Question

How do you simplify `\frac{1}{4} + \frac{3}{10} - \frac{2}{5}`?

Answer 1

`1/4+3/10-2/5=3/20`

Explanation:

This is addition and subtraction together of three fractions whose denominators are `4`, `10` and `5`.

To solve any such question what we need is Least Common Multiple of denominators.

For this let us list out denominators as product of their rime factors.

`4=2xx2`
`10=2xx5`
`5=5`

As `2` occurs maximum two times and `5` occurs maximum once only, LCM is `2xx2xx5=20`. We now write fractions with common denominator as `20`.

Now `1/4+3/10-2/5`

= `(1xx5)/(4xx5)+(3xx2)/(10xx2)-(2xx4)/(5xx4)`

= `5/20+6/20-8/20`

= `(5+6-8)/20`

= `3/20`