# How do you simplify 9 9/11 + 4 1/2?

Jul 7, 2017

#### Answer:

See a solution process below:

#### Explanation:

First, we need to convert the mixed numbers to improper fractions:

$9 \frac{9}{11} + 4 \frac{1}{2} \implies \left(9 + \frac{9}{11}\right) + \left(4 + \frac{1}{2}\right) \implies$

((11/11 xx 9 + 9/11) + ((2/2 xx 4) + 1/2) =>

$\left(\frac{99}{11} + \frac{9}{11}\right) + \left(\frac{8}{2} + \frac{1}{2}\right) \implies \frac{108}{11} + \frac{9}{2}$

Next, we need to put the fractions over a common denominator so we can add the numerators:

$\left(\frac{2}{2} \times \frac{108}{11}\right) + \left(\frac{11}{11} \times \frac{9}{2}\right) \implies \frac{216}{22} + \frac{99}{22} \implies$

$\frac{315}{22}$

Now, we can convert this improper fraction to a mixed number:

$\frac{308 + 7}{22} \implies \frac{308}{22} + \frac{7}{22} \implies 14 + \frac{7}{22} \implies$

$14 \frac{7}{22}$