Well done
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", "action": "warn"}, "timedwarning": {"message": "You are half way through your 10 minutes.
", "action": "warn"}}, "metadata": {"licence": "None specified", "description": ""}, "duration": 600, "question_groups": [{"pickingStrategy": "all-ordered", "name": "Group", "pickQuestions": 1, "questions": [{"name": "Addition and subtraction of fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}], "type": "question", "statement": "Evaluate the following additions and subtractions, giving each fraction in its simplest form.
", "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"d_coprime": {"description": "", "name": "d_coprime", "group": "Part a", "templateType": "anything", "definition": "d/gcd_cd"}, "hlcm2_j": {"description": "PART B
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", "name": "a", "group": "Part a", "templateType": "anything", "definition": "random(1..5)"}, "d": {"description": "PART A variable d - random number between 5 and 15.
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", "name": "a_coprimed_coprime", "group": "Part a", "templateType": "anything", "definition": "a_coprime*d_coprime"}, "o": {"description": "", "name": "o", "group": "Part c", "templateType": "anything", "definition": "random(5..15 except m except n except 7 except 11 except 13)"}, "lcm_d": {"description": "PART A lcm of b and d, divided by d
", "name": "lcm_d", "group": "Part a", "templateType": "anything", "definition": "lcm/d_coprime"}, "gcd2": {"description": "PART B
", "name": "gcd2", "group": "Part b", "templateType": "anything", "definition": "gcd(num2unsim,lcm2)"}, "c": {"description": "PART A variable c - random number between 1 and 5.
", "name": "c", "group": "Part a", "templateType": "anything", "definition": "random(1..5)"}, "m": {"description": "", "name": "m", "group": "Part c", "templateType": "anything", "definition": "random(5..12 except 7 except 11)"}, "clcm_d": {"description": "PART A variable c times the lcm of b and d, divided by d
", "name": "clcm_d", "group": "Part a", "templateType": "anything", "definition": "c_coprime*lcm_d"}, "h_coprime": {"description": "PART B
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", "name": "twolcm2", "group": "Part b", "templateType": "anything", "definition": "2*lcm2"}, "lcm2_j": {"description": "PART B
", "name": "lcm2_j", "group": "Part b", "templateType": "anything", "definition": "lcm2/j_coprime"}, "k": {"description": "", "name": "k", "group": "Part c", "templateType": "anything", "definition": "random(0.01..0.9#0.01)"}, "gcd": {"description": "PART A greatest common divisor of the variables alcmclcm and lcm
", "name": "gcd", "group": "Part a", "templateType": "anything", "definition": "gcd(alcmclcm,lcm)"}, "m_coprime": {"description": "", "name": "m_coprime", "group": "Part c", "templateType": "anything", "definition": "m/gcd(l,m)"}, "j_coprime": {"description": "PART B
", "name": "j_coprime", "group": "Part b", "templateType": "anything", "definition": "j/gcd_hj"}, "flcmhlcm": {"description": "PART B
", "name": "flcmhlcm", "group": "Part b", "templateType": "anything", "definition": "flcm2_g-hlcm2_j"}, "term1": {"description": "", "name": "term1", "group": "Part c", "templateType": "anything", "definition": "gcd3/simp"}, "alcm_b": {"description": "PART A variable a times the lcm of b and d, divided by b
", "name": "alcm_b", "group": "Part a", "templateType": "anything", "definition": "a_coprime*lcm_b"}, "a_coprime": {"description": "PART A
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", "name": "gcd_cd", "group": "Part a", "templateType": "anything", "definition": "gcd(c,d)"}, "lcm": {"description": "PART A lowest common multiple of variable b_coprime and variable d_coprime.
