7 questions on numeric fractions.
", "licence": "Creative Commons Attribution 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], []], "questions": [{"name": "Br\u00fcche zusammenfassen", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Helge M\u00fcnnich", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1885/"}], "tags": [], "metadata": {"description": "Addiere/Subtrahiere Brüche und kürze vollständig.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Die Regel für das {action1} von Brüchen ist \\[\\simplify{a/b+ {op}*(c/d)=(a*d+{op}*b*c)/(b*d)}.\\]
In diesem Fall haben wir:
\\[\\simplify[std,!unitFactor]{{a} / {g} + ({op*b} / {f}) = ({a} {f} + {g} * {op*b}) / ({g} * {f}) = {a*f+op*g*b}/{g*f}}.\\]
Beachte, dass dieser Bruch vollständig gekürzt ist, wenn Zähler und Nenner keine gemeinsame Teiler haben.
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", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "g", "dosomething", "f", "op", "action1", "action"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "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": "$\\displaystyle \\simplify[std]{{a} / {g} + ({op*b} / {f})} = $ [[0]]
\nAntwort ohne Dezimalzahlen und ohne Klammern.
\n", "stepsPenalty": 0.5, "steps": [{"type": "information", "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": "Die Regel für {action1} von Brüchen ist \\[\\simplify{a/b+ {op}*(c/d)=(a*d+{op}*b*c)/(b*d)}.\\]
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Reduce the following fractions to their lowest form.
", "advice": "We have:
\n$\\displaystyle \\simplify[noc]{{d[0]}/{f[0]}}=\\simplify[]{({a[0]}*{c[0]})/({b[0]}*{c[0]})}=\\simplify[all]{{a[0]}/{b[0]}}$. Common factor $\\var{c[0]}$.
\n$\\displaystyle \\simplify[noc]{{d[1]}/{f[1]}}=\\simplify[]{({a[1]}*{c[1]})/({b[1]}*{c[1]})}=\\simplify[all]{{a[1]}/{b[1]}}$. Common factor $\\var{c[1]}$.
\n$\\displaystyle \\simplify[noc]{{d[2]}/{f[2]}}=\\simplify[]{({a[2]}*{c[2]})/({b[2]}*{c[2]})}=\\simplify[std]{{a[2]}/{b[2]}}$. Common factor $\\var{c[2]}$.
\n$\\displaystyle \\simplify[noc]{{d[3]}/{f[3]}}=\\simplify[]{({a[3]}*{c[3]})/({b[3]}*{c[3]})}=\\simplify[std]{{a[3]}/{b[3]}}$. Common factor $\\var{c[3]}$.
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\nInput as fractions and do not include brackets in your answer.
\nYou can click on Show steps for help. You will not lose any marks if you do.
\n ", "stepsPenalty": 0, "steps": [{"type": "information", "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": "\nGiven a fraction $\\displaystyle \\frac{a}{b}$ then it is in lowest form if $a$ and $b$ have no common factors.
\nIf $c$ was a common factor then we could cancel the $c$ and we have converted the fraction into a fraction with smaller numbers.
\nFor example the fraction $\\displaystyle \\frac{18}{24}=\\frac{9 \\times 2}{12 \\times 2} = \\frac{9}{12}$ as we can cancel the common factor $2$.
\nBut 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).
\nOf course we could have spotted that $6$ was a common factor 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.
\n\n "}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 0.5, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a[0]}/{b[0]}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "maxlength": {"length": 4, "partialCredit": 0, "message": "
Input as a fraction in lowest form by cancelling common factors in the denominator and numerator.
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", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Questions testing understanding of numerators and denominators of numerical fractions.
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", "rulesets": {}, "parts": [{"prompt": "\n$\\dfrac{\\var{a}}{\\var{p}}$
If expressed with denominator $\\var{k}$, the numerator is [[0]].
\n \n \n ", "type": "gapfill", "marks": 0.0, "gaps": [{"minvalue": "{m}", "type": "numberentry", "maxvalue": "{m}", "marks": 1.0, "showPrecisionHint": false}]}, {"prompt": "\n$\\dfrac{\\var{s*t}}{\\var{t*k}}$
If expressed with denominator $\\var{k}$, the numerator is [[0]].
\n \n \n ", "type": "gapfill", "marks": 0.0, "gaps": [{"minvalue": "{s}", "type": "numberentry", "maxvalue": "{s}", "marks": 1.0, "showPrecisionHint": false}]}, {"prompt": "\n$\\dfrac{\\var{b}}{\\var{2*p2}}$
If expressed with denominator $\\var{l}$, the numerator is [[0]].
