Question

How do you simplify `30:75`?

Answer 1

`=2/5`

Explanation:

`30-:75`

`=30/75`

`=2/5times15/15`

`=2/5`

Answer 2

2:5

Explanation:

Simplifying a ratio is similar to simplifying a fraction.

That is we look for a common factor that divides into both numbers and 'cancel' them,

Since 30 has 0 as it's last digit and 75 has 5 , this indicates that 5 is a common factor as 5 divides into numbers whose last digit is 0/5.

Thus `(30÷5):(75÷5)=6:15`

We can simplify further by dividing both 6 and 15 by 3.

`rArr(6÷3):(15÷3)=2:5larr" in simplest form"`

A ratio can also be expressed as a fraction and simplified by 'scoring' out the number and replacing it by the value after division.

`rArr30:75=30/75=cancel(30)^6/cancel(75)^(15)=6/15=cancel(6)^2/cancel(15)^5=2/5`