Question

How do you simplify `30/80 + 40/100`?

Answer 1

Find a common denominator and divide out common factors.

Explanation:

`80 = 2 xx 2 xx2 xx2 xx 5`
`30 = 3 xx2 xx 5`

The common factors of `2 xx 5` can be divided out leaving

`30/80 = 3/8`

`100 = 2xx 2 xx xx 5 xx 5`
`40 = 2 xx 2 xx 2 xx 5`

The common factors of `2 xx 5` can be divided out leaving

`40/100 = 4/10`

8 and 10 have a common multiply of 40

`8 = 2 xx 2 xx2`
`10 = 2 xx 5`

The unique factors are `2 xx 2 xx 2 xx 5 = 40`
( the factor of 2 in ten is a repeat of the 3 factors of 2 in 8)

Now change both fractions to a faction with a denominator of 40

`(3 xx 5)/( 8 xx 5) + (4 xx 4)/( 10xx 4) = 15/40 + 16 /40`

These fractions can be added giving

`15/40 + 16/40 = 31/40`

there are no common factors between 31 and 40 so `31/40` is the final answer.