# How do you evaluate 2\frac{1}{3]-1\frac{1}{2}?

Mar 13, 2018

#### Answer:

$\frac{5}{6}$

#### Explanation:

Step 1: You have to Multiply the $3$ and the $2$ together and then add the $1$ and that would all be over $3$. Then you get

$2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$

Step 2: You do the same thing which is $2$ times $1$ and then add $1$ and that would be all over $2$. Then you get

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

Step 3: Combine together as

$\frac{7}{3} - \frac{3}{2}$

Next, you have to have a common denominator of $6$. $\frac{7}{3}$ times $2$ both top and bottom. Then $\frac{3}{2}$ is going to be times $3$ both top and bottom.

$\frac{7}{3} \times \frac{2}{2} = \frac{7 \times 2}{3 \times 2}$

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

Next, multiply top and bottom fractions individually, which gets to be

$\frac{14}{6} - \frac{9}{6} = \frac{14 - 9}{6} = \frac{5}{6}$

Mar 13, 2018

#### Answer:

$\frac{5}{6}$

#### Explanation:

First, change the mixed fractions into improper fractions by multiplying the whole number by the denominator and then adding the numerator.

$2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$

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

Next, find a common denominator and then multiply the top and the bottom by the same number.

$\frac{7}{3} \times \frac{2}{2} = \frac{14}{6}$

$\frac{3}{2} \times \frac{3}{3} = \frac{9}{6}$

Subtract the numerators.

$14 - 9 = 5$

Make sure to keep the denominator.

$\frac{5}{6}$