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{"name": "Numerical skills Add, Subtract and Divide Algebraic Fractions - Summative assessment", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "d"], "name": "Numerical skills Add, Subtract and Divide Algebraic Fractions - Summative assessment", "tags": ["algebraic fractions"], "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>Express with a common denominator: $\\frac{6+1}{6x}$</p>\n<p>The simplify if possible: $\\frac{7}{6x}$</p>\n<p></p>\n<p>Similarly to subtract, you use a common denominator: $\\frac{6-1}{6x}$</p>\n<p>Then simplify: $\\frac{5}{6x}$</p>\n<p></p>\n<p>To multiply algebraic fractions, you multiply the top and then the bottom.</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 one upside down and then multiply.</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>", "rulesets": {}, "parts": [{"variableReplacements": [], "prompt": "<p>\\[ \\frac{\\var{a}}{x} + \\frac{1}{\\var{b}x} \\]</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({a}*{b}+1)/({b}x)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "<p>\\[ \\frac{\\var{c}}{x} -&nbsp;\\frac{\\var{a}}{\\var{d}} \\]</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({c}*{d}-{a}*x)/({d}x)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "<p>\\[ \\frac{\\var{a}}{x} \\times&nbsp;\\frac{\\var{d}}{\\var{b}y} \\]</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({a}*{d})/({b}*x*y)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "<p>\\[ \\frac{\\var{d}}{x} \\div&nbsp;\\frac{\\var{c}}{\\var{a}y} \\]</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({a}*{d}*y)/({c}x)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "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).</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(2..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(7..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(10..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"notes": "", "description": "<p>Practice with adding, subtracting and dividing basic algebraic fractions</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}