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If expressed with denominator $\\var{l}$, the numerator is [[0]].
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", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Questions testing understanding of numerators and denominators of numerical fractions, and reduction to lowest terms.
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", "rulesets": {}, "parts": [{"prompt": "\n$\\dfrac{\\var{j}}{\\var{k}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\n \n \n ", "type": "gapfill", "marks": 0.0, "gaps": [{"minvalue": "{f}", "type": "numberentry", "maxvalue": "{f}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{g}", "type": "numberentry", "maxvalue": "{g}", "marks": 1.0, "showPrecisionHint": false}]}, {"prompt": "\n$\\dfrac{\\var{j2}}{\\var{k2}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\n \n \n ", "type": "gapfill", "marks": 0.0, "gaps": [{"minvalue": "{f2}", "type": "numberentry", "maxvalue": "{f2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{g2}", "type": "numberentry", "maxvalue": "{g2}", "marks": 1.0, "showPrecisionHint": false}]}], "type": "question", "variable_groups": [], "question_groups": [{"pickQuestions": 0, "questions": [], "pickingStrategy": "all-ordered", "name": ""}], "showQuestionGroupNames": false}, {"name": "Helge's copy of Numerical fractions 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Helge M\u00fcnnich", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1885/"}], "variables": {"c1": {"name": "c1", "definition": "u1/w1"}, "b1": {"name": "b1", "definition": "s1/t1"}, "g1": {"name": "g1", "definition": "gcd(a1*d1-b1*c1,b1*d1)"}, "a1": {"name": "a1", "definition": "r1/t1"}, "h1": {"name": "h1", "definition": "gcd(a1*c1,b1*d1)"}, "v1": {"name": "v1", "definition": "random(2..13 except [u1,s1,u11])"}, "u11": {"name": "u11", "definition": "s1*u1/r1"}, "r1": {"name": "r1", "definition": "random(1..11)"}, "j1": {"name": "j1", "definition": "gcd(a1*d1,b1*c1)"}, "u1": {"name": "u1", "definition": "random(1..11)"}, "w1": {"name": "w1", "definition": "gcd(u1,v1)"}, "s1": {"name": "s1", "definition": "random(2..13 except r1)"}, "t1": {"name": "t1", "definition": "gcd(r1,s1)"}, "f1": {"name": "f1", "definition": "gcd(a1*d1+b1*c1,b1*d1)"}, "d1": {"name": "d1", "definition": "v1/w1"}}, "showQuestionGroupNames": false, "advice": "\nFor addition and subtraction, write fractions so that they have a common denominator and then perform addition or subtraction on the numerators. One method of doing this is 'cross-multiplication'. The rules are :
\n\\[\\simplify{a/b+ c/d=(a*d+b*c)/(b*d)}.\\]
\\[\\simplify{a/b- c/d=(a*d-b*c)/(b*d)}.\\]
For multiplication and division the rules are simpler:
\n\\[\\simplify{(a/b)} * \\simplify{(c/d)=(a*c)/(b*d)}.\\]
\\[\\simplify{(a/b)} / \\simplify{(c/d)}=\\simplify{(a*d)/(b*c)}.\\]
Having applied these rules, it will be necessary to reduce the resulting fractions to lowest terms.
\n ", "tags": ["Arithmetic", "Fractions", "Lowest terms", "arithmetic", "fractions"], "rulesets": {}, "variable_groups": [], "progress": "testing", "type": "question", "statement": "Evaluate the following as fractions in lowest terms. Write the numerator and denominator of the lowest term fraction in the boxes provided.
