Practice with fractions
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "name": "Simplifying Numerical Fractions", "showQuestionGroupNames": false, "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');"}, "statement": "Express each of the following as a single fraction.
\n\n
To add or subtract two fractions, they must be expressed with a common denominator.
\nTo multiply two fractions, multiply the numerators and the denominators together.
\nTo divide two fractions, flip the second fraction upside down and then multiply.
\nEnter a fraction such as $\\frac{3}{4}$ as 3/4 using the \"/\" as the divide sign
", "functions": {}, "rulesets": {"std": ["all"]}, "tags": [], "ungrouped_variables": ["a", "b", "c", "d", "e", "ex"], "variablesTest": {"maxRuns": 100, "condition": ""}, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0}], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..4)", "description": ""}, "b": {"name": "b", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(5..15)", "description": ""}, "e": {"name": "e", "group": "Ungrouped variables", "templateType": "anything", "definition": "({a}/{b})+({c}/{d})", "description": ""}, "ex": {"name": "ex", "group": "Ungrouped variables", "templateType": "anything", "definition": "repeat(random(2..9),10)", "description": "Part e and f
"}, "c": {"name": "c", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..5)", "description": ""}, "d": {"name": "d", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(6..12)", "description": ""}}, "advice": "To add two fractions, they must be expressed with a common denominator.
\nFor example, if you have $\\frac{1}{3}+\\frac{2}{11}$, the common denominator would be $33$, from $(3 * 11)$.
\n$\\frac{11+6}{33}$
\n$\\frac{17}{33}$
\n\nSimilarly, to subtract two fractions, express them with a common denominator.
\n$\\frac{1}{3}-\\frac{2}{11}$
\n$=\\frac{11-6}{33}$
\n$=\\frac{5}{33}$
\n\nTo multiply two fractions, multiply the numerators and denominators together.
\n$\\frac{1}{3} \\times\\frac{2}{11}$
\n$=\\frac{1\\times 2}{3\\times11}$
\n$=\\frac{2}{33}$
\n\nTo divide two fractions, flip the second fraction upside down and then follow the steps to multiply.
\n$\\frac{1}{3} \\div \\frac{2}{11}$
\n$=\\frac{1}{3} \\times \\frac{11}{2}$
\n$=\\frac{1\\times11}{3\\times2}$
\n$=\\frac{11}{6}$
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