Simplifying a fraction with a common factor up to a square.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Express the fraction below in its simplest form:
\n\\[\\frac{\\var{x}}{\\var{y}}\\]
", "advice": "To simplify a fraction we need to divide both numbers by their common factors. The easiest way to do this is to keep dividing by the smallest number which divides both numbers. Since $\\var{SmallestFactor}$ divides both $\\var{x}$ and $\\var{y}$ then we can simplify
\n\\[\\frac{\\var{x}}{\\var{y}}\\]
\nto
\n\\[\\frac{\\var{x/SmallestFactor}}{\\var{y/SmallestFactor}}.\\]
\nWe keep doing this until there are no numbers (except 1) which divide both the numerator and denominator. This leaves us with a simplified form of
\n\\[\\frac{\\var{x}}{\\var{y}}=\\simplify[all,fractionNumbers]{{x/y}}.\\]
\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x_powers": {"name": "x_powers", "group": "Ungrouped variables", "definition": "[random(0..3),random(0..3),random(0,1),random(0,1)]", "description": "", "templateType": "anything", "can_override": false}, "y_powers": {"name": "y_powers", "group": "Ungrouped variables", "definition": "[random(0..3),random(0..3),random(0..2),random(0,1)]", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "2^x_powers[0]*3^x_powers[1]*5^x_powers[2]*7^x_powers[3]", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "2^y_powers[0]*3^y_powers[1]*5^y_powers[2]*7^y_powers[3]", "description": "", "templateType": "anything", "can_override": false}, "hcf_xy": {"name": "hcf_xy", "group": "Ungrouped variables", "definition": "2^min(x_powers[0],y_powers[0])*3^min(x_powers[1],y_powers[1])*5^min(x_powers[2],y_powers[2])", "description": "", "templateType": "anything", "can_override": false}, "primes": {"name": "primes", "group": "Ungrouped variables", "definition": "[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]", "description": "", "templateType": "anything", "can_override": false}, "Smallestfactor": {"name": "Smallestfactor", "group": "Ungrouped variables", "definition": "divisors(hcf_xy)[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "y<121 && xSimplifying a fraction with many factors up to cubed primes in common.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Express the fraction below in its simplest form:
\n\\[\\frac{\\var{x}}{\\var{y}}\\]
", "advice": "To simplify a fraction we need to divide both numbers by their common factors. The easiest way to do this is to keep dividing by the smallest number which divides both numbers. Since $\\var{SmallestFactor}$ divides both $\\var{x}$ and $\\var{y}$ then we can simplify
\n\\[\\frac{\\var{x}}{\\var{y}}\\]
\nto
\n\\[\\frac{\\var{x/SmallestFactor}}{\\var{y/SmallestFactor}}.\\]
\nWe keep doing this until there are no numbers (except 1) which divide both the numerator and denominator. This leaves us with a simplified form of
\n\\[\\frac{\\var{x}}{\\var{y}}=\\simplify[all,fractionNumbers]{{x/y}}.\\]
\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x_powers": {"name": "x_powers", "group": "Ungrouped variables", "definition": "[random(0..3),random(0..3),random(0..2),random(0,1)]", "description": "", "templateType": "anything", "can_override": false}, "y_powers": {"name": "y_powers", "group": "Ungrouped variables", "definition": "[random(0..3),random(0..3),random(0..3),random(0,1)]", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "2^x_powers[0]*3^x_powers[1]*5^x_powers[2]*7^x_powers[3]", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "2^y_powers[0]*3^y_powers[1]*5^y_powers[2]*7^y_powers[3]", "description": "", "templateType": "anything", "can_override": false}, "hcf_xy": {"name": "hcf_xy", "group": "Ungrouped variables", "definition": "2^min(x_powers[0],y_powers[0])*3^min(x_powers[1],y_powers[1])*5^min(x_powers[2],y_powers[2])", "description": "", "templateType": "anything", "can_override": false}, "primes": {"name": "primes", "group": "Ungrouped variables", "definition": "[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]", "description": "", "templateType": "anything", "can_override": false}, "Smallestfactor": {"name": "Smallestfactor", "group": "Ungrouped variables", "definition": "divisors(hcf_xy)[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "y>50&& y<500 && xThis question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "A mixed number is a number consisting of an integer and a proper fraction, i.e. a number in the form $ a \\displaystyle \\frac{b}{c}$ where $a$ is an integer and $\\displaystyle\\frac{b}{c}$ is a proper fraction: $b$ is smaller than $c$.
\nAn improper fraction is a fraction where the numerator is larger than the denominator, i.e. a number of the form $\\displaystyle\\frac{d}{e}$ where the numerator, $d$, is greater than the denominator, $e$.
