// Numbas version: finer_feedback_settings
{"name": "1.2 - Fractions - Add, subtract, multiply,divide (simple operations)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "1.2 - Fractions - Add, subtract, multiply,divide (simple operations)", "tags": [], "metadata": {"description": "<p>This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.</p>\n<p>All of these can be done without a calculator.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>These are basic questions to help you practice adding, subtracting, multiplying and dividing fractions.</p>\n<p>Attempt the questions&nbsp;without a calculator.</p>\n<p>Give your answer as a <em><strong>fraction.</strong></em></p>", "advice": "<p>When<strong> adding/subtracting</strong> fractions, you must first find a <em>common denominator</em> between the fractions. If they already have the same denominator then you only need to worry about adding/subtracting the numerators and dividing the result by the common denominator.</p>\n<p>For example:<br/>To find a common denominator of $\\frac{2}{5} + \\frac{7}{15}$, the most obvious would be $15$, because $5\\times3=15$. Therefore, you must multiply both sides of the fraction&nbsp;$\\frac{2}{5}$ by $3$ to obtain a new fraction $\\frac{6}{15}$. This is known as 'scaling up'.<br/>Now you can add the two fractions together (by adding the numerators) because they have the same denominator:<br/>$\\frac{6}{15}+\\frac{7}{15}=\\frac{13}{15}$.</p>\n<p>The same applies with&nbsp;subtraction as well as addition.</p>\n<p></p>\n<p>When <strong>multiplying</strong> fractions, you can simply multiply the two numerators and divide this by the multiplication of the two denominators.</p>\n<p>For example:<br/>$\\frac{a}{b}\\times\\frac{c}{d}$ = $\\frac{a\\times{c}}{b\\times{d}}$</p>\n<p>In some cases, it is possible to cancel out terms be capitalising on the associativity and commutativity of multiplication.</p>\n<p>e.g.</p>\n<p>For</p>\n<p>\\[ \\frac{10}{9} \\times \\frac{6}{5} \\]</p>\n<p>Rather than calculating $10 \\times 6 = 60$ and dividing this by $9 \\times 5 = 45$, we can recognise that the multiplication will give the same result as</p>\n<p>\\[ \\frac{10}{5} \\times \\frac{6}{9} \\]</p>\n<p>and then recognise that these fractions have simpler represenations of $2$ and $\\frac{2}{3}$ respectively, and so then we can calculate the solution to be $\\frac{4}{3}$ more easily.</p>\n<p></p>\n<p>When <strong>dividing</strong> fractions, you firstly need to reciprocate (flip) <i>the second fraction</i>, then multiply the numerators and denominators as you would a normal multiplication question.</p>\n<p>For example:<br/>$\\frac{a}{b} \\div \\frac{c}{d}$ would be flipped to become&nbsp;$\\frac{a}{b} \\div \\frac{d}{c}$ and then treated as a normal multiplication question (as explained above).</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"ii": {"name": "ii", "group": "Ungrouped variables", "definition": "random(1..jj-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "ee": {"name": "ee", "group": "Ungrouped variables", "definition": "random(1..ff-1) //random 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