// Numbas version: finer_feedback_settings
{"name": "Q1 Intro to Ratios", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["num11", "ans11", "ans12", "k", "num12", "boy", "number0", "number1", "number2", "low", "ans21", "ans22", "ans23", "l", "girl", "student", "ans31", "ans32", "ans33"], "name": "Q1 Intro to Ratios", "tags": ["rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>Watch the following video to understand ratios better!</p>\n<p><a href=\"http://www.mathtutor.ac.uk/arithmetic/ratios/video\">Ratios Video</a></p>\n<p></p>\n<p>Part 1:</p>\n<p>Divide both numbers by their highest common&nbsp;factor</p>\n<p></p>\n<p>Part 2:</p>\n<p>Divide both the number of boys and girls&nbsp;by their highest common&nbsp;factor</p>\n<p>$\\frac{\\var{boy}}{\\var{l}}$ : $\\frac{\\var{girl}}{\\var{l}}$</p>\n<p>$\\var{ans21}$ : $\\var{ans22}$</p>\n<p></p>\n<p>$\\frac{\\var{student}}{\\var{boy} + \\var{girl}} \\times \\var{girl} = \\var{ans23}$</p>\n<p></p>\n<p>Part 3:</p>\n<p>First get the lowest common denominator = $\\var{low}$</p>\n<p>$(\\frac{\\var{low}}{\\var{number0}}) \\times&nbsp;1 = \\var{ans31}$</p>\n<p>$(\\frac{\\var{low}}{\\var{number1}}) \\times&nbsp;5 = \\var{ans32}$</p>\n<p>$(\\frac{\\var{low}}{\\var{number2}}) \\times&nbsp;7 = \\var{ans33}$</p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Express the ratio $\\var{num11}$ : $\\var{num12}$ in its simplest form.</p>\n<p>[[0]]:[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>To express a ratio in its simplest form you always multiply or divide all parts by the same number.</p>\n<p>In this case you need to divide the ratios by a common factor. Can both numbers be divided by 2? Or maybe 3 or 4? Keep dividing both sides until you think it can't get any simpler.</p>\n<p>Alternatively you could find the highest common factor and divide by that.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}", "minValue": "{ans11}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans12}", "minValue": "{ans12}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>In a class there are $\\var{boy}$ boys and&nbsp;$\\var{girl}$ girls. Find the ratio of boys to girls in the class in its simplest form.</p>\n<p>[[0]]boys :&nbsp;[[1]]girls</p>\n<p>If the whole year group of&nbsp;$\\var{student}$ students is in the same ratio, how many girls are there in the year?</p>\n<p>[[2]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Express this ratio in its simplest form as above. Divide the&nbsp;$\\var{student}$ students into this ratio.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}", "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22}", "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans23}", "minValue": "{ans23}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Express $\\frac{1}{\\var{number0}}:\\frac{5}{\\var{number1}}:\\frac{7}{\\var{number2}}$ as a ratio in whole numbers.</p>\n<p></p>\n<p>[[0]]&nbsp;: [[1]]&nbsp;: [[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>This time we want to get rid of the fractions. To do this we will multiply all the parts by a number. Find the Lowest Common Multiple of the denominators (if its difficult to find you can always multiply the three denominators and use that). Multiply all the fractions by this number. Simplify your answer ratio into its simplest form as above.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}", "minValue": "{ans31}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}", "minValue": "{ans32}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans33}", "minValue": "{ans33}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Solve the following ratio questions:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"boy": {"definition": "ans21*l", "templateType": "anything", "group": "Ungrouped variables", "name": "boy", "description": ""}, "number0": {"definition": "random(2,3,4,6)", "templateType": "anything", "group": "Ungrouped variables", "name": "number0", "description": ""}, "k": {"definition": "random(6..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "num11": {"definition": "ans11*k", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "l": {"definition": "random(3..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "ans31": {"definition": "(low/number0)*1", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans22": {"definition": "random(3,4,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans12": {"definition": "random([5,7,11,13])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans11": {"definition": "random([1,2,3,4])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "num12": {"definition": "ans12*k", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "low": {"definition": "lcm([number0,number1,number2])", "templateType": "anything", "group": "Ungrouped variables", "name": "low", "description": ""}, "student": {"definition": "random(4..7)*(boy+girl)", "templateType": "anything", "group": "Ungrouped variables", "name": "student", "description": ""}, "number1": {"definition": "random(8,9,11,12)", "templateType": "anything", "group": "Ungrouped variables", "name": "number1", "description": ""}, "number2": {"definition": "random(10,13,15,16)", "templateType": "anything", "group": "Ungrouped variables", "name": "number2", "description": ""}, "ans32": {"definition": "(low/number1)*5", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "ans33": {"definition": "(low/number2)*7", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33", "description": ""}, "ans23": {"definition": "(student/(boy+girl))*girl", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23", "description": ""}, "girl": {"definition": "ans22*l", "templateType": "anything", "group": "Ungrouped variables", "name": "girl", "description": ""}, "ans21": {"definition": "random([3,4,5] except {ans22})", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}}, "metadata": {"description": "<p>Simplifying ratios</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}