// Numbas version: exam_results_page_options
{"name": "Fractions: multiplying, algebraic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Fractions: multiplying, algebraic", "tags": [], "metadata": {"description": "<p>Multiply two algebraic fractions (unfortunately their appearance doesn't really change) and cancel.&nbsp;</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Express the following as a single fraction. Use / as the fraction bar, use brackets to group the denominator and use * for multiplication between a term and a bracket, e.g. $\\dfrac{7(m+1)}{2n}$ is written 7*(m+1)/(2n)</p>", "advice": "<p>We can multiply the numerators and multiply the denominators. We can cancel common factors before or after multiplication.</p>\n<p>$\\displaystyle\\simplify{({a}x+{b})(y-{f})/({cf*ee}x)}\\times\\simplify{(({cf*f}x*y)/(({c}x+{d}y)(y-{f})))}=\\simplify{(({a}x+{b})(y-{f})({cf*f}x*y))/(({cf*ee}x)*({c}x+{d}y)(y-{f}))}$</p>\n<p>There is a common factor of $x$,<span data-jme-visible=\"cf=1\"> and</span> a common factor of $\\simplify{y-{f}}$ <span data-jme-visible=\"cf&lt;&gt;1\">and a common factor of $\\var{cf}$</span> which we can cancel to get</p>\n<p>$\\displaystyle\\simplify{(({a}x+{b})*({f}*y))/(({ee})({c}x+{d}y))}$.</p>\n<p></p>\n<p></p>\n<p>&nbsp;&nbsp;</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"numbers": {"name": "numbers", "group": "Ungrouped variables", "definition": "shuffle(shuffle(2..10)[0..2]+[-1,1])", "description": "", "templateType": "anything", "can_override": false}, "cf": {"name": "cf", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "<p>common factor of denominators</p>", "templateType": "anything", "can_override": false}, "extrafactor": {"name": "extrafactor", "group": "Ungrouped variables", "definition": "shuffle([2,3,5,7])[0..2]", "description": "<p>extra factors in the denominators</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "numbers[0]", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "numbers[1]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "numbers[2]", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "numbers[3]", "description": "", "templateType": "anything", "can_override": false}, "ee": {"name": "ee", "group": "Ungrouped variables", "definition": "extrafactor[0]", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "extrafactor[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["numbers", "cf", "extrafactor", "a", "b", "c", "d", "ee", "f"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle\\simplify{({a}x+{b})(y+{f})/({cf*ee}x)}\\times\\simplify{(({cf*f}x*y)/(({c}x+{d}y)(y+{f})))}=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({a}x+{b})({f}*y)/({ee}({c}x+{d}y))", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "m_strictinverse(\n     `! m_anywhere(?/?)\n     /\n     `! m_anywhere(?/?)`?\n   )", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}