# How do you add #3/4# and #5/9#?

##### 2 Answers

See the entire explanation below:

#### Explanation:

To add fractions with different denominators we need to first convert each fraction to have a common denominator.

To do this we can't change the value of either fraction and therefore need to multiply it by some form of

In the example you provided,

Now that the two fractions are over a common denominator we can add the numerators.

Hope this helps.

Explanation given using your example

#### Explanation:

A fraction's structure is

The word 'count' speaks for itself.

The word 'size indicator' is a number indicating how many of what you are counting it takes to make a whole 1 of something.

It takes 2 of

It takes 3 of

it takes 45 of

By the way; not normally done but you may write whole numbers the same way. That is, for example, 8 may be written as

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

It does not matter what you make the bottom numbers as long as they are the same.

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way a number looks without changing its value.

Now that the size indicators (denominators) are the same you may directly add the counts giving:

But 47 can be written as 36 + 11 so we can split this as:

But