\nTo convert an improper fraction into a mixed number, find out how many times the denominator $\\var{h_coprime/gcdb}$ goes into the numerator $\\var{num/gcdb}$. You can do this by dividing the numerator by the denominator and taking the whole number part or you can just add the denominator to itself until one more addition would make it bigger. This gives us a whole number part of our mixed fraction of $\\var{f}$.
\nThe numerator of our mixed fraction is what is left from dividing out the whole number. For this question that is $\\var{num/gcdb}-\\var{f*h_coprime}$.
\nFinally the denominator of our mixed fraction is just the denominator of the improper fraction.
\n\\[
\\frac{\\var{num/gcdb}}{\\var{h_coprime/gcdb}} = {\\var{f}\\frac{\\var{g_coprime}}{\\var{h_coprime}}}\\text{.}
\\]
Use this link to find some resources which will help you revise this topic.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"g": {"name": "g", "group": "Ungrouped variables", "definition": "random(1..h except h)", "description": "Random number between 1 and 15
", "templateType": "anything", "can_override": false}, "g_coprime": {"name": "g_coprime", "group": "Ungrouped variables", "definition": "g/gcd_gh", "description": "PART C
", "templateType": "anything", "can_override": false}, "gcd_gh": {"name": "gcd_gh", "group": "Ungrouped variables", "definition": "gcd(g,h)", "description": "PART C
", "templateType": "anything", "can_override": false}, "num": {"name": "num", "group": "Ungrouped variables", "definition": "((h_coprime*f)+g_coprime)", "description": "numerator for the improper fraction c(i)
", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(10 .. 24#1)", "description": "Random number between 1 and 24
", "templateType": "randrange", "can_override": false}, "h_coprime": {"name": "h_coprime", "group": "Ungrouped variables", "definition": "h/gcd_gh", "description": "PART C
", "templateType": "anything", "can_override": false}, "gcdb": {"name": "gcdb", "group": "Ungrouped variables", "definition": "gcd({num},{h_coprime})", "description": "gcd of num and h
", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(2 .. 5#1)", "description": "Random number between 1 and 5
", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["f", "g", "h", "gcd_gh", "g_coprime", "h_coprime", "num", "gcdb"], "variable_groups": [], "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"}, "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": "Write the improper fraction as a mixed number and reduce it down to its simplest form.
\n$\\displaystyle{\\frac{\\var{num/gcdb}}{\\var{h_coprime/gcdb}}} = $ [[2]]
spot use of a multiplier to get equivalent fractions with larger denominators.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "If we multiply the top and bottom of a fraction by a number (not zero) we get an equivalent fraction. We say equivalent because they represent the same amount of the whole.
\n\n\n\n
For example, suppose you cut a cake up into 3 parts and throw away one piece, what is left is
Notice in both situations you end up with the same amount of cake!
\n![](\"resources/question-resources/equivalent_fractions.svg\"/)
So $\\frac{2}{3}$ is equivalent to $\\frac{4}{6}$ and we can write \\[\\frac{2}{3}=\\frac{4}{6}.\\]
\nIf you look at the numbers you might notice that for the second cake we just doubled all the numbers, and in the second fraction all the numbers are two times those in the first fraction. In general equivalent fractions are formed by multiplying (or dividing) the top and bottom of a fraction by the same number.
\nSo if you were asked how a person got from $\\frac{\\var{num5}}{\\var{denom5}}$ to the equivalent fraction $\\frac{\\var{num6}}{\\var{denom6}}$ you ask yourself 'what do I multiply $\\var{num5}$ by to get $\\var{num6}$?' and 'what do I multiply $\\var{denom5}$ by to get $\\var{denom6}$?' and then realise they must have done the following
\n\\[\\frac{\\var{num5}}{\\var{denom5}}=\\frac{\\var{num5}\\times\\var{mult4}}{\\var{denom5}\\times\\var{mult4}}=\\frac{\\var{num6}}{\\var{denom6}}.\\]
\n\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {"std": ["all"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"denom5": {"name": "denom5", "group": "Ungrouped variables", "definition": "random(2..12 except num5)", "description": "", "templateType": "anything", "can_override": false}, "denom6": {"name": "denom6", "group": "Ungrouped variables", "definition": "denom5*mult4", "description": "", "templateType": "anything", "can_override": false}, "num6": {"name": "num6", "group": "Ungrouped variables", "definition": "num5*mult4", "description": "", "templateType": "anything", "can_override": false}, "num5": {"name": "num5", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "mult4": {"name": "mult4", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "FirstName": {"name": "FirstName", "group": "Ungrouped variables", "definition": "repeat(random([\"Ben\", \"He\"], [\"Annie\", \"She\"], [\"Matt\", \"He\"], [\"David\", \"He\"], [\"Steve\", \"He\"], [\"David\", \"He\"], [\"Scott\", \"He\"], [\"Fran\", \"She\"], [\"Jenny\", \"She\"], [\"Lyn\", \"She\"], [\"Judy-anne\", \"She\"], [\"Courtney\", \"She\"]),2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["num5", "denom5", "mult4", "num6", "denom6", "FirstName"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ".fractiontable table {\n width: 40%; \n padding: 0px; \n border-width: 0px; \n layout: fixed;\n}\n\n.fractiontable .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n width: 15%; \n border-bottom: 1px solid black; \n text-align: center;\n}\n\n.fractiontable .tdeq \n{\n width: 5%; \n border-bottom: 0px;\n font-size: x-large;\n}\n\n\n.fractiontable th {\n background-color:#aaa;\n}\n/*Fix the height of all cells EXCEPT table-headers to 40px*/\n.fractiontable td {\n height:40px;\n}\n"}, "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": "{FirstName[0][0]} has written $\\frac{\\var{num5}}{\\var{denom5}}$ in the equivalent form $\\frac{\\var{num6}}{\\var{denom6}}$.
