// Numbas version: finer_feedback_settings
{"name": "22.a Simplify fractions (easy)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "22.a Simplify fractions (easy)", "tags": [], "metadata": {"description": "<p>Cancelling down a single prime factor to simplify a fraction.&nbsp;</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 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. The easiest way to do this is to keep dividing by the smallest number which divides both numbers. Since $\\var{SmallestFactor}$ divides both $\\var{x}$ and $\\var{y}$ then we can simplify</p>\n<p>\\[\\frac{\\var{x}}{\\var{y}}\\]</p>\n<p>to</p>\n<p>\\[\\frac{\\var{x/SmallestFactor}}{\\var{y/SmallestFactor}}.\\]</p>\n<p>We keep doing this until there are no numbers (except 1) which divide both the numerator and denominator. This leaves us with a simplified form of</p>\n<p>\\[\\frac{\\var{x}}{\\var{y}}=\\simplify[all,fractionNumbers]{{x/y}}.\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Fractions\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\" target=\"_blank\" rel=\"noopener\"></a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x_powers": {"name": "x_powers", "group": "Ungrouped variables", "definition": "[random(0..3),random(0..3),random(0..1)]", "description": "", "templateType": "anything", "can_override": false}, "y_powers": {"name": "y_powers", "group": "Ungrouped variables", "definition": "[random(0..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": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "2^y_powers[0]*3^y_powers[1]*5^y_powers[2]", "description": "", "templateType": "anything", "can_override": false}, "hcf_xy": {"name": "hcf_xy", "group": "Ungrouped variables", "definition": "2^min(x_powers[0],y_powers[0])*3^min(x_powers[1],y_powers[1])*5^min(x_powers[2],y_powers[2])", "description": "", "templateType": "anything", "can_override": false}, "SmallestFactor": {"name": "SmallestFactor", "group": "Ungrouped variables", "definition": "divisors(hcf_xy)[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "sum(x_powers)<3 && hcf_xy>1 && sum(y_powers)<4 && x<y", "maxRuns": "500"}, "ungrouped_variables": ["x_powers", "y_powers", "x", "y", "hcf_xy", "SmallestFactor"], "variable_groups": [], "functions": {"show_factors": {"parameters": [["n", "number"]], "type": "string", "language": "jme", "definition": "latex(  // mark the output as a string of raw LaTeX\n  join(\n    map(\n      if(a=1,p,p+'^{'+a+'}'), // when the exponent is 1, return p, otherwise return p^{exponent}\n      [p,a],\n      filter(x[1]>0,x,zip(primes,factorise(n)))  // for all the primes p which are factors of n, return p and its exponent\n    ),\n    ' \\\\times ' // join all the prime powers up with \\times symbols\n  )\n)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x/y}", "maxValue": "{x/y}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "resources": []}]}], "contributors": [{"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}]}