// Numbas version: exam_results_page_options
{"name": "NG5 Multiply Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "NG5 Multiply Fractions", "tags": ["improper fractions", "mixed numbers", "multiplication of fractions", "multiplying fractions", "squared fraction", "taxonomy"], "metadata": {"description": "<p>Several problems involving the multiplication of fractions, with increasingly difficult examples, including&nbsp;a mixed fraction and a squared fraction. The final part is a word problem.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Evaluate the following multiplication, giving the answer in its simplest form.</p>", "advice": "<h4></h4>\n<p>To multiply $\\displaystyle\\frac{\\var{a_coprime}}{\\var{c_coprime}}\\times\\frac{\\var{b_coprime}}{\\var{d_coprime}}$, address the numerators and denominators separately.</p>\n<p>Multiply the numerators across both fractions.</p>\n<p style=\"text-align: center;\">$\\var{a_coprime}\\times\\var{b_coprime}=\\var{ab}$,</p>\n<p>and then multiply the denominators across both fractions.</p>\n<p style=\"text-align: center;\">$\\var{c_coprime}\\times\\var{d_coprime}=\\var{cd}$.</p>\n<p>The values of the multiplied numerators and denominators will be the numerator and denominator of the new fraction: $\\displaystyle\\frac{\\var{ab}}{\\var{cd}}$.</p>\n<p>This answer may need simplifying down, and to do this, find the greatest common divisor in both the numerator and denominator and divide by this number.</p>\n<p>The greatest common divisor of $\\var{ab}$ and $\\var{cd}$ is $\\var{gcd}$.</p>\n<p>By using $\\var{gcd}$ to cancel down the fraction, the final answer is $\\displaystyle\\simplify{{ab}/{cd}}$.</p>\n<p style=\"text-align: center;\"></p>\n<p style=\"text-align: center;\"><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>\n<h4></h4>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"k": {"name": "k", "group": "Part b", "definition": "random(1..7 except j)", "description": "<p>Random number between 1 and 20</p>", "templateType": "anything", "can_override": false}, "bb": {"name": "bb", "group": "Part d", "definition": "28*aa", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", 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