# What is one-half of one and two thirds?

Dec 19, 2016

$r = \frac{2}{3}$

#### Explanation:

We can rewrite this problem as

What is $\frac{1}{2}$ of $1 \frac{1}{3}$?

When dealing with fractions the word "of" means "times" or "to multiply".

Also, let's call the value we are looking for $r$:

So we can again rewrite this as:

$r = \frac{1}{2} \times 1 \frac{1}{3}$

To complete this problem we need to convert the mixed fraction to an improper fraction. We do this by multiplying the integer by the proper form of $1$ and then adding it to the fraction:

$r = \frac{1}{2} \times \left(\left(\textcolor{red}{\frac{3}{3}} \times 1\right) + \frac{1}{3}\right)$

$r = \frac{1}{2} \times \left(\textcolor{red}{\frac{3}{3}} + \frac{1}{3}\right)$

$r = \frac{1}{2} \times \frac{3 + 1}{3}$

$r = \frac{1}{2} \times \frac{4}{3}$

$r = \frac{1 \times 4}{2 \times 3}$

$r = \frac{4}{6}$

$r = \frac{2 \times 2}{2 \times 3}$

$r = \left(\frac{2}{2}\right) \times \left(\frac{2}{3}\right)$

$r = 1 \times \frac{2}{3}$

$r = \frac{2}{3}$