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", "name": "flcm2_g", "group": "Part b", "templateType": "anything", "definition": "f_coprime*lcm2_g"}, "lcm2_g": {"description": "PART B
", "name": "lcm2_g", "group": "Part b", "templateType": "anything", "definition": "lcm2/g_coprime"}, "term2": {"description": "", "name": "term2", "group": "Part c", "templateType": "anything", "definition": "gcd3/m_coprime"}, "n": {"description": "", "name": "n", "group": "Part c", "templateType": "anything", "definition": "random(1..5)"}, "alcmclcm": {"description": "PART A
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", "name": "f_coprime", "group": "Part b", "templateType": "anything", "definition": "f/gcd_fg"}, "num1": {"description": "", "name": "num1", "group": "Part c", "templateType": "anything", "definition": "(k_simp*term1)+(l_coprime*term2)-(n_coprime*term3)"}, "c_coprime": {"description": "", "name": "c_coprime", "group": "Part a", "templateType": "anything", "definition": "c/gcd_cd"}, "num2unsim": {"description": "PART B
", "name": "num2unsim", "group": "Part b", "templateType": "anything", "definition": "flcmhlcm+twolcm2"}, "l_coprime": {"description": "", "name": "l_coprime", "group": "Part c", "templateType": "anything", "definition": "l/gcd_lm"}}, "functions": {}, "tags": ["adding and subtracting fractions", "adding fractions", "converting between decimals and fractions", "converting integers to fractions", "fractions", "Fractions", "integers", "manipulation of fractions", "subtracting fractions", "taxonomy"], "variable_groups": [{"name": "Part a", "variables": ["a", "a_coprime", "b", "b_coprime", "gcd_ab", "c", "c_coprime", "d", "d_coprime", "gcd_cd", "lcm", "a_coprimed_coprime", "c_coprimeb_coprime", "lcm_b", "lcm_d", "alcm_b", "clcm_d", "alcmclcm", "gcd", "num", "denom"]}, {"name": "Part b", "variables": ["f", "f_coprime", "g", "g_coprime", "gcd_fg", "h", "h_coprime", "j", "j_coprime", "gcd_hj", "lcm2", "lcm2_g", "flcm2_g", "lcm2_j", "hlcm2_j", "flcmhlcm", "twolcm2", "num2unsim", "gcd2"]}, {"name": "Part c", "variables": ["k", "gcd_k100", "k_simp", "simp", "l", "l_coprime", "m", "m_coprime", "gcd_lm", "n", "n_coprime", "o", "o_coprime", "gcd_no", "gcd1", "gcd3", "term1", "term2", "term3", "num1", "gcd_numgcd3"]}], "parts": [{"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "num", "showFeedbackIcon": true, "minValue": "num", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "denom", "showFeedbackIcon": true, "minValue": "denom", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "$\\displaystyle\\frac{\\var{a_coprime}}{\\var{b_coprime}}+\\frac{\\var{c_coprime}}{\\var{d_coprime}}=$
$\\displaystyle\\frac{\\var{f_coprime}}{\\var{g_coprime}}-\\frac{\\var{h_coprime}}{\\var{j_coprime}}+2=$
$\\displaystyle \\var{k}+\\frac{\\var{l}}{\\var{m}}-\\frac{\\var{n}}{\\var{o}}=$
Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.
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\nTo add or subtract fractions, we need to have a common denominator on both fractions.
\nTo get a common denominator, we need to find the lowest common multiple of the two denominators.
\nThe lowest common multiple of $\\var{b_coprime}$ and $\\var{d_coprime}$ is $\\var{lcm}.$
\nThis will be the new denominator, and we need to multiply each fraction individually to ensure we get this denominator.
\nFor $\\displaystyle\\frac{\\var{a_coprime}}{\\var{b_coprime}}$, we need to multiply the fraction by $\\displaystyle\\frac{\\var{lcm_b}}{\\var{lcm_b}}$ to give $\\displaystyle\\frac{\\var{alcm_b}}{\\var{lcm}}.$
\nFor $\\displaystyle\\frac{\\var{c_coprime}}{\\var{d_coprime}}$, we need to multiply the fraction by $\\displaystyle\\frac{\\var{lcm_d}}{\\var{lcm_d}}$ to give $\\displaystyle\\frac{\\var{clcm_d}}{\\var{lcm}}.$
\nNow that we have each fraction in terms of a common denominator, we can now add the fractions together.
