Question

How do you subtract `\frac { 27} { 13} - \frac { 1} { 4}`?

Answer 1

`27/13-1/4=95/52`

Explanation:

To find:

`27/13-1/4`

Multiples of 13 are `13,26,39,52,65`
Multiples of 4 are `4,8,12,16,20,24,28,32,36,40,44,48,52,56,60`

The common multiples of 13 and 4 are
`52,...`

The least common multiple of 13 and 4 is 52

`27/13=(27xx4)/(13xx4)=108/52`

`1/4=(1xx13)/(4xx13)=13/52`

Hence,

`27/13-1/4=108/52-13/52`

The denominator is common.

`27/13-1/4=(108-13)/52`

`27/13-1/4=95/52`

Answer 2

Find a common denominator multiply by the factors to make the two fractions equal then subtract them and divide out any resulting common factors.

Explanation:

13 is prime so there are no common factors between 13 and 4. The common denominator will be the product of 13 and 4

`13 xx 4 = 52`

`( 27 xx 4) / (13 xx 4) - ( 1 xx 13 )/( 4 xx 13)` this gives

`108 /52 - 13/52` Subtracting

`95 /52` There are no common factors between 95 and 52.

Dividing by 52 changes the improper fraction to a mixed number.

`95/52 = 1 43/52`