7 questions on numeric fractions.
", "licence": "Creative Commons Attribution 4.0 International"}, "timing": {"timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "shufflequestions": false, "questions": [], "percentpass": 0.0, "allQuestions": true, "pickQuestions": 0, "type": "exam", "feedback": {"showtotalmark": true, "advicethreshold": 0.0, "showanswerstate": true, "showactualmark": true, "allowrevealanswer": true}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Combining fractions", "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/"}], "tags": ["adding fractions", "combining fractions", "Fractions", "fractions", "lowest form of a fraction", "subtracting fractions"], "variables": {"a": {"definition": "random(1..11)", "group": "Ungrouped variables", "name": "a", "templateType": "anything", "description": ""}, "action1": {"definition": "switch(op=-1,'taking away',op=1,'adding')", "group": "Ungrouped variables", "name": "action1", "templateType": "anything", "description": ""}, "op": {"definition": "random(1,-1)", "group": "Ungrouped variables", "name": "op", "templateType": "anything", "description": "Operation to perform: 1 for add, -1 for subtract
"}, "f": {"definition": "switch(\n g=2,\n random(3..11#2),\n g=3,\n random(2,4,5,7,8,10,11),\n g=4,\n random(3,5,7,9,11),\n g=5, \n random(2,3,4,6,7,8,9,11),\n g=6,\n random(5,7,11),\n g=7,\n random(2,3,4,5,6,8,9,10,11),\n g=8,\n random(3,5,7,9,11),\n g=9,\n random(2,4,5,7,8,10,11),\n g=10,\n random(3,7,9),\n g=11,\n random(2..10),\n g=12,\n random(5,7,11)\n)", "group": "Ungrouped variables", "name": "f", "templateType": "anything", "description": ""}, "dosomething": {"definition": "switch(op=-1,'Take away',op=1,'Add')", "group": "Ungrouped variables", "name": "dosomething", "templateType": "anything", "description": "Operation to perform
"}, "action": {"definition": "switch(op=-1,'Taking away',op=1,'Adding')", "group": "Ungrouped variables", "name": "action", "templateType": "anything", "description": ""}, "g": {"definition": "switch(\n a=1, \n random(2..11),\n a=2,\n random(3..11#2),\n a=3,\n random(4,5,7,8,10,11),\n a=4,\n random(5,7,9,11),\n a=5, \n random(6,7,8,9,11),\n a=6,\n random(7,11),\n a=7,\n random(8,9,10,11),\n a=8,\n random(9,11),\n a=9,\n random(10,11),\n a=10,\n 11,\n a=11,\n 12\n)", "group": "Ungrouped variables", "name": "g", "templateType": "anything", "description": ""}, "b": {"definition": "switch(\n f=2,\n 1,\n f=3,\n random(1,2),\n f=4,\n random(1,3),\n f=5, \n random(1..4),\n f=6,\n random(1,5),\n f=7,\n random(1..6),\n f=8,\n random(1,3,5,7),\n f=9,\n random(1,2,4,5,7,8),\n f=10,\n random(1,3,7,9),\n f=11,\n random(1..10)\n)", "group": "Ungrouped variables", "name": "b", "templateType": "anything", "description": ""}}, "metadata": {"description": "Add/subtract fractions and reduce to lowest form.
", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "gaps": [{"showpreview": true, "notallowed": {"strings": ["+", ".", "(", ")", "1-", "2-", "3-", "4-", "5-", "6-", "7-", "8-", "9-"], "message": "You must write your answer in the form p/q for integers p and q
", "partialCredit": 0, "showStrings": false}, "checkvariablenames": false, "showFeedbackIcon": true, "checkingaccuracy": 0.0001, "expectedvariablenames": [], "answersimplification": "std", "musthave": {"strings": ["/"], "message": "You must write your answer in the form p/q for integers p and q.
", "partialCredit": 0, "showStrings": false}, "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// we just want two sets of brackets, each containing two terms\n// or one of the brackets might not have a constant term\n// or for repeated roots, you might write (x+a)^2\nvar rule = Numbas.jme.compile('m_any(m_number;a/m_number;b,-m_number;a/m_number;b)');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n this.setCredit(0,'Your answer is not in the form $\\\\frac{a}{b}$.');\n} else {\n var a = m.a.tok.value;\n var b = m.b.tok.value;\n if(Numbas.math.gcd(a,b)!=1) {\n this.setCredit(0,\"The fraction you gave has not been fully reduced.\");\n }\n}"}}, "checkingtype": "absdiff", "marks": 1, "vsetrangepoints": 5, "answer": "{a*f+op*b*g}/{g*f}", "type": "jme", "maxlength": {"message": "Your answer is too long.
