", "showFeedbackIcon": true, "scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "extensions": [], "variable_groups": [], "variablesTest": {"condition": "{a}*{d}>{c}*{b}", "maxRuns": 100}, "preamble": {"js": "", "css": ""}, "statement": "<p>Rearrange the following expression to make V the subject:</p>\n<p>&nbsp; &nbsp; &nbsp;\\(\\frac{\\var{a}V+1}{\\var{b}R+3}=\\frac{\\var{c}V+5}{\\var{d}R+7}\\)</p>", "ungrouped_variables": ["a", "b", "c", "d"], "rulesets": {}, "name": "Maria's copy of Manipulation of formula 2", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Manipulation of&nbsp;algebraic fractions</p>"}, "functions": {}, "advice": "<p>When one fraction equals another fraction we can clear both fractions by cross-multiplying:</p>\n<p style=\"text-align: center;\">\\((\\var{a}V+1)*(\\var{d}R+7)=(\\var{b}R+3)*(\\var{c}V+5)\\)</p>\n<p style=\"text-align: center;\">\\(\\simplify{{a}*{d}}VR+\\simplify{7*{a}}V+\\var{d}R+7=\\simplify{{b}*{c}}VR+\\simplify{5*{b}}R+\\simplify{3*{c}}V+15\\)</p>\n<p>Gathering all the terms involving \\(V\\) to the left hand side and moving all other terms to the right hand side gives</p>\n<p style=\"text-align: center;\">\\(\\simplify{{a}*{d}-{b}*{c}}VR+\\simplify{7*{a}-3*{c}}V=\\simplify{5*{b}-{d}}R+8\\)</p>\n<p>Factoring \\(V\\) out on the left hand side&nbsp;</p>\n<p style=\"text-align: center;\">\\(V(\\simplify{{a}*{d}-{b}*{c}}R+\\simplify{7*{a}-3*{c}})=\\simplify{5*{b}-{d}}R+8\\)</p>\n<p>Thus</p>\n<p style=\"text-align: center;\">\\(V=\\frac{\\simplify{5*{b}-{d}}R+8}{\\simplify{{a}*{d}-{b}*{c}}R+\\simplify{7*{a}-3*{c}}}\\)</p>", "tags": [], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}