// Numbas version: finer_feedback_settings
{"name": "Fractions: Lowest form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"chcp": {"definition": "if(gcd(a,d)=1,d,chcp(a,b,c,random(b..c)))", "type": "number", "parameters": [["a", "number"], ["b", "number"], ["c", "number"], ["d", "number"]], "language": "jme"}}, "variables": {"c": {"templateType": "anything", "name": "c", "definition": "[random(2..9),random(2..9),random(2..9),random(40..70)]", "group": "Ungrouped variables", "description": ""}, "d": {"templateType": "anything", "name": "d", "definition": "map(c[x]*a[x],x,0..3)", "group": "Ungrouped variables", "description": ""}, "a": {"templateType": "anything", "name": "a", "definition": "[random(-9..-5),random(5..9),random(11..19),random(35..61)]", "group": "Ungrouped variables", "description": ""}, "f": {"templateType": "anything", "name": "f", "definition": "map(c[x]*b[x],x,0..3)", "group": "Ungrouped variables", "description": ""}, "b": {"templateType": "anything", "name": "b", "definition": "map(chcp(a[x],2,9,random(2..9)),x,0..2)+chcp(a[3],40,80,random(40..80))", "group": "Ungrouped variables", "description": ""}}, "question_groups": [{"name": "", "questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0}], "rulesets": {"noc": ["std", "!simplifyFractions"], "std": ["all", "fractionNumbers"]}, "ungrouped_variables": ["a", "c", "b", "d", "f"], "advice": "<p>We have:</p>\n  <p>$\\displaystyle \\simplify[noc]{{d[0]}/{f[0]}}=\\simplify[]{({a[0]}*{c[0]})/({b[0]}*{c[0]})}=\\simplify[all]{{a[0]}/{b[0]}}$. Common factor $\\var{c[0]}$.</p>\n  <p>$\\displaystyle \\simplify[noc]{{d[1]}/{f[1]}}=\\simplify[]{({a[1]}*{c[1]})/({b[1]}*{c[1]})}=\\simplify[all]{{a[1]}/{b[1]}}$. Common factor $\\var{c[1]}$.</p>\n  <p>$\\displaystyle \\simplify[noc]{{d[2]}/{f[2]}}=\\simplify[]{({a[2]}*{c[2]})/({b[2]}*{c[2]})}=\\simplify[all]{{a[2]}/{b[2]}}$. Common factor $\\var{c[2]}$.</p>\n  <p>$\\displaystyle \\simplify[noc]{{d[3]}/{f[3]}}=\\simplify[]{({a[3]}*{c[3]})/({b[3]}*{c[3]})}=\\simplify[all]{{a[3]}/{b[3]}}$. Common factor $\\var{c[3]}$.</p>", "type": "question", "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": ["Fractions", "SFY0001", "cancellation", "cancelling", "cancelling ", "checked2015", "common factor", "denominator", "lowest form", "numerator"], "name": "Fractions: Lowest form", "variable_groups": [], "statement": "<p>Reduce the following fractions to their lowest form.</p>", "showQuestionGroupNames": false, "preamble": {"css": "", "js": ""}, "metadata": {"notes": "<p><strong>11/08/2012:</strong></p>\n                    <p>Added tags.</p>\n                    <p>Added description.</p>\n                    <p>Function chcp(a,b,c,d) gives number coprime to a in the range b..c, d is usually random(b..c) for redundant reasons!</p>\n                    <p>Note that the answer is constrained by max length as well as requiring / and no brackets.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions.&nbsp;</p>"}, "parts": [{"showCorrectAnswer": true, "scripts": {}, "stepsPenalty": 0, "prompt": "<p>$\\displaystyle \\simplify[noc]{{d[0]}/{f[0]}}\\;=$[[0]],$\\;\\;\\displaystyle \\simplify[noc]{{d[1]}/{f[1]}}\\;=$[[1]],$\\;\\;\\displaystyle \\simplify[noc]{{d[2]}/{f[2]}}\\;=$[[2]],$\\;\\;\\displaystyle \\simplify[noc]{{d[3]}/{f[3]}}\\;=$[[3]]</p>\n      <p>Input as fractions and do not include brackets in your answer.</p>\n      <p>You can click on Show steps for help. You will not lose any marks if you do.</p>", "type": "gapfill", "marks": 0, "gaps": [{"scripts": {}, "checkingaccuracy": 0.001, "musthave": {"strings": ["/"], "message": "<p>Input as a fraction.</p>", "partialCredit": 0, "showStrings": false}, "vsetrange": [0, 1], "marks": 0.5, "type": "jme", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "maxlength": {"length": 4, "message": "<p>Input as a fraction in lowest form by cancelling common factors in the denominator and numerator.