# How do you simplify 5 1/2 + 2 7/9?

May 21, 2018

See a solution process below:

#### Explanation:

First, convert each number from a mixed number into an improper fraction:

$5 \frac{1}{2} = 5 + \frac{1}{2} = \left(\frac{2}{2} \times 5\right) + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{10 + 1}{2} = \frac{11}{2}$

$2 \frac{7}{9} = 2 + \frac{7}{9} = \left(\frac{9}{9} \times 2\right) + \frac{7}{9} = \frac{18}{9} + \frac{7}{9} = \frac{18 + 7}{9} = \frac{25}{9}$

To add fractions they must be over a common denominator:

$\frac{11}{2} = \frac{11}{2} \times \frac{9}{9} = \frac{11 \times 9}{2 \times 9} = \frac{99}{18}$

$\frac{25}{9} = \frac{25}{9} \times \frac{2}{2} = \frac{25 \times 2}{9 \times 2} = \frac{50}{18}$

We can now rewrite and add the numerators over the common denominator as:

$\frac{99}{18} + \frac{50}{18} = \frac{99 + 50}{18} = \frac{149}{18}$

If necessary, we can covert this to a mixed number as:

$\frac{149}{18} = \frac{144 + 5}{18} = \frac{144}{18} + \frac{5}{18} = 8 + \frac{5}{18} = 8 \frac{5}{18}$