\n$\\displaystyle\\frac{\\var{alcm_b}}{\\var{lcm}}+\\frac{\\var{clcm_d}}{\\var{lcm}}=\\frac{(\\var{alcm_b}+\\var{clcm_d})}{\\var{lcm}}=\\frac{\\var{alcmclcm}}{\\var{lcm}}.$
\nFrom this, we can try to simplify the result down by finding the greatest common divisor of the numerator and denominator and dividing the whole fraction by this amount.
\nThe greatest common divisor of $\\var{alcmclcm}$ and $\\var{lcm}$ is $\\var{gcd}.$
\nSimplifying using this value gives a final answer of $\\displaystyle\\frac{\\var{num}}{\\var{denom}}.$
\nTherefore, the expression cannot be simplified further, and $\\displaystyle\\frac{\\var{num}}{\\var{denom}}$ is the final answer.
\n\n$\\displaystyle\\frac{\\var{f_coprime}}{\\var{g_coprime}}-\\frac{\\var{h_coprime}}{\\var{j_coprime}}+2.$
\n\nThe two fractions can be individually multiplied to achieve a common denominator of the lowest common multiple, $\\var{lcm2}.$
\n$\\displaystyle\\frac{\\var{f_coprime}}{\\var{g_coprime}}$ becomes $\\displaystyle\\frac{\\var{flcm2_g}}{\\var{lcm2}}$ and $\\displaystyle\\frac{\\var{h_coprime}}{\\var{j_coprime}}$ becomes $\\displaystyle\\frac{\\var{hlcm2_j}}{\\var{lcm2}}.$
\nWe can now subtract the second fraction from the first.
\n$\\displaystyle\\frac{\\var{flcm2_g}}{\\var{lcm2}}-\\frac{\\var{hlcm2_j}}{\\var{lcm2}}=\\frac{\\var{flcmhlcm}}{\\var{lcm2}}.$
\nFrom this, the question asks us to add $2$. We need to change the mixed number, $2$, into an improper fraction.
\n$\\displaystyle2=2\\bigg(\\frac{\\var{lcm2}}{\\var{lcm2}}\\bigg)=\\frac{\\var{twolcm2}}{\\var{lcm2}}.$
\nWe can now continue with the question.
\n$\\displaystyle\\frac{\\var{flcmhlcm}}{\\var{lcm2}}+\\frac{\\var{twolcm2}}{\\var{lcm2}}=\\frac{\\var{num2unsim}}{\\var{lcm2}}.$
\nWe can look to simplify by dividing by the greatest common divisor of $\\var{num2unsim}$ and $\\var{lcm2}$ which is $\\var{gcd2}.$
\nSimplifying by this value gives the final answer $\\displaystyle\\simplify{{num2unsim}/{lcm2}}.$
\nTherefore, no further simplification is possible, and $\\displaystyle\\simplify{{num2unsim}/{lcm2}}$ is the final answer.
\n\n$\\displaystyle\\var{k}+\\frac{\\var{l_coprime}}{\\var{m_coprime}}-\\frac{\\var{n_coprime}}{\\var{o_coprime}}.$
\nWe need to convert the decimal into a fraction and to do this, we need to multiply it by $10$ for every decimal place.
\n$\\displaystyle\\frac{\\var{k}}{1}\\times\\frac{100}{100}=\\frac{\\var{100k}}{100}.$
\nWe should look to simplify by dividing by the greatest common divisor which is $\\var{gcd_k100}.$
\nTherefore, it is not possible to simplify any further, and the fraction stays as
\nSimplifying by this value gives the fraction
\n\\[\\simplify{{{100k}}/{100}}\\text{.}\\]
\nThe original expression is now $\\displaystyle\\frac{\\var{k_simp}}{\\var{simp}}+\\frac{\\var{l_coprime}}{\\var{m_coprime}}-\\frac{\\var{n_coprime}}{\\var{o_coprime}}.$
\nWe can multiply each fraction individually to achieve the common denominator $\\var{gcd3}$.
