# I have 2/3 0f 4 1/3 how much more do i need to equal 4 1/3 ?

May 24, 2018

$1 \frac{4}{9}$

#### Explanation:

First, find out what $\frac{2}{3}$ of $4 \frac{1}{3}$ is.

$\frac{2}{3} \times 4 \frac{1}{3} = \frac{2}{3} \times \frac{13}{3} = \frac{26}{9} = 2 \frac{8}{9}$

Next, find the difference.

$4 \frac{1}{3} - 2 \frac{8}{9} = 4 \frac{3}{9} - 2 \frac{8}{9} = 1 \frac{4}{9}$

$1 \frac{4}{9}$

#### Explanation:

Let's first work this through with an easier set of numbers.

Let's say that there is a series of books you are reading. There are 3 books in the set. You have $\frac{2}{3}$ already - how many more books do we need to get to 3 books?

We can do this a few ways, but I'll point out that if we already have $\frac{2}{3}$ of the books, we need the other $\frac{1}{3}$. With our books, that's:

$3 \times \frac{1}{3} = \frac{3}{3} = 1$ book more.

And so now to the question - we want $4 \frac{1}{3}$ in total and we already have $\frac{2}{3}$ of that. So we need the other $\frac{1}{3}$. We can calculate it this way (I'll convert the mixed number to an improper fraction first):

$4 \frac{1}{3} \times \frac{1}{3} = \frac{13}{3} \times \frac{1}{3} = \frac{13}{9} = 1 \frac{4}{9}$

So we already have $2 \frac{8}{9}$ and once we have the other $1 \frac{4}{9}$, we'll indeed have:

$2 \frac{8}{9} + 1 \frac{4}{9} = 3 \frac{12}{9} = 4 \frac{3}{9} = 4 \frac{1}{3}$