\n\nWhat has {FirstName[0][0]} done to the first fraction in order to get the second? {FirstName[0][1]} has multiplied the top and bottom by [[0]] .
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "mult4", "maxValue": "mult4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "22.f Equivalent fractions - divide both terms", "extensions": [], "custom_part_types": [], "resources": ["question-resources/equivalent_fractions.svg"], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "Finding equivalent fractions, and expressing fractions in other equivalent forms.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "If we divide the top and bottom of a fraction by a number (not zero) we get an equivalent fraction. We say equivalent because they represent the same amount of the whole.
\n\n\n\n
For example, suppose you cut it into 6 parts and throw away two parts, what is left is four sixths of the whole cake, that is, $\\frac{4}{6}$ of the whole cake. Now suppose you have another identical cake, this time you cut a cake up into 3 parts and throw away one piece, what is left is two thirds of the whole cake, that is, $\\frac{2}{3}$ of the whole cake.
\nNotice in both situations you end up with the same amount of cake!
\n
So $\\frac{4}{6}$ is equivalent to $\\frac{2}{3}$ and we can write \\[\\frac{4}{6}=\\frac{2}{3}.\\]
\nIf you look at the numbers you might notice that for the second cake we just halved all the numbers, and in the second fraction all the numbers are half of those in the first fraction. In general equivalent fractions are formed by dividing (or multiplying) the top and bottom of a fraction by the same number.
\nSo if you were asked how a person got from $\\frac{\\var{num2*mult5}}{\\var{denom2*mult5}}$ to the equivalent fraction $\\frac{\\var{num2}}{\\var{denom2}}$ you ask yourself 'what do I divide $\\var{num2*mult5}$ by to get $\\var{num2}$?' and 'what do I divide $\\var{denom2*mult5}$ by to get $\\var{denom2}$?' and then realise they must have done the following
\n\\[\\frac{\\var{num2*mult5}}{\\var{denom2*mult5}}=\\frac{\\var{num2*mult5}\\div\\var{mult5}}{\\var{denom2*mult5}\\div\\var{mult5}}=\\frac{\\var{num2}}{\\var{denom2}}.\\]
\n\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {"std": ["all"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"denom1": {"name": "denom1", "group": "Ungrouped variables", "definition": "random(2..12 except num1)", "description": "", "templateType": "anything", "can_override": false}, "denom2": {"name": "denom2", "group": "Ungrouped variables", "definition": "denom1*mult1", "description": "", "templateType": "anything", "can_override": false}, "num1": {"name": "num1", "group": "Ungrouped variables", "definition": "random(1..12)", "description": "", "templateType": "anything", "can_override": false}, "num2": {"name": "num2", "group": "Ungrouped variables", "definition": "num1*mult1", "description": "", "templateType": "anything", "can_override": false}, "mult1": {"name": "mult1", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "mult5": {"name": "mult5", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "Names": {"name": "Names", "group": "Ungrouped variables", "definition": "repeat(random([\"Ben\", \"He\"], [\"Annie\", \"She\"], [\"Matt\", \"He\"], [\"David\", \"He\"], [\"Steve\", \"He\"], [\"David\", \"He\"], [\"Scott\", \"He\"], [\"Fran\", \"She\"], [\"Jenny\", \"She\"], [\"Lyn\", \"She\"], [\"Judy-anne\", \"She\"], [\"Courtney\", \"She\"]),2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["num1", "denom1", "mult1", "num2", "denom2", "Names", "mult5"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ".fractiontable table {\n width: 40%; \n padding: 0px; \n border-width: 0px; \n layout: fixed;\n}\n\n.fractiontable .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n width: 15%; \n border-bottom: 1px solid black; \n text-align: center;\n}\n\n.fractiontable .tdeq \n{\n width: 5%; \n border-bottom: 0px;\n font-size: x-large;\n}\n\n\n.fractiontable th {\n background-color:#aaa;\n}\n/*Fix the height of all cells EXCEPT table-headers to 40px*/\n.fractiontable td {\n height:40px;\n}\n"}, "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": "{Names[1][0]} has written $\\frac{\\var{num2*mult5}}{\\var{denom2*mult5}}$ in the equivalent form $\\frac{\\var{num2}}{\\var{denom2}}$.
