// Numbas version: exam_results_page_options {"name": "Select the fraction not equivalent to the others - small denominators", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"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}

\n

All but one of these fractions are equivalent to $\\displaystyle\\frac{\\var{m_coprime}}{\\var{n_coprime}}$.

\n

The 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": {}, "name": "Select the fraction not equivalent to the others - small denominators", "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"}, "extensions": [], "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": ["

$\\displaystyle\\frac{\\var{mone}}{\\var{none}}$

", "

$\\displaystyle\\frac{\\var{mtwo}}{\\var{ntwo}}$

", "

$\\displaystyle\\frac{\\var{mthree}}{\\var{nthree}}$

", "

$\\displaystyle\\frac{\\var{mfour}}{\\var{nfour}}$

", "

$\\displaystyle\\frac{\\var{mfive}}{\\var{nfive}}$

"], "type": "1_n_2", "showFeedbackIcon": true, "minMarks": 0}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}