// Numbas version: exam_results_page_options
{"name": "Arithmetic with Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "m", "n", "nm"], "name": "Arithmetic with Fractions", "tags": ["adding fractions", "Arithmetic", "arithmetic", "dividing fractions", "fractions", "Fractions", "multiplying fractions"], "preamble": {"css": "", "js": ""}, "advice": "<p>a) When adding fractions you first need to put them over a common denominator.</p>\n<p>See <a href=\"http://www.mathsisfun.com/fractions_addition.html\">http://www.mathsisfun.com/fractions_addition.html</a> for explanations and examples.</p>\n<p>b) When multiplying $ \\dfrac{a}{b} \\times \\dfrac{c}{d}$ we get $ \\dfrac{ab}{cd}$. It might then be possible to simplify the answer by cancelling common factors.</p>\n<p>See&nbsp;<a href=\"http://www.mathsisfun.com/fractions_multiplication.html\">http://www.mathsisfun.com/fractions_multiplication.html</a> for explanations and examples.</p>\n<p>c) $ \\dfrac{\\var{a}}{\\var{b}} \\div \\dfrac{\\var{c}}{\\var{d}}$ is equivalent to $ \\dfrac{\\var{a}}{\\var{b}}&nbsp; \\times \\dfrac{\\var{d}}{\\var{c}}$.</p>\n<p>After cancelling this is $ \\dfrac{\\var{n}}{\\var{m}} $.</p>\n<p>See <a href=\"http://www.mathsisfun.com/fractions_division.html\">http://www.mathsisfun.com/fractions_division.html</a> for some more examples and an explanation of this method.</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\displaystyle {\\dfrac {\\var{n}} {\\var{m}}} + {\\dfrac {\\var{d}} {\\var{c}}}$</p>\n<p>&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>You need to give your answer as a fraction not a decimal.</p>", "showStrings": false, "strings": ["."], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({c}*{n}+{m}*{d})/({m}*{c})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>&nbsp;$\\displaystyle {\\dfrac {\\var{b}} {\\var{a}}}&nbsp; \\times {\\dfrac {\\var{c}} {\\var{d}}}$</p>\n<p>&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{m}/{n}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>&nbsp;$\\displaystyle {\\dfrac {\\var{a}} {\\var{b}}}&nbsp; \\div {\\dfrac {\\var{c}} {\\var{d}}}$</p>\n<p>&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{n}/{m}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Evaluate and simplify the following, giving your answers as exact single fractions:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "{n}*{c}", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(6..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "{m}*{d}", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(2..7 except c)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "m": {"definition": "nm[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "n": {"definition": "nm[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "nm": {"definition": "satisfy(\n//variables to be defined using nm\n[n,m],\n//definition of variables\n[random(3..5),random(2..5)],\n//condition on the variables, m and n forcec to be coprime\n[gcd(m,n)=1]\n\n)", "templateType": "anything", "group": "Ungrouped variables", "name": "nm", "description": ""}}, "metadata": {"description": "<p>Addition, multiplication and division of fractions.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}