Question

How do you write `18/54` in simplest form?

Answer 1

`1/3`

Explanation:

We have to find a `color(blue)"common factor"` that will divide into 18 and 54 and reduce the fraction.
This process is referred to as `color(blue)"cancelling"`

If you can see that 18 is a factor of 18 and 54 then the fraction can be simplified immediately.

`rArr18/54=(18÷18)/(54÷18)=1/3`

Usually written as `18/54=cancel(18)^1/cancel(54)^3=1/3`

A fraction is in `color(blue)"simplest form"` when no other factor apart from 1 will divide exactly into the numerator/denominator.

Otherwise, begin with the lowest common factor, and continue the process until simplified form is reached.

Proceeding with factor of `color(red)(2)`

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

Now with a factor of `color(red)(3)" and " color(red)(3)" again"`

`cancel(9)^3/cancel(27)^9=3/9=cancel(3)^1/cancel(9)^3=1/3larr" in simplest form"`