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{"name": "NG1 Simplify (cancel down) Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "NG1 Simplify (cancel down) Fractions", "tags": [], "metadata": {"description": "Calculating the LCM and HCF of numbers by using prime factorisation.", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Express the fraction below in its simplest form:</p>\n<p>\\[\\frac{\\var{x}}{\\var{y}}\\]</p>", "advice": "<p>To simplify a fraction we need to divide both numbers by their common factors.</p>\n<p>We can write $\\var{x}$ and $\\var{y}$ as a product of prime factors as follows:</p>\n<p>$\\var{x}=\\var{show_factors(x)}$</p>\n<p>$\\var{y}=\\var{show_factors(y)}$.</p>\n<p>So to fully simplify the fraction we need to divide both $\\var{x}$ and $\\var{y}$ by</p>\n<p>\\[\\var{show_factors(hcf_xy)}.\\]</p>\n<p>This gives us the fraction</p>\n<p>\\[\\frac{\\var{x/hcf_xy}}{\\var{y/hcf_xy}}\\]</p>\n<p><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>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"x_powers": {"name": "x_powers", "group": "Ungrouped variables", "definition": "[random(1..3),random(0..3),random(0,1)]", "description": "", "templateType": "anything", "can_override": false}, "y_powers": {"name": "y_powers", "group": "Ungrouped variables", "definition": "[random(1..3),random(0..3),random(0,1)]", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "2^x_powers[0]*3^x_powers[1]*5^x_powers[2]", "description": "", 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