// Numbas version: exam_results_page_options
{"name": "Fractions: multiplying, algebraic and integer", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Fractions: multiplying, algebraic and integer", "tags": [], "metadata": {"description": "<p>A very simple algebraic fraction multiplied by a whole number. No cancelling is required by design.&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 write the whole number as a fraction over $1$, then we can multiply the numerators and multiply the denominators. We can cancel any common factors before or after multiplication.</p>\n<p>$\\begin{align*}\\displaystyle \\simplify[alwaysTimes,!simplifyFractions]{(w+{f})/{j} * {d}}&amp;=\\simplify[alwaysTimes,!simplifyFractions]{(w+{f})/{j} * ({d}/1)}\\\\[3pt]&amp;=\\simplify[alwaysTimes,!simplifyFractions]{(w+{f})*{d}/({j} * 1)}\\\\[3pt]&amp;=\\simplify{({d}w+{d*f})/{j}}\\end{align*}$</p>\n<p>Note, there are no common factors to cancel.</p>\n<p></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"d": {"name": "d", "group": "Ungrouped variables", "definition": "random([2,3,5,7,11])", "description": "", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "random([2,4,3,9,5,25,7,49,11] except [d, d^2])", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["d", "j", "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>$\\displaystyle \\simplify[alwaysTimes,!simplifyFractions]{(w+{f})/{j} * {d}}=$[[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": "({d}w+{d*f})/{j}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "m_strictinverse(\n     `! m_anywhere(?/?)\n     /\n     `! m_anywhere(?/?)`?\n   )", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "w", "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/"}]}