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

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

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

If you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

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common factor

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Rewrite this fraction in its simplest form:

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

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

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To reduce/simplify a 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.

Divide the top and bottom by the highest common factor, or divide the top and bottom by common factors as they are found (until the only common factor is $1$).

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

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

In 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!

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

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

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