// Numbas version: exam_results_page_options {"name": "Add two fractions with different denominators (some negative numbers)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "(a<>1 or b<>2 or c<>-3 or d<>4) and gcd(a,b)=1 and gcd(c,d)=1 and b<>d and (a<0 or c<0)", "maxRuns": 100}, "variable_groups": [], "statement": "

Add the following fractions using the formula $\\dfrac{a}{b}+\\dfrac{c}{d}=\\frac{\\boxed{ad}+\\boxed{bc}}{\\boxed{bd}}=\\frac{\\boxed{ad+bc}}{\\boxed{bd}}$.

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An example of a correct calculation would be $\\dfrac{1}{2}+\\dfrac{-3}{4}=\\frac{\\boxed{4}+\\boxed{-6}}{\\boxed{8}}=\\frac{\\boxed{-2}}{\\boxed{8}}$.

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Note that in the intermediate stage, you have to use the denominator $bd$ to be marked correct, you should not use a smaller common denominator (if one exists). Also note the final fraction should be left as it is and should not be entered in lowest form (if this is different).

", "functions": {}, "name": "Add two fractions with different denominators (some negative numbers)", "ungrouped_variables": ["a", "b", "c", "d"], "parts": [{"type": "gapfill", "showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "prompt": "

{a}{b} $\\ +\\ $ {c}{d} $\\ =\\ $ [[0]] $\\ +\\ $ [[1]] [[2]] $\\ =\\ $ [[3]][[4]].

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The correct calculation is $\\dfrac{\\var{a}}{\\var{b}}+\\dfrac{\\var{c}}{\\var{d}}=\\frac{\\boxed{\\var{a*d}}+\\boxed{\\var{b*c}}}{\\boxed{\\var{b*d}}}=\\frac{\\boxed{\\var{a*d+b*c}}}{\\boxed{\\var{b*d}}}$.

", "tags": [], "extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

This question tests a student's ability to add two fractions with different denominators (at least one of them is negative).

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This is the denominator of the second fraction.

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Numerator of the first fraction.

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This is the numerator of the second fraction.

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This is the denominator of the first fraction.

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