// Numbas version: exam_results_page_options
{"name": "Fractions: dividing, 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: dividing, algebraic and integer", "tags": [], "metadata": {"description": "<p>A whole number divided by a very simple algebraic fraction. No cancelling is required by design.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Evaluate the following and write your answer as a single fraction. Use &nbsp;/ to signify a fraction or division, for example $\\frac{2a-1}{x+3}$ is written (2a-1)/(x+3). Simplify/cancel where possible.</p>", "advice": "<p><span data-jme-visible=\"seed=0\">Note that by looking at the length of the fraction bars we can determine that $\\displaystyle \\simplify[alwaysTimes,!simplifyFractions]{{d}/((x+{f})/{j})}$ represents $\\displaystyle \\var{d} \\div \\simplify{(x+{f})/{j}}$.</span></p>\n<p>We can write the whole number as a fraction over $1$, and then we can do the division by multiplying by the reciprocal. We can cancel any common factors before or after multiplication.</p>\n<p>$\\begin{align*}\\var{d} \\div \\simplify{(x+{f})/{j}}&amp;=\\frac{\\var{d}}{1}\\div\\simplify{(x+{f})/{j}}\\\\[3pt]&amp;=\\frac{\\var{d}}{1}\\times\\simplify{{j}/(x+{f})}\\\\[3pt]&amp;=\\simplify[alwaysTimes,!simplifyFractions]{{d}*{j}/(1*(x+{f}))}\\\\[3pt]&amp;=\\simplify{{d*j}/(x+{f})}\\end{align*}$</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": "numbers[0]", "description": "", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "abs(numbers[1])", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "numbers[2]", "description": "", "templateType": "anything", "can_override": false}, "seed": {"name": "seed", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "<p>determines how the division is displayed</p>", "templateType": "anything", "can_override": false}, "numbers": {"name": "numbers", "group": "Ungrouped variables", "definition": "shuffle(-10..12 except [-1,0,1])[0..3]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["d", "j", "f", "seed", "numbers"], "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><span data-jme-visible=\"seed=0\">$\\displaystyle \\simplify[alwaysTimes,!simplifyFractions]{{d}/((x+{f})/{j})}=$</span><span data-jme-visible=\"seed=1\">$\\displaystyle \\var{d} \\div \\simplify{((x+{f})/{j})}=$</span>[[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*j}/(x+{f})", "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": "x", "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/"}]}