# Question #a69d2

Jan 30, 2017

$\frac{247}{20} = 12 \frac{7}{20} = 12.35$

#### Explanation:

Which answer you choose depends on whether you want to use only decimals or only fractions.

If you use fractions, you must first restate the problem using only fractions.

$\left(- \frac{1}{4} + 3\right) + \left(- \frac{1}{5} + 5\right) - \left(- \frac{5}{2} - 2 \frac{3}{10}\right)$

We can restate this, writing the mixed fraction $2 \frac{3}{10}$ as the improper fraction $\frac{23}{10}$.

$\left(- \frac{1}{4} + 3\right) + \left(- \frac{1}{5} + 5\right) - \left(- \frac{5}{2} - \frac{23}{10}\right)$

Inside each of the parentheses, add or subtract the fractions.

$\left(\frac{11}{4}\right) + \left(\frac{24}{5}\right) - \left(- \frac{48}{10}\right)$

Get rid of the negatives by applying the principle that a negative times a negative is a positive.

$\left(\frac{11}{4}\right) + \left(\frac{24}{5}\right) + \left(\frac{48}{10}\right)$

Notice the greatest common denominator is $20$ because $10 \times 2 = 20$, $5 \times 4 = 20$, and $4 \times 5 = 20$. This gives

$\left(\frac{11 \times 5}{4 \times 5}\right) + \left(\frac{24 \times 4}{5 \times 4}\right) + \left(\frac{48 \times 2}{10 \times 2}\right)$

Or

$\frac{55}{20} + \frac{96}{20} + \frac{96}{20} = \frac{247}{20} = 12 \frac{7}{20} = \frac{12}{35}$