# How do you evaluate (- 4\frac { 1} { 2} ) - 1\frac { 1} { 3}?

Mar 8, 2017

Convert both mixed numbers to improper fractions and add them. The result is $- 5 \frac{5}{6}$

#### Explanation:

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

$- 1 \frac{1}{3} = - \frac{4}{3}$

Now to subtract the two fractions, it is necessary to find a common denominator. Multiply both denominators to get the common denominator of $6$, then make equivalent fractions.

$- \frac{9}{2} \times \frac{3}{3} = - \frac{27}{6}$
$- \frac{4}{3} \times \frac{2}{2} = - \frac{8}{6}$

Now you can add the the negative values of both fractions

$\left(- \frac{27}{6}\right) + \left(- \frac{8}{6}\right) = - \frac{35}{6}$ This is an improper fraction so it is best to convert the the answer to a mixed number.

$- \frac{35}{6} = - 5 \frac{5}{6}$

Mar 11, 2017

$- 5 \frac{5}{6}$

#### Explanation:

$\left(- 4 \frac{1}{2}\right) - 1 \frac{1}{3}$

the fractions in each mixed number should have a common denominator.

$2 \cdot 3 = 6$

$\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}$

$\frac{1}{3} = \frac{1 \cdot 2}{3 \cdot 2} = \frac{2}{6}$

now we have $\left(- 4 \frac{3}{6}\right) - 1 \frac{2}{6}$.

first subtract the whole numbers:

$- 4 - 1 = - 5$

then the fractions:

$- \frac{3}{6} - \frac{2}{6} = - \frac{5}{6}$

$- 5 - \frac{5}{6} = - 5 \frac{5}{6}$
answer: $- 5 \frac{5}{6}$