\n\nWhat has {Names[1][0]} done to the first fraction in order to get the second? {Names[1][1]} has divided the top and bottom by [[0]] .
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "mult5", "maxValue": "mult5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "22.g Finding equivalent fractions", "extensions": [], "custom_part_types": [], "resources": ["question-resources/equivalent_fractions.svg"], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "Finding equivalent fractions, and expressing fractions in their simplest form.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "These are equivalent fractions so the same number that multiplied the numerator must multiply the denominator.
\n\n\n\n
For example given:
\n\\[\\frac{\\var{num1}}{\\var{denom1}}=\\frac{}{\\var{denom2}}\\]
\nyou can see the denominator of $\\var{denom1}$ was multiplied by $\\var{mult1}$ to become $\\var{denom2}$, so to make an equivalent fraction, we would need to multiply the numerator by $\\var{mult1}$ as well. So the blank must be $\\var{num1}\\times \\var{mult1}$ which is $\\var{num2}$. Your working might look like this:
\n\\[\\frac{\\var{num1}}{\\var{denom1}}=\\frac{\\var{num1}\\times \\var{mult1}}{\\var{denom1}\\times \\var{mult1}}=\\frac{\\var{num2}}{\\var{denom2}}.\\]
\n\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {"std": ["all"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"denom1": {"name": "denom1", "group": "Ungrouped variables", "definition": "random(2..12 except num1)", "description": "", "templateType": "anything", "can_override": false}, "num4": {"name": "num4", "group": "Ungrouped variables", "definition": "num1*mult3", "description": "", "templateType": "anything", "can_override": false}, "denom3": {"name": "denom3", "group": "Ungrouped variables", "definition": "denom1*mult2", "description": "", "templateType": "anything", "can_override": false}, "denom2": {"name": "denom2", "group": "Ungrouped variables", "definition": "denom1*mult1", "description": "", "templateType": "anything", "can_override": false}, "num1": {"name": "num1", "group": "Ungrouped variables", "definition": "random(1..12)", "description": "", "templateType": "anything", "can_override": false}, "num2": {"name": "num2", "group": "Ungrouped variables", "definition": "num1*mult1", "description": "", "templateType": "anything", "can_override": false}, "num3": {"name": "num3", "group": "Ungrouped variables", "definition": "num1*mult2", "description": "", "templateType": "anything", "can_override": false}, "denom4": {"name": "denom4", "group": "Ungrouped variables", "definition": "denom1*mult3", "description": "", "templateType": "anything", "can_override": false}, "mult3": {"name": "mult3", "group": "Ungrouped variables", "definition": "random(2..10 except [mult1, mult2])", "description": "", "templateType": "anything", "can_override": false}, "mult2": {"name": "mult2", "group": "Ungrouped variables", "definition": "random(2..10 except mult1)", "description": "", "templateType": "anything", "can_override": false}, "mult1": {"name": "mult1", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["num1", "denom1", "mult1", "num2", "denom2", "mult2", "num3", "denom3", "mult3", "num4", "denom4"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ".fractiontable table {\n width: 40%; \n padding: 0px; \n border-width: 0px; \n layout: fixed;\n}\n\n.fractiontable .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n width: 15%; \n border-bottom: 1px solid black; \n text-align: center;\n}\n\n.fractiontable .tdeq \n{\n width: 5%; \n border-bottom: 0px;\n font-size: x-large;\n}\n\n\n.fractiontable th {\n background-color:#aaa;\n}\n/*Fix the height of all cells EXCEPT table-headers to 40px*/\n.fractiontable td {\n height:40px;\n}\n"}, "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": "Please enter numbers to create equivalent fractions.
\n| {num1} | \n= | \n[[0]] | \n= | \n{num3} | \n= | \n[[2]] | \n
| {denom1} | \n\n | {denom2} | \n\n | [[1]] | \n\n | {denom4} | \n