# How do you add \frac { 7} { - 2} + \frac { 2} { 5}?

Aug 11, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$- \frac{7}{2} + \frac{2}{5}$

Now, we need to put the fractions over a common denominator by multiplying each fraction by the appropriate form of $1$:

$\left(\frac{5}{5} \times - \frac{7}{2}\right) + \left(\frac{2}{2} \times \frac{2}{5}\right) \implies$

$\frac{5 \times - 7}{5 \times 2} + \frac{2 \times 2}{2 \times 5}$

$- \frac{35}{10} + \frac{4}{10}$

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

$\frac{- 35 + 4}{10} \implies$

$- \frac{31}{10}$

Aug 11, 2017

$- \frac{31}{10}$

#### Explanation:

Find the LCD:

We can write out the factors of both $2$ and $5$ to determine this.

$2 : 2 , 4 , 6 , 8 , \textcolor{red}{10}$
$5 : 5 , \textcolor{red}{10} , 15$

The LCD is thus $10$, therefore:

$\left[- \frac{7}{2} \left(\frac{5}{5}\right)\right] + \left[\frac{2}{5} \left(\frac{2}{2}\right)\right] \leftarrow$ We manipulate the fractions in such a way that the denominator is 10

$- \frac{35}{10} + \frac{4}{10}$

$= - \frac{31}{10}$