// Numbas version: exam_results_page_options
{"name": "Simplifying Numerical 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", "b", "c", "d", "e", "ex"], "name": "Simplifying Numerical Fractions", "tags": ["Fractions", "fractions"], "preamble": {"css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n", "js": "document.createElement('fraction');\ndocument.createElement('numerator');\ndocument.createElement('denominator');"}, "advice": "<p>To add two fractions, they must be expressed with a common denominator.</p>\n<p>For example, if you have $\\frac{1}{3}+\\frac{2}{11}$, the common denominator would be $33$, from $(3 * 11)$.</p>\n<p>$\\frac{11+6}{33}$</p>\n<p>$\\frac{17}{33}$</p>\n<p></p>\n<p>Similarly, to subtract two fractions, express them with a common denominator.</p>\n<p>$\\frac{1}{3}-\\frac{2}{11}$</p>\n<p>$=\\frac{11-6}{33}$</p>\n<p>$=\\frac{5}{33}$</p>\n<p></p>\n<p>To multiply two fractions, multiply the numerators and denominators together.</p>\n<p>$\\frac{1}{3} \\times\\frac{2}{11}$</p>\n<p>$=\\frac{1\\times 2}{3\\times11}$</p>\n<p>$=\\frac{2}{33}$</p>\n<p></p>\n<p>To divide two fractions, flip&nbsp;the second fraction&nbsp;upside down and then follow the steps to multiply.</p>\n<p>$\\frac{1}{3} \\div \\frac{2}{11}$</p>\n<p>$=\\frac{1}{3} \\times \\frac{11}{2}$</p>\n<p>$=\\frac{1\\times11}{3\\times2}$</p>\n<p>$=\\frac{11}{6}$</p>", "rulesets": {"std": ["all"]}, "parts": [{"prompt": "<p>$ \\var{a}\\over\\var{b} $ + $ \\var{c}\\over\\var{d}$$=$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "({a}/{b})+({c}/{d})", "minValue": "({a}/{b})+({c}/{d})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$ \\var{a}\\over\\var{b} $ -&nbsp;$ \\var{c}\\over\\var{d} $$=$&nbsp;</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "({a}/{b})-({c}/{d})", "minValue": "({a}/{b})-({c}/{d})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\frac{\\var{a}}{\\var{b}} \\times \\frac{\\var{c}}{\\var{d}}=$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "({a}/{b})*({c}/{d})", "minValue": "({a}/{b})*({c}/{d})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\frac{\\var{a}}{\\var{b}} \\div &nbsp;\\frac{\\var{c}}{\\var{d}}=$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "({a}/{b})/({c}/{d})", "minValue": "({a}/{b})/({c}/{d})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p><fraction><numerator>$\\frac{\\var{ex[0]}}{\\var{ex[1]}}$</numerator><denominator>$\\frac{\\var{ex[2]}}{\\var{ex[3]}}$</denominator></fraction>&nbsp; $=$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "({ex[0]}/{ex[1]})/({ex[2]}/{ex[3]})", "minValue": "({ex[0]}/{ex[1]})/({ex[2]}/{ex[3]})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p><fraction><numerator>$\\frac{\\var{ex[4]}}{\\var{ex[5]}}+\\frac{\\var{ex[6]}}{\\var{ex[7]}}$</numerator><denominator>$\\frac{\\var{ex[8]}}{\\var{ex[9]}}$</denominator></fraction>&nbsp; $=$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(({ex[4]}/{ex[5]})+({ex[6]}/{ex[7]}))/({ex[8]}/{ex[9]})", "minValue": "(({ex[4]}/{ex[5]})+({ex[6]}/{ex[7]}))/({ex[8]}/{ex[9]})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}], "statement": "<p><strong>Express each of the following as a single fraction.</strong></p>\n<p><strong></strong></p>\n<p>To add or subtract two fractions,&nbsp;they must be expressed&nbsp;with a common denominator.</p>\n<p>To multiply two fractions, multiply the numerators and the denominators&nbsp;together.</p>\n<p>To divide two fractions, flip the second fraction upside down and then multiply.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(5..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "e": {"definition": "({a}/{b})+({c}/{d})", "templateType": "anything", "group": "Ungrouped variables", "name": "e", "description": ""}, "d": {"definition": "random(6..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "ex": {"definition": "repeat(random(2..9),10)", "templateType": "anything", "group": "Ungrouped variables", "name": "ex", "description": "<p>Part e and f</p>"}}, "metadata": {"notes": "", "description": "<p>Practice with 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": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}]}]}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}]}