\n\\[\\frac{\\var{k_simp}}{\\var{simp}}\\text{ becomes }\\frac{\\var{k_simp*term1}}{\\var{gcd3}}\\text{, }\\frac{\\var{l_coprime}}{\\var{m_coprime}}\\text{ becomes }\\frac{\\var{l_coprime*term2}}{\\var{gcd3}}\\text{ and }\\frac{\\var{n_coprime}}{\\var{o_coprime}}\\text{ becomes }\\frac{\\var{n_coprime*term3}}{\\var{gcd3}}\\text{.}\\]
\nWe can now complete the addition.
\n\\[\\frac{\\var{k_simp*term1}}{\\var{gcd3}}+\\frac{\\var{l_coprime*term2}}{\\var{gcd3}}-\\frac{\\var{n_coprime*term3}}{\\var{gcd3}}=\\frac{\\var{(k_simp*term1)+(l_coprime*term2)-(n_coprime*term3)}}{\\var{gcd3}}\\text{.}\\]
\nWe should look to simplify this fraction by dividing by the highest common divisor, $\\var{gcd_numgcd3}.$
\nSimplifying by this value gives the final answer
\nTherefore, it is not possible to simplify the fraction any further and the final answer is
\n\\[\\simplify{{num1}/{gcd3}}\\text{.}\\]
"}, {"name": "Select the fraction not equivalent to the others - large denominators", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "advice": "To find the odd fraction out, reduce each fraction to lowest terms.
\n\\begin{align}
\\frac{\\var{osix}}{\\var{psix}}=\\frac{\\var{o_coprime}}{\\var{p_coprime}}\\times\\frac{\\var{six}}{\\var{six}} \\\\[0.5em]
\\frac{\\var{oseven}}{\\var{pseven}}=\\frac{\\var{o_coprime}}{\\var{p_coprime}}\\times\\frac{\\var{seven}}{\\var{seven}} \\\\[0.5em]
\\frac{\\var{oeight}}{\\var{peight}}=\\displaystyle\\frac{\\var{o_coprime}}{\\var{p_coprime}}\\times\\frac{\\var{eight}}{\\var{eight}} \\\\[0.5em]
\\frac{\\var{onine}}{\\var{pnine}}=\\frac{\\var{o_coprime}}{\\var{p_coprime}}\\times\\frac{\\var{nine}}{\\var{nine}} \\\\[0.5em]
\\frac{\\var{oten}}{\\var{pten}} = \\frac{\\var{oten/gcd(oten,pten)}}{\\var{pten/gcd(oten,pten)}} \\times \\frac{\\var{gcd(oten,pten)}}{\\var{gcd(oten,pten)}}
\\end{align}
The odd fraction out is $\\displaystyle\\frac{\\var{oten}}{\\var{pten}}$.
