How can the GCF be used to write a fraction?

Question

3560 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-06T06:22:35

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

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

$color(white)()$
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:

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 $14$ .

$color(white)()$
Having found the GCF, we can now write:

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

Alternatively, we can express the division implicitly:

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