Question

How do you simplify the fraction 27/54?

Answer 1

`1/2`

Explanation:

To simplify the fraction consider the `color(blue)"common factors"` of the numerator/denominator and `color(blue)"cancel"` them.

That is 27 and 54 have a `color(blue)"common factor"` of 27 and thus can be `color(blue)"cancelled"` by dividing both by 27.

`rArr27/54=cancel(27)^1/cancel(54)^2=1/2`

A slightly longer approach is to cancel by the lowest common factor which is 3 and repeat the process.

`rArr27/54=cancel(27)^9/cancel(54)^(18)=9/18`

now cancel by 3 again.

`rArr9/18=cancel(9)^3/cancel(18)^6=3/6`

cancel by 3 again.

`3/6=cancel(3)^1/cancel(6)^2=1/2larr" in simplest form"`

The fraction is said to be in `color(blue)"simplest form"` when no other factor but 1 will divide into numerator/denominator.