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{"name": "Fractions: dividing, algebraic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Fractions: dividing, algebraic", "tags": [], "metadata": {"description": "<p>A simple algebraic fraction dividing by another. Cancelling is recommended.</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><span data-jme-visible=\"seed=0\">Note that by looking at the length of the fraction bars we can determine that $\\displaystyle \\frac{\\simplify{((x+{a})/({d}x))}}{\\simplify{((x+{f})/{j})}}$ represents $\\displaystyle \\simplify{((x+{a})/({d}x))} \\div \\simplify{((x+{f})/{j})}$.</span></p>\n<p>We can do the division by multiplying by the reciprocal. We can cancel any common factors before or after multiplication.</p>\n<p>$\\begin{align*}\\displaystyle \\simplify{((x+{a})/({d}x))} \\div \\simplify{((x+{f})/{j})}&amp;=\\simplify{((x+{a})/({d}x))} \\times \\simplify{({j}/(x+{f}))}\\\\[3pt]&amp;=\\simplify[!simplifyFractions]{((x+{a})*{j})/({d}x(x+{f}))}\\end{align*}$</p>\n<p><span data-jme-visible=\"cf=1 and f&lt;&gt;a\">Note, there are no common factors to cancel.</span></p>\n<p><span data-jme-visible=\"cf&lt;&gt;1\">There is a common factor of $\\var{cf}$, so we divide the numerator and the denominator by $\\var{cf}$ in order to remove it.</span></p>\n<p><span data-jme-visible=\"cf&lt;&gt;1\">&nbsp;$\\begin{align*}\\displaystyle\\simplify[!simplifyFractions]{((x+{a})*{j})/({d}x(x+{f}))}&amp;=\\frac{(\\simplify{x+{a}})\\times \\var{j}\\div \\var{cf}}{(\\var{d}\\div\\var{cf})\\simplify{x(x+{f})}}\\\\[3pt]&amp;=\\simplify{((x+{a})*{j})/({d}x(x+{f}))}.\\end{align*}$</span></p>\n<p><span data-jme-visible=\"f=a\">There is a common factor of $(\\simplify{x+{a}})$, so we divide the numerator and denominator by $(\\simplify{x+{a}})$ in order to remove it.</span></p>\n<p><span data-jme-visible=\"f=a\">$\\begin{align*}\\displaystyle\\simplify{((x+{a})*{j})/({d}x(x+{f}))}&amp;=\\frac{(\\simplify{x+{a}})\\div \\simplify{(x+{a})*{j/cf}}}{\\simplify{{d/cf}x(x+{f})}\\div(\\simplify{x+{f}})}\\\\[3pt]&amp;=\\simplify{{j}/({d}x)}.\\end{align*}</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"d": {"name": "d", "group": "Ungrouped variables", "definition": "abs(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..4]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(numbers[3],f)", "description": "", "templateType": "anything", "can_override": false}, "cf": {"name": "cf", "group": "Ungrouped variables", "definition": "gcd(j,d)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["d", "j", "f", "seed", "numbers", "a", "cf"], "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 \\frac{\\simplify{((x+{a})/({d}x))}}{\\simplify{((x+{f})/{j})}}=$</span><span data-jme-visible=\"seed=1\">$\\displaystyle \\simplify{((x+{a})/({d}x))} \\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": "{j}(x+{a})/(({d}x)*(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/"}]}