", "functions": {}, "parts": [{"marks": 0.0, "gaps": [{"marks": 1.0, "showPrecisionHint": false, "minvalue": "{(a1*d1+b1*c1)/f1}", "type": "numberentry", "maxvalue": "{(a1*d1+b1*c1)/f1}"}, {"marks": 1.0, "showPrecisionHint": false, "minvalue": "{b1*d1/f1}", "type": "numberentry", "maxvalue": "{b1*d1/f1}"}], "type": "gapfill", "prompt": "\n$\\dfrac{\\var{a1}}{\\var{b1}} + \\dfrac{\\var{c1}}{\\var{d1}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\n \n \n "}, {"marks": 0.0, "gaps": [{"marks": 1.0, "showPrecisionHint": false, "minvalue": "{(a1*d1-b1*c1)/g1}", "type": "numberentry", "maxvalue": "{(a1*d1-b1*c1)/g1}"}, {"marks": 1.0, "showPrecisionHint": false, "minvalue": "{b1*d1/g1}", "type": "numberentry", "maxvalue": "{b1*d1/g1}"}], "type": "gapfill", "prompt": "\n$\\dfrac{\\var{a1}}{\\var{b1}} - \\dfrac{\\var{c1}}{\\var{d1}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\t\t \n \n "}, {"marks": 0.0, "gaps": [{"marks": 1.0, "showPrecisionHint": false, "minvalue": "{a1*c1/h1}", "type": "numberentry", "maxvalue": "{a1*c1/h1}"}, {"marks": 1.0, "showPrecisionHint": false, "minvalue": "{b1*d1/h1}", "type": "numberentry", "maxvalue": "{b1*d1/h1}"}], "type": "gapfill", "prompt": "\n$\\dfrac{\\var{a1}}{\\var{b1}} \\times \\dfrac{\\var{c1}}{\\var{d1}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\t\t \n \n "}, {"marks": 0.0, "gaps": [{"marks": 1.0, "showPrecisionHint": false, "minvalue": "{a1*d1/j1}", "type": "numberentry", "maxvalue": "{a1*d1/j1}"}, {"marks": 1.0, "showPrecisionHint": false, "minvalue": "{b1*c1/j1}", "type": "numberentry", "maxvalue": "{b1*c1/j1}"}], "type": "gapfill", "prompt": "\n$\\dfrac{\\var{a1}}{\\var{b1}} \\div \\dfrac{\\var{c1}}{\\var{d1}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\t\t \n \n "}], "metadata": {"notes": "", "description": "Questions testing understanding of numerators and denominators of numerical fractions, and reduction to lowest terms.
", "licence": "Creative Commons Attribution 4.0 International"}, "question_groups": [{"name": "", "pickQuestions": 0, "questions": [], "pickingStrategy": "all-ordered"}]}, {"name": "Helge's copy of Numerical fractions 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Helge M\u00fcnnich", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1885/"}], "tags": ["Fractions", "Lowest terms", "fractions"], "functions": {}, "advice": "\nPerform the various operations required in the order dictated by BIDMAS.
\nFor addition and subtraction, write fractions so that they have a common denominator and then perform addition or subtraction on the numerators. One method of doing this is 'cross-multiplication'. The rules are :
\n\\[\\simplify{a/b+ c/d=(a*d+b*c)/(b*d)}.\\]
\\[\\simplify{a/b- c/d=(a*d-b*c)/(b*d)}.\\]
For multiplication and division the rules are simpler:
\n\\[\\simplify{(a/b)} * \\simplify{(c/d)=(a*c)/(b*d)}.\\]
\\[\\simplify{(a/b)} / \\simplify{(c/d)}=\\simplify{(a*d)/(b*c)}.\\]
Having applied these rules, it will be necessary to reduce the resulting fractions to lowest terms.
\n ", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Questions testing addition, subtraction, multiplication of numerical fractions and reduction to lowest terms. They also test BIDMAS in the context of fractions.