\n", "statement": "", "variables": {"five": {"name": "five", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(1..7 except one except two except three except four)"}, "o": {"name": "o", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(1..7 except p except m)"}, "six": {"name": "six", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(1..10 except one except two except three except four except five)"}, "oten": {"name": "oten", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "o_coprime*ten+random(-6..6 except 0)"}, "pten": {"name": "pten", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "p_coprime*ten+random(-2..2 except 0)"}, "m": {"name": "m", "group": "Ungrouped variables", "templateType": "anything", "description": "Random number between 1 and 10
", "definition": "random(1..7)"}, "pseven": {"name": "pseven", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "p_coprime*seven"}, "eight": {"name": "eight", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(6..15 except one except two except three except four except five except six except seven)"}, "nine": {"name": "nine", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(4..12 except one except two except three except four except five except six except seven except eight)"}, "three": {"name": "three", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(1..6 except one except two)"}, "psix": {"name": "psix", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "p_coprime*six"}, "ten": {"name": "ten", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(1..10 except one except two except three except four except five except six except seven except eight except nine)"}, "four": {"name": "four", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(5..20 except one except two except three)"}, "two": {"name": "two", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(2..15 except one)"}, "peight": {"name": "peight", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "p_coprime*eight"}, "o_coprime": {"name": "o_coprime", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "o/gcd_op"}, "osix": {"name": "osix", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "o_coprime*six"}, "pnine": {"name": "pnine", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "p_coprime*nine"}, "seven": {"name": "seven", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(1..6 except one except two except three except four except five except six)"}, "n": {"name": "n", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(7..15 except m)"}, "onine": {"name": "onine", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "o_coprime*nine"}, "one": {"name": "one", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(2..10)"}, "p_coprime": {"name": "p_coprime", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "p/gcd_op"}, "gcd_op": {"name": "gcd_op", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "gcd(o,p)"}, "oeight": {"name": "oeight", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "o_coprime*eight"}, "oseven": {"name": "oseven", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "o_coprime*seven"}, "p": {"name": "p", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(7..15 except n)"}}, "tags": ["equivalent fractions", "fractions", "Fractions", "taxonomy"], "ungrouped_variables": ["m", "n", "one", "two", "three", "four", "five", "o", "p", "gcd_op", "o_coprime", "p_coprime", "six", "osix", "psix", "seven", "oseven", "pseven", "eight", "oeight", "peight", "nine", "onine", "pnine", "ten", "oten", "pten"], "functions": {}, "preamble": {"js": "", "css": "fraction {\n display: inline-block;\n vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n float: left;\n width: 100%;\n text-align: center;\n line-height: 2.5em;\n}\nfraction > numerator {\n border-bottom: 1px solid;\n padding-bottom: 5px;\n}\nfraction > denominator {\n padding-top: 5px;\n}\nfraction input {\n line-height: 1em;\n}\n\nfraction .part {\n margin: 0;\n}\n\n.table-responsive, .fractiontable {\n display:inline-block;\n}\n.fractiontable {\n padding: 0; \n border: 0;\n}\n\n.fractiontable .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n border-bottom: 1px solid black; \n text-align: center;\n}\n\n\n.fractiontable tr {\n height: 3em;\n}\n"}, "type": "question", "variable_groups": [], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "Given five fractions, identify the odd fraction out. The denominators are mainly two or three digits long.
", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"variableReplacements": [], "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "prompt": "From the options below, select the fraction which is not equivalent to the others.
", "matrix": [0, 0, 0, 0, "1"], "scripts": {}, "displayColumns": 0, "showCorrectAnswer": true, "distractors": ["", "", "", "", ""], "shuffleChoices": true, "marks": 0, "type": "1_n_2", "choices": ["$\\displaystyle\\frac{\\var{osix}}{\\var{psix}}$
", "$\\displaystyle\\frac{\\var{oseven}}{\\var{pseven}}$
", "$\\displaystyle\\frac{\\var{oeight}}{\\var{peight}}$
", "$\\displaystyle\\frac{\\var{onine}}{\\var{pnine}}$
", "$\\displaystyle\\frac{\\var{oten}}{\\var{pten}}$
"], "showFeedbackIcon": true, "minMarks": 0}]}, {"name": "Select the fraction not equivalent to the others - small denominators", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "advice": "To find the odd fraction out, reduce each fraction to lowest terms.
\n\\begin{align}
\\frac{\\var{mone}}{\\var{none}} &= \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\times\\frac{\\var{one}}{\\var{one}} \\\\[0.5em]
\\frac{\\var{mtwo}}{\\var{ntwo}} &= \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\times\\frac{\\var{two}}{\\var{two}} \\\\[0.5em]
\\frac{\\var{mthree}}{\\var{nthree}} &= \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\times\\frac{\\var{three}}{\\var{three}} \\\\[0.5em]
\\frac{\\var{mfour}}{\\var{nfour}} &= \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\times\\frac{\\var{four}}{\\var{four}} \\\\[0.5em]
\\frac{\\var{mfive}}{\\var{nfive}} &= \\frac{\\var{mfive/gcd(mfive,nfive)}}{\\var{nfive/gcd(mfive,nfive)}} \\times \\frac{\\var{gcd(mfive,nfive)}}{\\var{gcd(mfive,nfive)}}
\\end{align}
All but one of these fractions are equivalent to $\\displaystyle\\frac{\\var{m_coprime}}{\\var{n_coprime}}$.
