how do you add `2\frac { 1} { 2} + 2\frac { 2} { 3}`?

First, the numbers must be changed to an improper fraction, meaning that there are no whole numbers. I am going to demonstrate how to do this with the `2 1/2`.

Step 1: To start off, you must multiply the denominater

`2 1/color(red)2`

by the whole number

`color(blue)2 1/color(red)2`

to get the equation `color(blue)2*color(red)2`, which equals `4`.

Step 2: Now, you must add the number we just got

`color(green)4`

to the numerator

`2 color(teal)1/2`

getting the equation `color(green)4+color(teal)1`, which equals `5`. Now that 5, becomes our numerator, but the denominater stays the same, which leaves us with the improper fraction of `5/2`.

You can now do the same thing with the other fraction, resulting in the equation `5/2+8/3`.

The next step to solve this problem is to change the denominators so that they are common, or the same number. The first common number they have, is `6`, since `2*3=6` and `3*2=6`.

Since 2 (the denominater) has to be multiplied by 3 to get to 6, 5 (the numerator) must also be multiplied by 3.

`(5*3)/ (2*3)`

This results in the fraction of `15/6`.

Now, in the other fraction, since 3 (denominater) must be multiplied by 2 to get 6, 8 (the numerator) must also be multiplied by 2.

`(8*2)/(3*2)`

This results in the fraction of `16/6`.

Now that the denominaters are the same, the numerators must be added to complete the problem.

`15+16=31`

That is your new numerator, which is put over the common denominater of 6, to get `31/6`.