# How do you evaluate \frac { 8} { 5} + \frac { 2} { 9} =?

Mar 4, 2018

See a solution process below:

#### Explanation:

To evaluate this expression the fractions must be over common denominators. We can multiply each fraction by the appropriate form of $1$ so we can add the fractions:

$\frac{8}{5} + \frac{2}{9} \implies$

$\left(\frac{9}{9} \times \frac{8}{5}\right) + \left(\frac{5}{5} \times \frac{2}{9}\right) \implies$

$\frac{9 \times 8}{9 \times 5} + \frac{5 \times 2}{5 \times 9} \implies$

$\frac{72}{45} + \frac{10}{45}$

We can now add the numerators of the two fractions over the common denominator:

$\frac{72 + 10}{45} \implies$

$\frac{82}{45}$

If necessary, we can convert this improper fraction into a mixed number:

$\frac{82}{45} = \frac{45 + 37}{45} = \frac{45}{45} + \frac{37}{45} = 1 + \frac{37}{45} = 1 \frac{37}{45}$

$\frac{8}{5} + \frac{2}{9} = \frac{82}{45}$

Or

$\frac{8}{5} + \frac{2}{9} = 1 \frac{37}{45}$

Mar 4, 2018

$\frac{82}{45}$

#### Explanation:

It's easier to evaluate fractions when you have the same denominator for each, so let's do that first.

The common base between 5 and 9 is 45

$\frac{8}{5} \cdot 9 + \frac{2}{9} \cdot 5$

$= \frac{72}{45} + \frac{10}{45}$

Note: When multiplying with fractions, make sure to multiply both numerator and denominator.

So now we see $\frac{72}{45} + \frac{10}{45}$ , we can add 72 and 10 together to get:

$\frac{82}{45}$

Since there is no common factor that can be used to reduce the fraction, the answer is $\frac{82}{45}$