", "length": 7, "partialCredit": 0}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacements": []}], "steps": [{"variableReplacementStrategy": "originalfirst", "type": "information", "showFeedbackIcon": true, "marks": 0, "showCorrectAnswer": true, "prompt": "The rule for {action1} fractions is \\[\\simplify{a/b+ {op}*(c/d)=(a*d+{op}*b*c)/(b*d)}.\\]
", "variableReplacements": [], "scripts": {}}], "type": "gapfill", "showFeedbackIcon": true, "stepsPenalty": 0.5, "marks": 0, "showCorrectAnswer": true, "prompt": "$\\displaystyle \\simplify[std]{{a} / {g} + ({op*b} / {f})} = $ [[0]]
\nNo decimal numbers allowed.
\nDo not include brackets in your answer.
\nYou can get help by clicking on Show steps.
", "variableReplacements": [], "scripts": {}}], "functions": {}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"]}, "ungrouped_variables": ["a", "b", "g", "dosomething", "f", "op", "action1", "action"], "advice": "The rule for {action1} fractions is \\[\\simplify{a/b+ {op}*(c/d)=(a*d+{op}*b*c)/(b*d)}.\\]
In this case we have:
\\[\\simplify[std,!unitFactor]{{a} / {g} + ({op*b} / {f}) = ({a} * {f} + {g} * {op*b}) / ({g} * {f}) ={a*f+op*g*b}/{g*f}}.\\]
Note that this fraction is in its lowest form as there are no common factors in the denominator and the numerator.
{dosomething} the following fractions and reduce the resulting fraction to lowest form.
", "type": "question"}, {"name": "Fractions: Lowest form", "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/"}], "functions": {"chcp": {"definition": "//This produces a number coprime to a in the range b to c. Usually choose d initally to be random in the range\n if(gcd(a,d)=1,d,chcp(a,b,c,random(b..c)))", "type": "number", "language": "jme", "parameters": [["a", "number"], ["b", "number"], ["c", "number"], ["d", "number"]]}}, "tags": ["Fractions", "cancellation", "cancelling", "common factor", "coprime", "denominator", "fractions", "lowest form of a fraction", "numerator"], "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 $\\var{c[3]}$.
", "rulesets": {"std": ["all", "fractionNumbers"], "noc": ["std", "!simplifyFractions"]}, "parts": [{"stepspenalty": 0.0, "prompt": "\n$\\displaystyle \\simplify[noc]{{d[0]}/{f[0]}}\\;=$[[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]]
\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 ", "gaps": [{"notallowed": {"message": "Input as a fraction in lowest form without brackets.
", "showstrings": false, "strings": ["(", "."], "partialcredit": 0.0}, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "musthave": {"message": "Input as a fraction.
", "showstrings": false, "strings": ["/"], "partialcredit": 0.0}, "maxlength": {"length": 4.0, "message": "Input as a fraction in lowest form by cancelling common factors in the denominator and numerator.
", "partialcredit": 0.0}, "answer": "{a[0]}/{b[0]}", "marks": 0.5, "checkvariablenames": false, "type": "jme", "answersimplification": "std"}, {"notallowed": {"message": "Input as a fraction in lowest form without brackets.
", "showstrings": false, "strings": ["(", "."], "partialcredit": 0.0}, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "musthave": {"message": "Input as a fraction.
", "showstrings": false, "strings": ["/"], "partialcredit": 0.0}, "maxlength": {"length": 3.0, "message": "Input as a fraction in lowest form by cancelling common factors in the denominator and numerator.
", "partialcredit": 0.0}, "answer": "{a[1]}/{b[1]}", "marks": 0.5, "checkvariablenames": false, "type": "jme", "answersimplification": "std"}, {"notallowed": {"message": "Input as a fraction in lowest form. Do not include brackets in your answer.
", "showstrings": false, "strings": ["(", "."], "partialcredit": 0.0}, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "musthave": {"message": "Input as a fraction.