\nThe odd fraction out is $\\displaystyle\\frac{\\var{mfive}}{\\var{nfive}}$.
", "statement": "", "variables": {"five": {"name": "five", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(1..7 except one except two except three except four)"}, "m_coprime": {"name": "m_coprime", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "m/gcd_mn"}, "mthree": {"name": "mthree", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "m_coprime*three"}, "ntwo": {"name": "ntwo", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "n_coprime*two"}, "mfive": {"name": "mfive", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "m_coprime*five+random(-4..4 except 0)"}, "mtwo": {"name": "mtwo", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "m_coprime*two"}, "four": {"name": "four", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(5..20 except one except two except three)"}, "none": {"name": "none", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "n_coprime*one"}, "nthree": {"name": "nthree", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "n_coprime*three"}, "two": {"name": "two", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(2..15 except one)"}, "m": {"name": "m", "group": "Ungrouped variables", "templateType": "anything", "description": "Random number between 1 and 10
", "definition": "random(1..7)"}, "nfive": {"name": "nfive", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "n_coprime*five"}, "n": {"name": "n", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(7..15 except m)"}, "one": {"name": "one", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(2..10)"}, "gcd_mn": {"name": "gcd_mn", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "gcd(m,n)"}, "n_coprime": {"name": "n_coprime", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "n/gcd_mn"}, "nfour": {"name": "nfour", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "n_coprime*four"}, "mone": {"name": "mone", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "m_coprime*one"}, "three": {"name": "three", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(1..6 except one except two)"}, "mfour": {"name": "mfour", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "m_coprime*four"}}, "tags": ["equivalent fractions", "small denominators", "taxonomy"], "ungrouped_variables": ["m", "n", "gcd_mn", "m_coprime", "n_coprime", "one", "mone", "none", "two", "mtwo", "ntwo", "three", "mthree", "nthree", "four", "mfour", "nfour", "five", "mfive", "nfive"], "functions": {}, "preamble": {"js": "", "css": "fraction {\n display: inline-block;\n vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n float: left;\n width: 100%;\n text-align: center;\n line-height: 2.5em;\n}\nfraction > numerator {\n border-bottom: 1px solid;\n padding-bottom: 5px;\n}\nfraction > denominator {\n padding-top: 5px;\n}\nfraction input {\n line-height: 1em;\n}\n\nfraction .part {\n margin: 0;\n}\n\n.table-responsive, .fractiontable {\n display:inline-block;\n}\n.fractiontable {\n padding: 0; \n border: 0;\n}\n\n.fractiontable .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n border-bottom: 1px solid black; \n text-align: center;\n}\n\n\n.fractiontable tr {\n height: 3em;\n}\n"}, "type": "question", "variable_groups": [], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "Given five fractions, identify the one which is not equivalent to the others by reducing to lowest terms.
", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"variableReplacements": [], "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "matrix": [0, 0, "0", 0, "1"], "scripts": {}, "displayColumns": 0, "showCorrectAnswer": true, "distractors": ["", "", "", "", ""], "shuffleChoices": true, "marks": 0, "prompt": "From the options below, select the fraction which is not equivalent to the others.
", "choices": ["$\\displaystyle\\frac{\\var{mone}}{\\var{none}}$
", "$\\displaystyle\\frac{\\var{mtwo}}{\\var{ntwo}}$
", "$\\displaystyle\\frac{\\var{mthree}}{\\var{nthree}}$
", "$\\displaystyle\\frac{\\var{mfour}}{\\var{nfour}}$
", "$\\displaystyle\\frac{\\var{mfive}}{\\var{nfive}}$
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