// Numbas version: finer_feedback_settings
{"name": "22.e Equivalent fractions factor difference", "extensions": [], "custom_part_types": [], "resources": [["question-resources/equivalent_fractions.svg", "equivalent_fractions.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "22.e Equivalent fractions factor difference", "tags": ["cancelling", "equal fractions", "equivalent fractions", "Fractions", "fractions", "lowest form", "reducing fractions", "simplest form", "simplifying"], "metadata": {"description": "<p>spot use of a multiplier to get equivalent fractions with larger denominators.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>If we multiply the top and bottom of a fraction by a&nbsp;number (not zero) we get an equivalent fraction. We say equivalent because they represent the same amount of the whole.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example, suppose you cut a cake up into 3 parts and throw away one piece, what is left is <g class=\"gr_ gr_20 gr-alert gr_spell ContextualSpelling multiReplace\" id=\"20\" data-gr-id=\"20\">two thirds</g> of the whole cake, that is, $\\frac{2}{3}$ of the whole cake. Now suppose you have another identical cake, this time you cut it into 6 parts and throw away&nbsp;two parts, what is left is four sixths of the whole cake, that is, $\\frac{4}{6}$ of the whole cake.</p>\n<p>Notice in both situations you end up with the same amount of cake!&nbsp;</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/equivalent_fractions.svg\"/></p>\n<p>So $\\frac{2}{3}$ is equivalent to $\\frac{4}{6}$ and we can write \\[\\frac{2}{3}=\\frac{4}{6}.\\]</p>\n<p>If you look at the numbers you might notice that for the second cake we just doubled all the numbers, and in the second fraction all the numbers are two times those in the first fraction. In general equivalent fractions are formed by multiplying (or dividing) the top and bottom of a fraction by the same number.&nbsp;</p>\n<p>So if you were asked how a person got from $\\frac{\\var{num5}}{\\var{denom5}}$ to the equivalent fraction $\\frac{\\var{num6}}{\\var{denom6}}$ you ask yourself 'what do I multiply $\\var{num5}$ by to get $\\var{num6}$?' and 'what do I multiply $\\var{denom5}$ by to get $\\var{denom6}$?' and then realise they must have done the following</p>\n<p>\\[\\frac{\\var{num5}}{\\var{denom5}}=\\frac{\\var{num5}\\times\\var{mult4}}{\\var{denom5}\\times\\var{mult4}}=\\frac{\\var{num6}}{\\var{denom6}}.\\]</p>\n<p></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": {"std": ["all"]}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"denom5": {"name": "denom5", "group": "Ungrouped variables", "definition": "random(2..12 except num5)", "description": "", "templateType": "anything", "can_override": false}, "denom6": {"name": "denom6", "group": "Ungrouped variables", "definition": "denom5*mult4", "description": "", "templateType": "anything", "can_override": false}, "num6": {"name": "num6", "group": "Ungrouped variables", "definition": "num5*mult4", "description": "", "templateType": "anything", "can_override": false}, "num5": {"name": "num5", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "mult4": {"name": "mult4", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "FirstName": {"name": "FirstName", "group": "Ungrouped variables", "definition": "repeat(random([\"Ben\", \"He\"], [\"Annie\", \"She\"], [\"Matt\", \"He\"], [\"David\", \"He\"], [\"Steve\", \"He\"], [\"David\", \"He\"], [\"Scott\", \"He\"], [\"Fran\", \"She\"], [\"Jenny\", \"She\"], [\"Lyn\", \"She\"], [\"Judy-anne\", \"She\"], [\"Courtney\", \"She\"]),2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["num5", "denom5", "mult4", "num6", "denom6", "FirstName"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ".fractiontable table {\n  width: 40%; \n  padding: 0px; \n  border-width: 0px; \n  layout: fixed;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  width: 15%; \n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n.fractiontable .tdeq \n{\n  width: 5%; \n  border-bottom: 0px;\n  font-size: x-large;\n}\n\n\n.fractiontable th {\n    background-color:#aaa;\n}\n/*Fix the height of all cells EXCEPT table-headers to 40px*/\n.fractiontable td {\n    height:40px;\n}\n"}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{FirstName[0][0]} has written $\\frac{\\var{num5}}{\\var{denom5}}$ in the equivalent form $\\frac{\\var{num6}}{\\var{denom6}}$.</p>\n<p></p>\n<p>What has {FirstName[0][0]} done to the first&nbsp;fraction in order to&nbsp;get the second? {FirstName[0][1]} has multiplied the top and bottom by&nbsp;[[0]]&nbsp;.</p>", "gaps": [{"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": "mult4", "maxValue": "mult4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"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/"}], "resources": ["question-resources/equivalent_fractions.svg"]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"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/"}]}