", "showstrings": false, "strings": ["/"], "partialcredit": 0.0}, "maxlength": {"length": 4.0, "message": "Input as a fraction in lowest form by cancelling common factors in the denominator and numerator.
", "partialcredit": 0.0}, "answer": "{a[2]}/{b[2]}", "marks": 0.5, "checkvariablenames": false, "type": "jme", "answersimplification": "std"}, {"notallowed": {"message": "Input as a fraction in lowest form. Do not include brackets in your answer.
", "showstrings": false, "strings": ["(", "."], "partialcredit": 0.0}, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "showpreview": true, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "musthave": {"message": "Input as a fraction.
", "showstrings": false, "strings": ["/"], "partialcredit": 0.0}, "maxlength": {"length": 5.0, "message": "Input as a fraction in lowest form by cancelling common factors in the denominator and numerator.
", "partialcredit": 0.0}, "answer": "{a[3]}/{b[3]}", "marks": 1.5, "checkvariablenames": false, "type": "jme", "answersimplification": "std"}], "steps": [{"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 ", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "statement": "
Reduce the following fractions to their lowest form.
", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "[random(-9..-5),random(5..9),random(11..19),random(35..61)]", "name": "a"}, "c": {"definition": "[random(2..9),random(2..9),random(2..9),random(40..70)]", "name": "c"}, "b": {"definition": "map(chcp(a[x],2,9,random(2..9)),x,0..2)+chcp(a[3],40,80,random(40..80))", "name": "b"}, "d": {"definition": "map(c[x]*a[x],x,0..3)", "name": "d"}, "f": {"definition": "map(c[x]*b[x],x,0..3)", "name": "f"}}, "metadata": {"notes": "\n \t\t11/08/2012:
\n \t\tAdded tags.
\n \t\tAdded description.
\n \t\tFunction chcp(a,b,c,d) gives number coprime to a in the range b..c, d is usually random(b..c) for redundant reasons!
\n \t\tNote that the answer is constrained by max length as well as requiring / and no brackets.
\n \t\t", "description": "Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions.
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Numerical fractions 1", "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/"}], "functions": {}, "tags": ["Fractions", "fractions"], "advice": "No Advice.
", "rulesets": {}, "parts": [{"prompt": "\n$\\dfrac{\\var{a}}{\\var{p}}$
If expressed with denominator $\\var{k}$, the numerator is [[0]].
\n \n \n ", "gaps": [{"minvalue": "{m}", "type": "numberentry", "maxvalue": "{m}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"prompt": "\n$\\dfrac{\\var{s*t}}{\\var{t*k}}$
If expressed with denominator $\\var{k}$, the numerator is [[0]].
\n \n \n ", "gaps": [{"minvalue": "{s}", "type": "numberentry", "maxvalue": "{s}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"prompt": "\n$\\dfrac{\\var{b}}{\\var{2*p2}}$
If expressed with denominator $\\var{l}$, the numerator is [[0]].
\n \n \n ", "gaps": [{"minvalue": "{n}", "type": "numberentry", "maxvalue": "{n}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"prompt": "\n$\\dfrac{\\var{t2*s2}}{\\var{t2*l}}$
If expressed with denominator $\\var{l}$, the numerator is [[0]].
\n \n \n ", "gaps": [{"minvalue": "{s2}", "type": "numberentry", "maxvalue": "{s2}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "statement": "Express each the following fractions as a fraction with the given denominator. Write the numerator in the given box.
", "variable_groups": [], "progress": "testing", "type": "question", "variables": {"a": {"definition": "random(2..29)", "name": "a"}, "p2": {"definition": "random(5,7,11,13,17)", "name": "p2"}, "c": {"definition": "2*p2", "name": "c"}, "b": {"definition": "random(2..29 except a)", "name": "b"}, "s2": {"definition": "random(2..7 except s)", "name": "s2"}, "k": {"definition": "p*q", "name": "k"}, "m": {"definition": "a*q", "name": "m"}, "l": {"definition": "2*p2*q2", "name": "l"}, "n": {"definition": "b*q2", "name": "n"}, "q": {"definition": "random(5,7,11,13,17)", "name": "q"}, "p": {"definition": "random(5,7,11,13,17)", "name": "p"}, "s": {"definition": "random(2..7)", "name": "s"}, "q2": {"definition": "random(5,7,11,13,17)", "name": "q2"}, "t": {"definition": "random(2..11)", "name": "t"}, "t2": {"definition": "random(2..11 except t)", "name": "t2"}}, "metadata": {"notes": "", "description": "Questions testing understanding of numerators and denominators of numerical fractions.
