Question

How do you write the answer `3/16 times 4/9` in simplest form?

Answer 1

`1/12`

Explanation:

`3/16*4/9`
`=cancel(3)/(cancel(16)color(red)(4))*cancel(4)/(cancel(9)color(red)(3))`
`=1/12`

Answer 2

`1/12`

Explanation:

When multiplying 2 or more fractions together we can `color(blue)"cancel"` any common factors on the numerators with values on the denominators, dividing each by the common factor.

`rArr(3÷3)/(16÷4)xx(4÷4)/(9÷3)=1/4xx1/3=1/12`

This is usually done by 'scoring out' the value to be cancelled.

`rArrcancelcolor(red)(3)^1/cancelcolor(blue)(16)^4xxcancelcolor(blue)(4)^1/cancelcolor(red)(9)^3=(1xx1)/(4xx3)=1/12larr" in simplest form"`

A fraction is in `color(blue)"simplest form"` when the numerator/denominator have only 1 as a common factor.