</p>", "partialCredit": 0}, "answer": "{a[0]}/{b[0]}", "showpreview": true, "vsetrangepoints": 5, "notallowed": {"strings": ["(", "."], "message": "<p>Input as a fraction in lowest form without brackets.</p>", "partialCredit": 0, "showStrings": false}, "answersimplification": "std", "expectedvariablenames": []}, {"scripts": {}, "checkingaccuracy": 0.001, "musthave": {"strings": ["/"], "message": "<p>Input as a fraction.</p>", "partialCredit": 0, "showStrings": false}, "vsetrange": [0, 1], "marks": 0.5, "type": "jme", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "maxlength": {"length": 3, "message": "<p>Input as a fraction in lowest form by cancelling common factors in the denominator and numerator.</p>", "partialCredit": 0}, "answer": "{a[1]}/{b[1]}", "showpreview": true, "vsetrangepoints": 5, "notallowed": {"strings": ["(", "."], "message": "<p>Input as a fraction in lowest form without brackets.</p>", "partialCredit": 0, "showStrings": false}, "answersimplification": "std", "expectedvariablenames": []}, {"scripts": {}, "checkingaccuracy": 0.001, "musthave": {"strings": ["/"], "message": "<p>Input as a fraction.</p>", "partialCredit": 0, "showStrings": false}, "vsetrange": [0, 1], "marks": 0.5, "type": "jme", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "maxlength": {"length": 4, "message": "<p>Input as a fraction in lowest form by cancelling common factors in the denominator and numerator.</p>", "partialCredit": 0}, "answer": "{a[2]}/{b[2]}", "showpreview": true, "vsetrangepoints": 5, "notallowed": {"strings": ["(", "."], "message": "<p>Input as a fraction in lowest form. Do not include brackets in your answer.</p>", "partialCredit": 0, "showStrings": false}, "answersimplification": "std", "expectedvariablenames": []}, {"scripts": {}, "checkingaccuracy": 0.001, "musthave": {"strings": ["/"], "message": "<p>Input as a fraction.</p>", "partialCredit": 0, "showStrings": false}, "vsetrange": [0, 1], "marks": 1.5, "type": "jme", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "maxlength": {"length": 5, "message": "<p>Input as a fraction in lowest form by cancelling common factors in the denominator and numerator.</p>", "partialCredit": 0}, "answer": "{a[3]}/{b[3]}", "showpreview": true, "vsetrangepoints": 5, "notallowed": {"strings": ["(", "."], "message": "<p>Input as a fraction in lowest form. Do not include brackets in your answer.</p>", "partialCredit": 0, "showStrings": false}, "answersimplification": "std", "expectedvariablenames": []}], "steps": [{"showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information", "prompt": "<p>Given a fraction $\\displaystyle \\frac{a}{b}$ then it is in lowest form if $a$ and $b$ have no common factors.&nbsp;</p>\n          <p>If $c$ was a common factor then we could cancel the $c$ and we have converted the fraction into a fraction with smaller numbers.</p>\n          <p>For example the fraction $\\displaystyle \\frac{18}{24}=\\frac{9 \\times 2}{12 \\times 2} = \\frac{9}{12}$ as we can cancel the common factor $2$.</p>\n          <p>But we are not yet finished as $\\displaystyle \\frac{9}{12}=\\frac{3 \\times 3}{4 \\times 3} = \\frac{3}{4}$ on cancelling the common factor $3$. We cannot go any further as $3$ and $4$ have no common factors (other than $1$, which is never considered as a factor).</p>\n          <p>Of &nbsp;course we could have spotted that $6$ was a common factor &nbsp;as $\\displaystyle \\frac{18}{24}=\\frac{3 \\times 6}{4 \\times 6}=\\frac{3}{4}$ , but it is perfectly OK to do it in stages as we did above. Just make sure that your final fraction does not have common factors.</p>\n          <p>&nbsp;</p>"}]}], "contributors": [{"name": "Owen Jepps", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1195/"}]}]}], "contributors": [{"name": "Owen Jepps", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1195/"}]}