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

Mar 2, 2018

See below.

#### Explanation:

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 $2 \frac{1}{2}$.

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

$2 \frac{1}{\textcolor{red}{2}}$

by the whole number

$\textcolor{b l u e}{2} \frac{1}{\textcolor{red}{2}}$

to get the equation $\textcolor{b l u e}{2} \cdot \textcolor{red}{2}$, which equals $4$.

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

$\textcolor{g r e e n}{4}$

to the numerator

$2 \frac{\textcolor{t e a l}{1}}{2}$

getting the equation $\textcolor{g r e e n}{4} + \textcolor{t e a l}{1}$, which equals $5$. Now that 5, becomes our numerator, but the denominater stays the same, which leaves us with the improper fraction of $\frac{5}{2}$.

You can now do the same thing with the other fraction, resulting in the equation $\frac{5}{2} + \frac{8}{3}$.

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 $2 \cdot 3 = 6$ and $3 \cdot 2 = 6$.

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

$\frac{5 \cdot 3}{2 \cdot 3}$

This results in the fraction of $\frac{15}{6}$.

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.

$\frac{8 \cdot 2}{3 \cdot 2}$

This results in the fraction of $\frac{16}{6}$.

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 $\frac{31}{6}$.