Question

How do you simplify `35/56`?

Answer 1

We can factor the numerator and denominator as:

`35/56 => (7 xx 5)/(7 xx 8) => (color(red)(cancel(color(black)(7))) xx 5)/(color(red)(cancel(color(black)(7))) xx 8) => 5/8`

Answer 2

`(35div7)/(56div7) = 5/8`

Explanation:

To write a fraction in its simplest form, you divide the numerator and denominator by the highest common factor.

`35 and 56` are both multiples of `7" "HCF=7`

`(35div7)/(56div7) = 5/8`

Dividing by `7/7` is the same as dividing by `1`. This does not change the value, only what a number looks like.

We often call this process 'cancelling'

`cancel35^5/cancel56^8 = 5/8`

Compare the decimals:

`35/56 = 0.625 and 5/8= 0.625`