", "notes": ""}, "variables": {"d2": {"definition": "v2/w2", "name": "d2"}, "k2": {"definition": "gcd(a2*d2*f2-b2*c2*f2-b2*d2*e2,b2*d2*f2)", "name": "k2"}, "u2": {"definition": "random(1..9)", "name": "u2"}, "f2": {"definition": "y2/z2", "name": "f2"}, "s2": {"definition": "random(2..11 except r2)", "name": "s2"}, "o2": {"definition": "random(1..9)", "name": "o2"}, "g2": {"definition": "o2/q2", "name": "g2"}, "x2": {"definition": "random(1..9)", "name": "x2"}, "y2": {"definition": "random(2..11 except [u2,s2,v2,x2,x21,x22])", "name": "y2"}, "x22": {"definition": "-x21", "name": "x22"}, "j2": {"definition": "gcd(a2*d2*f2-b2*c2*f2+b2*d2*e2,b2*d2*f2)", "name": "j2"}, "t2": {"definition": "gcd(r2,s2)", "name": "t2"}, "b2": {"definition": "s2/t2", "name": "b2"}, "i2": {"definition": "gcd(a2*d2*f2+b2*c2*f2+b2*d2*e2,b2*d2*f2)", "name": "i2"}, "v2": {"definition": "random(2..11 except [u2,s2,u21])", "name": "v2"}, "l2": {"definition": "gcd(a2*d2*f2+b2*c2*e2,b2*d2*f2)", "name": "l2"}, "p2": {"definition": "random(2..11 except o2)", "name": "p2"}, "h2": {"definition": "p2/q2", "name": "h2"}, "m2": {"definition": "gcd(a2*d2*f2*h2+b2*c2*f2*g2+b2*d2*e2*h2,b2*d2*f2*h2)", "name": "m2"}, "w2": {"definition": "gcd(u2,v2)", "name": "w2"}, "x21": {"definition": "s2*v2*x2/(r2*v2-s2*u2)", "name": "x21"}, "a2": {"definition": "r2/t2", "name": "a2"}, "z2": {"definition": "gcd(x2,y2)", "name": "z2"}, "q2": {"definition": "gcd(o2,p2)", "name": "q2"}, "e2": {"definition": "x2/z2", "name": "e2"}, "u21": {"definition": "s2*u2/r2", "name": "u21"}, "c2": {"definition": "u2/w2", "name": "c2"}, "r2": {"definition": "random(1..9)", "name": "r2"}}, "progress": "ready", "statement": "Evaluate the following as fractions in lowest terms. Write the numerator and denominator of the lowest term fraction in the boxes provided.
", "rulesets": {}, "parts": [{"prompt": "\n$\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} + \\dfrac{\\var{e2}}{\\var{f2}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\n \n \n ", "type": "gapfill", "marks": 0.0, "gaps": [{"minvalue": "{(a2*d2*f2+b2*c2*f2+b2*d2*e2)/i2}", "type": "numberentry", "maxvalue": "{(a2*d2*f2+b2*c2*f2+b2*d2*e2)/i2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{(b2*d2*f2)/i2}", "type": "numberentry", "maxvalue": "{(b2*d2*f2)/i2}", "marks": 1.0, "showPrecisionHint": false}]}, {"prompt": "\n$\\dfrac{\\var{a2}}{\\var{b2}} - \\dfrac{\\var{c2}}{\\var{d2}} + \\dfrac{\\var{e2}}{\\var{f2}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\n \n \n ", "type": "gapfill", "marks": 0.0, "gaps": [{"minvalue": "{(a2*d2*f2-b2*c2*f2+b2*d2*e2)/j2}", "type": "numberentry", "maxvalue": "{(a2*d2*f2-b2*c2*f2+b2*d2*e2)/j2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{(b2*d2*f2)/j2}", "type": "numberentry", "maxvalue": "{(b2*d2*f2)/j2}", "marks": 1.0, "showPrecisionHint": false}]}, {"prompt": "\n$\\dfrac{\\var{a2}}{\\var{b2}} - \\dfrac{\\var{c2}}{\\var{d2}} - \\dfrac{\\var{e2}}{\\var{f2}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\n \n \n ", "type": "gapfill", "marks": 0.0, "gaps": [{"minvalue": "{(a2*d2*f2-b2*c2*f2-b2*d2*e2)/k2}", "type": "numberentry", "maxvalue": "{(a2*d2*f2-b2*c2*f2-b2*d2*e2)/k2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{(b2*d2*f2)/k2}", "type": "numberentry", "maxvalue": "{(b2*d2*f2)/k2}", "marks": 1.0, "showPrecisionHint": false}]}, {"prompt": "\n$\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} \\times \\dfrac{\\var{e2}}{\\var{f2}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\n \n \n ", "type": "gapfill", "marks": 0.0, "gaps": [{"minvalue": "{(a2*d2*f2+b2*c2*e2)/l2}", "type": "numberentry", "maxvalue": "{(a2*d2*f2+b2*c2*e2)/l2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{(b2*d2*f2)/l2}", "type": "numberentry", "maxvalue": "{(b2*d2*f2)/l2}", "marks": 1.0, "showPrecisionHint": false}]}, {"prompt": "\n$\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} \\times \\dfrac{\\var{g2}}{\\var{h2}}+\\dfrac{\\var{e2}}{\\var{f2}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\n \n \n ", "type": "gapfill", "marks": 0.0, "gaps": [{"minvalue": "{(a2*d2*f2*h2+b2*c2*f2*g2+b2*d2*e2*h2)/m2}", "type": "numberentry", "maxvalue": "{(a2*d2*f2*h2+b2*c2*f2*g2+b2*d2*e2*h2)/m2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{(b2*d2*f2*h2)/m2}", "type": "numberentry", "maxvalue": "{(b2*d2*f2*h2)/m2}", "marks": 1.0, "showPrecisionHint": false}]}], "type": "question", "variable_groups": [], "question_groups": [{"pickQuestions": 0, "questions": [], "pickingStrategy": "all-ordered", "name": ""}], "showQuestionGroupNames": false}, {"name": "Helge's copy of Simplifying fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Helge M\u00fcnnich", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1885/"}], "parts": [{"type": "gapfill", "prompt": "\n\\[\\simplify{{g} / ({a} + {s1} * ({b * g} / {f}))}\\]
Input your answer here: [[0]]
Your answer must be of the form a/b for suitable integers a and b. No decimal numbers allowed.
