Reduced or simplified form of a fraction by cancelling the greatest common divisor (gcd) of numerator and denominator (i.e dividing out by it)

\nThe greatest common factor are designed to be one of the following 2,4,5,10,20,25,50,100,125,250

"}, "variables": {"anum": {"name": "anum", "definition": "a/badg", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num": {"name": "num", "definition": "a*c/badg", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "den": {"name": "den", "definition": "b*c/badg", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "a": {"name": "a", "definition": "random(1..100)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "b": {"name": "b", "definition": "random(1..100 except a)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "c": {"name": "c", "definition": "random(2,4,5,10,20,25,50,100,125,250)", "templateType": "anything", "group": "Ungrouped variables", "description": "common factor

"}, "badg": {"name": "badg", "definition": "gcd(a,b)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "aden": {"name": "aden", "definition": "b/badg", "templateType": "anything", "group": "Ungrouped variables", "description": ""}}, "parts": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "gaps": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "correctAnswerFraction": true, "maxValue": "num/den", "minValue": "num/den", "variableReplacementStrategy": "originalfirst", "allowFractions": true, "mustBeReducedPC": 0, "marks": 1, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "unitTests": [], "mustBeReduced": true, "type": "numberentry"}], "unitTests": [], "steps": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "prompt": "To reduce this fraction we need to find common factors in the numerator and denominator, that is we need to find numbers that divide into both the top number and the bottom number.

\nNotice that $\\var{num}$ and $\\var{den}$ are both divisible by $\\var{c}$. So we will divide both numbers by this common factor $\\var{c}$:

\n\\begin{align}\\frac{\\var{num}}{\\var{den}}&=\\frac{\\var{num}\\div\\var{c}}{\\var{den}\\div \\var{c}}\\\\&=\\simplify{{anum}/{aden}}\\end{align}

\nIn this case, our common factor was equal to the original denominator so simplifying was actually just the same as evaluating the fraction by doing the division!

\nNow $\\var{anum}$ and $\\var{aden}$ have no common factors (other than $1$) and so $\\frac{\\var{anum}}{\\var{aden}}$ is reduced.

\nTo summarise, simplifying/reducing/cancelling fractions require you to know divisibility tests and be able to do divisions. You need to practice these skills to get better at simplifying fractions.

", "customMarkingAlgorithm": "", "type": "information"}], "variableReplacementStrategy": "originalfirst", "prompt": "Rewrite this fraction in its simplest form:

\n$\\displaystyle\\frac{\\var{num}}{\\var{den}}=$ [[0]]

\n**Note:** Use the / to signify the fraction bar. For example, $\\frac{1}{2}$ is entered as $1/2$.

Write the following question down on paper and evaluate it without using a calculator.

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