// Numbas version: exam_results_page_options
{"name": "Algebraic Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "name": "Algebraic Fractions", "preamble": {"css": "", "js": ""}, "functions": {}, "variable_groups": [], "rulesets": {}, "metadata": {"description": "<p>Practice with adding, subtracting and dividing basic algebraic fractions</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "parts": [{"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "jme", "checkingType": "absdiff", "marks": 1, "vsetRangePoints": 5, "prompt": "<p>\\[ \\frac{\\var{a}}{x} + \\frac{1}{\\var{b}x} \\]</p>", "answerSimplification": "all", "checkVariableNames": false, "answer": "({a}*{b}+1)/({b}x)", "showCorrectAnswer": true, "unitTests": [], "expectedVariableNames": [], "showFeedbackIcon": true, "failureRate": 1, "checkingAccuracy": 0.001, "showPreview": true, "scripts": {}, "vsetRange": [0, 1]}, {"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "jme", "checkingType": "absdiff", "marks": 1, "vsetRangePoints": 5, "prompt": "<p>\\[ \\frac{\\var{c}}{x} -&nbsp;\\frac{\\var{a}}{\\var{d}} \\]</p>", "answerSimplification": "all", "checkVariableNames": false, "answer": "({c}*{d}-{a}*x)/({d}x)", "showCorrectAnswer": true, "unitTests": [], "expectedVariableNames": [], "showFeedbackIcon": true, "failureRate": 1, "checkingAccuracy": 0.001, "showPreview": true, "scripts": {}, "vsetRange": [0, 1]}, {"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "jme", "checkingType": "absdiff", "marks": 1, "vsetRangePoints": 5, "prompt": "<p>\\[ \\frac{\\var{a}}{x} \\times&nbsp;\\frac{\\var{d}}{\\var{b}y} \\]</p>", "answerSimplification": "all", "checkVariableNames": false, "answer": "({a}{d})/({b}xy)", "showCorrectAnswer": true, "unitTests": [], "expectedVariableNames": [], "showFeedbackIcon": true, "failureRate": 1, "checkingAccuracy": 0.001, "showPreview": true, "scripts": {}, "vsetRange": [0, 1]}, {"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "jme", "checkingType": "absdiff", "marks": 1, "vsetRangePoints": 5, "prompt": "<p>\\[ \\frac{\\var{d}}{x} \\div&nbsp;\\frac{\\var{c}}{\\var{a}y} \\]</p>", "answerSimplification": "all", "checkVariableNames": false, "answer": "({a}{d}y)/({c}x)", "showCorrectAnswer": true, "unitTests": [], "expectedVariableNames": [], "showFeedbackIcon": true, "failureRate": 1, "checkingAccuracy": 0.001, "showPreview": true, "scripts": {}, "vsetRange": [0, 1]}, {"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "jme", "checkingType": "absdiff", "marks": 1, "vsetRangePoints": 5, "prompt": "<p><span style=\"display: inline !important; float: none; background-color: transparent; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">\\[ \\frac{\\var{a}}{x} + \\frac{1}{(\\var{c} -\\var{f}x)} \\]</span></p>", "answerSimplification": "all", "checkVariableNames": false, "answer": "({a}{c} + (1 - {a}{f})x)/(x({c} -{f}x))", "showCorrectAnswer": true, "unitTests": [], "expectedVariableNames": [], "showFeedbackIcon": true, "failureRate": 1, "checkingAccuracy": 0.001, "showPreview": true, "scripts": {}, "vsetRange": [0, 1]}, {"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "jme", "checkingType": "absdiff", "marks": 1, "vsetRangePoints": 5, "prompt": "<p><span style=\"display: inline !important; float: none; background-color: transparent; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">\\[ \\frac{\\var{c}}{(\\var{d} + y)} - \\frac{\\var{b}}{(\\var{a} + x)}\\]</span></p>", "answerSimplification": "all", "checkVariableNames": false, "answer": "({a}{c} -{b}{d} + {c}x - {b}y)/(({d} + y)({a} + x))", "showCorrectAnswer": true, "unitTests": [], "expectedVariableNames": [], "showFeedbackIcon": true, "failureRate": 1, "checkingAccuracy": 0.001, "showPreview": true, "scripts": {}, "vsetRange": [0, 1]}], "variables": {"a": {"name": "a", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..8)"}, "b": {"name": "b", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)"}, "d": {"name": "d", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..15)"}, "f": {"name": "f", "description": "", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(2..12#1)"}, "c": {"name": "c", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)"}}, "advice": "<p>To add two algebraic fractions you use the same procedure as you would with numbers.</p>\n<p>For example: $\\frac{1}{x}+\\frac{1}{6x}$</p>\n<p>The simplest common denominator in this case is $6x$</p>\n<p>To get a single fraction we alter each fraction to get an equivalent one with the common denominator <span style=\"display: inline !important; float: none; background-color: transparent; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">$\\frac{6}{6x}+\\frac{1}{6x}$</span></p>\n<p>Then we combine the fractions by adding the top row together $\\frac{6+1}{6x}$</p>\n<p>The&nbsp;<span style=\"display: inline !important; float: none; background-color: transparent; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">collect like terms</span> if possible: $\\frac{7}{6x}$</p>\n<p></p>\n<p>Similarly to subtract, you use a similar method to adding but to combine the fractions you subtract: $\\frac{6-1}{6x}$</p>\n<p>Then collect like terms if possible: $\\frac{5}{6x}$</p>\n<p></p>\n<p>To multiply algebraic fractions, you multiply the top and then multiply the bottom terms.</p>\n<p>$\\frac{1}{x} \\times\\frac{1}{6x}$</p>\n<p>$=\\frac{1\\times1}{x\\times6x}$</p>\n<p>$=\\frac{1}{6x^2}$</p>\n<p></p>\n<p>To divide algebraic fractions to turn the second fraction upside down and then multiply the fractions together.</p>\n<p>$\\frac{1}{x} \\div\\frac{1}{6x}$</p>\n<p>$=\\frac{1}{x} \\times\\frac{6x}{1}$</p>\n<p>=6 (since the $x$ cancels out)</p>\n<p></p>", "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["a", "b", "c", "d", "f"], "statement": "<p><strong>Express the following as a single fraction.</strong></p>\n<p>You will need to type your answer in the form (numerator)/(denominator). For this system please note the bractets need to be around&nbsp;<strong>all of the numerator or denominator</strong> for it to be marked correct. For these examples don't forget to simplify them and collect like terms on the numerator.</p>", "type": "question", "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}, {"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}, {"name": "Jo-Ann Lyons", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2630/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}, {"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}, {"name": "Jo-Ann Lyons", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2630/"}]}