Question

How do you simplify `1/4 + 1/5`?

Answer 1

`:. 9/20`

Explanation:

To simplify `1/4 + 1/5`, we need to make both of the fractions as the same base.

`=> (1)/4 + 1/5`

`=> 5/20 + 4/20`

`:. 9/20`

Answer 2

Rewrite each fraction so they have the same denominator.

Explanation:

Least Common Multiple (LCM) Route:

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28
Multiples of 5 are 5, 10 ,15, 20, 25, 30
The Smallest Multiple that 4 and 5 have in common is 20.

Change `1/4` to a denominator of 20 by multiplying top and bottom by 5: `1/4 * 5/5 = 5/20`.

Change `1/5` to a denominator of 20 by multiplying top and bottom by 4: `1/5 * 4/4 = 4/20`.

Now Add the 2 new fractions together and simplify if possible:
`5/20 + 4/20 = 9/20`

Cross Multiply Route:
`a/c + b/d = (ad + bc)/(cd)`

`1/4 + 1/5 = (1*5 + 1*4)/(4*5) = (5 + 4)/20 = 9/20`

Remember to always Simplify if possible.