How do I add two fractions? (plus example)

Adding (and subtracting) fractions is more difficult than multiplying them because we need to make sure that the denominators (bottom numbers) are equal in both fractions.

To do this, we may need to change the way we have written the fractions (without actually changing the fractions themselves).

Given the problem

(a/b) + (c/d),

we need to ensure that the denominators are equal.

To do this:

- multiply the top and bottom of the left hand side fraction by b

- multiply the top and bottom of the right hand side fraction by d

(Because we multiply the top AND bottom of the fraction, we essentially still have the same fraction, just written in a different way.)

We now have 

(ad/bd) + (cb/bd).

The denominators are now equal, so we can simply rewrite this as

(ad+cb)/bd, which is our final answer.

 

 

Example: Find (3/4) + (2/5).

We need to 

- multiply top and bottom of left fraction by 5

- multiply top and bottom of right fraction by 4

This gives

((3 x 5) / (4 x 5) )    +    ((2 x 4) / (4 x 5))

which is equal to 

(15/20) + (8/20).

We can now add the fractions (only add the top numbers together!) to get the answer,

23/20.