Question

How can the GCF be used to write a fraction?

Answer 1

Divide both the numerator and denominator by their GCF to get a fraction in lowest terms.

Explanation:

The GCF (greatest common factor) can be used to express a fraction in simplest terms:

• Find the GCF of the numerator and denominator.

• Divide both the numerator and denominator by the GCF.

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For example, to express `70/42` in lowest terms, first find the GCF of `70` and `42`.

My favourite method to find the GCF of two numbers goes as follows:

• Divide the larger number by the smaller to get a quotient and remainder.

• If the remainder is zero, then the smaller number is the GCF.

• Otherwise, repeat with the smaller number and the remainder.

So in my example:

`70/42 = 1` with remainder `28`

`42/28 = 1` with remainder `14`

`28/14 = 2` with remainder `0`

So the GCF of `70` and `42` is `14`.

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Having found the GCF, we can now write:

`70/42 = ((70/14)) / ((42/14))= 5/3`

Alternatively, we can express the division implicitly:

`70/42 = (5 xx color(red)(cancel(color(black)(14))))/(3 xx color(red)(cancel(color(black)(14)))) = 5/3`