\nDo not include brackets in your answer.
\n ", "marks": 0.0, "gaps": [{"maxlength": {"length": 7.0, "message": "answer too long
", "partialcredit": 0.0}, "answersimplification": "std", "answer": "{g*f}/{a*f+s1*b*g}", "marks": 1.0, "musthave": {"message": "You must write your answer in the form p/q for integers p and q
", "showstrings": false, "partialcredit": 0.0, "strings": ["/"]}, "vsetrange": [0.0, 1.0], "notallowed": {"message": "You must write your answer in the form p/q for integers p and q
", "showstrings": false, "partialcredit": 0.0, "strings": ["+", ".", "(", ")", "1-", "2-", "3-", "4-", "5-", "6-", "7-", "8-", "9-"]}, "vsetrangepoints": 5.0, "type": "jme", "checkingtype": "absdiff", "checkingaccuracy": 0.0001}]}], "functions": {}, "statement": "Write the following expression as a single fraction in its lowest form:
", "variable_groups": [], "showQuestionGroupNames": false, "progress": "ready", "type": "question", "advice": "We have:
\\[\\simplify[std]{{g} / ({a} + {s1} * ({b * g} / {f})) = {g} / (({a} * {f} + {s1} * {b * g}) / {f}) ={g} / (({a * f + s1 * b * g}) / {f})= ({f}*{g}) / ({a * f + s1 * b * g}) = ({g * f} / {(a * f + s1 * b * g)})}\\]
Here we use the result that dividing by a fraction $\\frac{a}{b}$ is the same as multiplying by $\\frac{b}{a}$.
The resulting fraction is in lowest form i.e. the top and bottom do not have a common factor.
Find $\\displaystyle \\frac{a} {b + \\frac{c}{d}}$ as a single fraction in the form $\\displaystyle \\frac{p}{q}$ for integers $p$ and $q$.
", "notes": "\n \t\t5/08/2012:
\n \t\tAdded description.
\n \t\t", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"s": {"name": "s", "definition": "random(1,-1)"}, "g": {"name": "g", "definition": "switch(a=1, random(2..11),a=2,random(3..11#2),a=3,random(4,5,7,8,10,11),a=4,random(5,7,9,11),a=5, random(6,7,8,9,11),a=6,random(7,11),a=7,random(8,9,10,11),a=8,random(9,11),a=9,random(10,11),a=10,11,a=11,12)"}, "b": {"name": "b", "definition": "switch(f=2,1,f=3,random(1,2),f=4,random(1,3),f=5, random(1..4),f=6,random(1,5),f=7,random(1..6),f=8,random(1,3,5,7),f=9,random(1,2,4,5,7,8),f=10,random(1,3,7,9),f=11,random(1..10))"}, "s1": {"name": "s1", "definition": "if(a*f+s*b*g=1,-s,s)"}, "f": {"name": "f", "definition": "switch(g=2,random(3..11#2),g=3,random(2,4,5,7,8,10,11),g=4,random(3,5,7,9,11),g=5, random(2,3,4,6,7,8,9,11),g=6,random(5,7,11),g=7,random(2,3,4,5,6,8,9,10,11),g=8,random(3,5,7,9,11),g=9,random(2,4,5,7,8,10,11),g=10,random(3,7,9),g=11,random(2..10),g=12,random(5,7,11))"}, "a": {"name": "a", "definition": "random(1..11)"}}}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": false, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "inreview"}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "type": "exam", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Helge M\u00fcnnich", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1885/"}], "extensions": ["stats"], "custom_part_types": [], "resources": []}