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Numerical fractions 2", "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/"}], "functions": {}, "tags": ["Fractions", "Lowest terms", "fractions"], "advice": "No Advice.
", "rulesets": {}, "parts": [{"prompt": "\n$\\dfrac{\\var{j}}{\\var{k}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\n \n \n ", "gaps": [{"minvalue": "{f}", "type": "numberentry", "maxvalue": "{f}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{g}", "type": "numberentry", "maxvalue": "{g}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"prompt": "\n$\\dfrac{\\var{j2}}{\\var{k2}}$
In lowest terms, the numerator is [[0]], the denominator is [[1]]
\n \n \n ", "gaps": [{"minvalue": "{f2}", "type": "numberentry", "maxvalue": "{f2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{g2}", "type": "numberentry", "maxvalue": "{g2}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "statement": "Reduce the following fractions to lowest terms. Write the numerator and denominator of the lowest term fraction in the boxes provided.
", "variable_groups": [], "progress": "testing", "type": "question", "variables": {"a": {"definition": "random(2..50)", "name": "a"}, "f2": {"definition": "a2/d2", "name": "f2"}, "b": {"definition": "random(2..50 except a)", "name": "b"}, "d": {"definition": "gcd(a,b)", "name": "d"}, "g": {"definition": "b/d", "name": "g"}, "f": {"definition": "a/d", "name": "f"}, "h2": {"definition": "random(2..25)", "name": "h2"}, "h": {"definition": "random(2..25)", "name": "h"}, "k": {"definition": "g*h", "name": "k"}, "j": {"definition": "f*h", "name": "j"}, "j2": {"definition": "f2*h2", "name": "j2"}, "k2": {"definition": "g2*h2", "name": "k2"}, "a2": {"definition": "random(2..50)", "name": "a2"}, "b2": {"definition": "random(2..50 except a2)", "name": "b2"}, "d2": {"definition": "gcd(a2,b2)", "name": "d2"}, "g2": {"definition": "b2/d2", "name": "g2"}}, "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"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "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/"}], "functions": {}, "tags": ["Arithmetic", "Fractions", "Lowest terms", "arithmetic", "fractions"], "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 ", "rulesets": {}, "parts": [{"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 ", "gaps": [{"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}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"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 ", "gaps": [{"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}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"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 ", "gaps": [{"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}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"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 ", "gaps": [{"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}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "statement": "Evaluate the following as fractions in lowest terms. Write the numerator and denominator of the lowest term fraction in the boxes provided.
", "variable_groups": [], "progress": "testing", "type": "question", "variables": {"f1": {"definition": "gcd(a1*d1+b1*c1,b1*d1)", "name": "f1"}, "r1": {"definition": "random(1..11)", "name": "r1"}, "g1": {"definition": "gcd(a1*d1-b1*c1,b1*d1)", "name": "g1"}, "s1": {"definition": "random(2..13 except r1)", "name": "s1"}, "h1": {"definition": "gcd(a1*c1,b1*d1)", "name": "h1"}, "u1": {"definition": "random(1..11)", "name": "u1"}, "j1": {"definition": "gcd(a1*d1,b1*c1)", "name": "j1"}, "t1": {"definition": "gcd(r1,s1)", "name": "t1"}, "a1": {"definition": "r1/t1", "name": "a1"}, "v1": {"definition": "random(2..13 except [u1,s1,u11])", "name": "v1"}, "b1": {"definition": "s1/t1", "name": "b1"}, "w1": {"definition": "gcd(u1,v1)", "name": "w1"}, "u11": {"definition": "s1*u1/r1", "name": "u11"}, "c1": {"definition": "u1/w1", "name": "c1"}, "d1": {"definition": "v1/w1", "name": "d1"}}, "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"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "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/"}], "functions": {}, "tags": ["Fractions", "Lowest terms", "fractions"], "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 ", "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 ", "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}], "type": "gapfill", "marks": 0.0}, {"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 ", "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}], "type": "gapfill", "marks": 0.0}, {"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 ", "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}], "type": "gapfill", "marks": 0.0}, {"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 ", "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}], "type": "gapfill", "marks": 0.0}, {"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 ", "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": "gapfill", "marks": 0.0}], "statement": "Evaluate the following as fractions in lowest terms. Write the numerator and denominator of the lowest term fraction in the boxes provided.
", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"f2": {"definition": "y2/z2", "name": "f2"}, "h2": {"definition": "p2/q2", "name": "h2"}, "j2": {"definition": "gcd(a2*d2*f2-b2*c2*f2+b2*d2*e2,b2*d2*f2)", "name": "j2"}, "w2": {"definition": "gcd(u2,v2)", "name": "w2"}, "b2": {"definition": "s2/t2", "name": "b2"}, "y2": {"definition": "random(2..11 except [u2,s2,v2,x2,x21,x22])", "name": "y2"}, "d2": {"definition": "v2/w2", "name": "d2"}, "q2": {"definition": "gcd(o2,p2)", "name": "q2"}, "s2": {"definition": "random(2..11 except r2)", "name": "s2"}, "u2": {"definition": "random(1..9)", "name": "u2"}, "k2": {"definition": "gcd(a2*d2*f2-b2*c2*f2-b2*d2*e2,b2*d2*f2)", "name": "k2"}, "m2": {"definition": "gcd(a2*d2*f2*h2+b2*c2*f2*g2+b2*d2*e2*h2,b2*d2*f2*h2)", "name": "m2"}, "x21": {"definition": "s2*v2*x2/(r2*v2-s2*u2)", "name": "x21"}, "o2": {"definition": "random(1..9)", "name": "o2"}, "x22": {"definition": "-x21", "name": "x22"}, "g2": {"definition": "o2/q2", "name": "g2"}, "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"}, "a2": {"definition": "r2/t2", "name": "a2"}, "x2": {"definition": "random(1..9)", "name": "x2"}, "c2": {"definition": "u2/w2", "name": "c2"}, "z2": {"definition": "gcd(x2,y2)", "name": "z2"}, "e2": {"definition": "x2/z2", "name": "e2"}, "p2": {"definition": "random(2..11 except o2)", "name": "p2"}, "r2": {"definition": "random(1..9)", "name": "r2"}, "t2": {"definition": "gcd(r2,s2)", "name": "t2"}, "l2": {"definition": "gcd(a2*d2*f2+b2*c2*e2,b2*d2*f2)", "name": "l2"}, "u21": {"definition": "s2*u2/r2", "name": "u21"}}, "metadata": {"notes": "", "description": "Questions testing addition, subtraction, multiplication of numerical fractions and reduction to lowest terms. They also test BIDMAS in the context of fractions.
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "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/"}], "functions": {}, "tags": ["fractions", "lowest form", "simplifying fractions"], "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.
\\[\\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 ", "gaps": [{"musthave": {"message": "You must write your answer in the form p/q for integers p and q
", "showstrings": false, "strings": ["/"], "partialcredit": 0.0}, "checkingaccuracy": 0.0001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 1.0, "answer": "{g*f}/{a*f+s1*b*g}", "type": "jme", "notallowed": {"message": "You must write your answer in the form p/q for integers p and q
", "showstrings": false, "strings": ["+", ".", "(", ")", "1-", "2-", "3-", "4-", "5-", "6-", "7-", "8-", "9-"], "partialcredit": 0.0}, "maxlength": {"length": 7.0, "message": "answer too long
", "partialcredit": 0.0}}], "type": "gapfill", "marks": 0.0}], "statement": "Write the following expression as a single fraction in its lowest form:
", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(1..11)", "name": "a"}, "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))", "name": "b"}, "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)", "name": "g"}, "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))", "name": "f"}, "s1": {"definition": "if(a*f+s*b*g=1,-s,s)", "name": "s1"}, "s": {"definition": "random(1,-1)", "name": "s"}}, "metadata": {"notes": "\n \t\t5/08/2012:
\n \t\tAdded description.
\n \t\t", "description": "Find $\\displaystyle \\frac{a} {b + \\frac{c}{d}}$ as a single fraction in the form $\\displaystyle \\frac{p}{q}$ for integers $p$ and $q$.
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "extensions": ["stats"], "custom_part_types": [], "resources": []}