Question

What is the sum of `1/9, 2/3,` and `5/18`?

Answer 1

`1 1/18`

Explanation:

These fractions have different denominators (bottom numbers) so you can't add them directly. You have to change the denominators on some of them to make it easier. It has to be a common multiple, so lets choose `18` as our target.

To get `1/9` to change to `"something"/18`, you have to multiply the bottom by `2`, since `2 * 9 = 18`. However, you also have to keep it the same value, so multiply the top by `2` as well.

`1/9 * 2/2 = (1*2)/(9*2) = 2/18`

Do the same thing with `2/3`, though you have to multiply this by `6/6` to get `3 * 6 = 18` on the bottom.

`2/3 * 6/6 = (2*6)/(3*6) = 12/18`

Now you can add them up easily

`1/9 + 2/3 + 5/18 = 2/18 + 12/18 + 5/18`

`= (2 + 12 + 5)/18 = 19/18 = 1 1/18`