// Numbas version: finer_feedback_settings
{"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", "group": "Part d", "definition": "bb/7", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Part b", "definition": "random(1 .. 7#1)", "description": "<p>Random number between 1 and 20.</p>", "templateType": "randrange", "can_override": false}, "cd": {"name": "cd", "group": "Part a", "definition": "c_coprime*d_coprime", "description": "<p>Variable c times variable d.</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Part a", "definition": "random(2..12 except c)", "description": "<p>Random number from 1 to 12.</p>", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Part a", "definition": "random(2 .. 12#1)", "description": "<p>Random number from 1 to 12.</p>", "templateType": "randrange", "can_override": false}, "l": {"name": "l", "group": "Part c", "definition": "random(1..12)", "description": "", "templateType": "anything", "can_override": false}, "numif": {"name": "numif", "group": "Part b", "definition": "(f*h_coprime)+g_coprime", "description": "<p>Numerator of the improper fraction converted from a mixed number.</p>", "templateType": "anything", "can_override": false}, "gcd_gh": {"name": "gcd_gh", "group": "Part b", "definition": "gcd(g,h)", "description": "", "templateType": "anything", "can_override": false}, "fh": {"name": "fh", "group": "Part b", "definition": "f*h_coprime", "description": "<p>Variable f times variable h</p>", "templateType": "anything", "can_override": false}, "g_coprime": {"name": "g_coprime", "group": "Part b", "definition": "g/gcd_gh", "description": "", "templateType": "anything", "can_override": false}, "j_coprime": {"name": "j_coprime", "group": "Part b", "definition": "j/gcd_kj", "description": "", "templateType": "anything", "can_override": false}, "gcd_kj": {"name": "gcd_kj", "group": "Part b", "definition": "gcd(k,j)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Part b", "definition": "random(1 .. 4#1)", "description": "<p>Random number between 1 and 4 - integer part of the mixed number.</p>", "templateType": "randrange", "can_override": false}, "c_coprime": {"name": "c_coprime", "group": "Part a", "definition": "c/gcd_ac", "description": "", "templateType": "anything", "can_override": false}, "gcd": {"name": "gcd", "group": "Part a", "definition": "gcd(ab,cd)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Part a", "definition": "random(2 .. 12#1)", "description": "<p>Random number from 1 to 12.</p>", "templateType": "randrange", "can_override": false}, "d_coprime": {"name": "d_coprime", "group": "Part a", "definition": "d/gcd_bd", "description": "", "templateType": "anything", "can_override": false}, "ddcc": {"name": "ddcc", "group": "Part d", "definition": "dd*cc", "description": "", "templateType": "anything", "can_override": false}, "gcdb": {"name": "gcdb", "group": "Part b", 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"<p>Random number between 1 and 20.</p>", "templateType": "randrange", "can_override": false}, "num": {"name": "num", "group": "Part b", "definition": "k_coprime*{numif/gcda}", "description": "<p>Numerator of gap 0</p>", "templateType": "anything", "can_override": false}, "m_coprime": {"name": "m_coprime", "group": "Part c", "definition": "m/gcd_lm", "description": "", "templateType": "anything", "can_override": false}, "aa": {"name": "aa", "group": "Part d", "definition": "random(1..6)", "description": "", "templateType": "anything", "can_override": false}, "gcda": {"name": "gcda", "group": "Part b", "definition": "gcd({numif},{h_coprime})", "description": "<p>gcd of the numerator of the improper fraction</p>", "templateType": "anything", "can_override": false}, "h_coprime": {"name": "h_coprime", "group": "Part b", "definition": "h/gcd_gh", "description": "", "templateType": "anything", "can_override": false}, "ee": {"name": "ee", "group": "Part d", "definition": "ddcc/4", 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