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{"name": "NG8 - Ordering fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "NG8 - Ordering fractions", "tags": [], "metadata": {"description": "<p>Put fractions in size order.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Which of these two fractions is the largest?</p>", "advice": "<p>To find which is bigger of $\\frac{\\var{top1}}{\\var{bot1}}$ and $\\frac{\\var{top2}}{\\var{bot2}}$ we need them to have the same denominator. A way to do this is to multiply the top and bottom of $\\frac{\\var{top1}}{\\var{bot1}}$ by $\\var{bot2}$ and multiply the top and bottom of $\\frac{\\var{top2}}{\\var{bot2}}$ by {bot1}. This doesn't change the the value of the fractions as this is just like multiplying by one.</p>\n<p>\\[\\frac{\\var{top1}}{\\var{bot1}}=\\frac{\\var{top1*bot2}}{\\var{bot1*bot2}},\\quad \\frac{\\var{top2}}{\\var{bot2}}=\\frac{\\var{top2*bot1}}{\\var{bot1*bot2}}\\]</p>\n<p>Now we can easily see which is bigger by comparing the numerator.</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Fractions\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"top1": {"name": "top1", "group": "Ungrouped variables", "definition": "random(1..(bot1-1))", "description": "", "templateType": "anything", "can_override": false}, "top2": {"name": "top2", "group": "Ungrouped variables", "definition": "random(1..(bot2-1))", "description": "", "templateType": "anything", "can_override": false}, "bot1": {"name": "bot1", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "bot2": {"name": "bot2", "group": "Ungrouped variables", "definition": "random(1..10 except bot1)", "description": "", "templateType": "anything", "can_override": false}, "frac1": {"name": "frac1", "group": "Ungrouped variables", "definition": "top1/bot1", "description": "", "templateType": "anything", "can_override": false}, "frac2": {"name": "frac2", "group": "Ungrouped variables", "definition": "top2/bot2", "description": "", "templateType": "anything", "can_override": false}, "Is1Bigger": {"name": "Is1Bigger", "group": "Ungrouped variables", "definition": "award(1,frac1>frac2)", "description": "", "templateType": "anything", "can_override": false}, "Is2Bigger": {"name": "Is2Bigger", "group": "Ungrouped variables", "definition": "award(1,frac2>frac1)", "description": "", "templateType": "anything", "can_override": false}, "Question": {"name": "Question", "group": "Ungrouped variables", "definition": "[string(top1)+\"/\"+string(bot1),string(top2)+\"/\"+string(bot2)]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(frac1-frac2)>0", "maxRuns": "250"}, "ungrouped_variables": ["top1", "top2", "bot1", "bot2", "frac1", "frac2", "Is1Bigger", "Is2Bigger", "Question"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": "Question", "matrix": "[Is1Bigger,Is2Bigger]"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"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/"}]}]}], "contributors": [{"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/"}]}