# How do you simplify 7/8 - (4/5 + 1 3/4)?

Apr 20, 2018

$- \frac{67}{40}$

#### Explanation:

There is a mixed number in the expression. Let's make that an improper fraction:
$\setminus \textcolor{red}{1 \left(\frac{3}{4}\right) = \frac{4}{4} + \frac{3}{4} = \frac{7}{4}}$
$\setminus \therefore \frac{7}{8} - \left(\frac{4}{5} + \setminus \textcolor{red}{\frac{7}{4}}\right)$
Now make everything common denominator. That means LCM of 8, 5, 4 (which is 40).

Thus:
$\frac{7}{8} \left(\frac{5}{5}\right) - \left[\frac{4}{5} \left(\frac{8}{8}\right) + \frac{7}{4} \left(\frac{10}{10}\right)\right]$

$\frac{7 \left(5\right) - \left[4 \left(8\right) + 7 \left(10\right)\right]}{40} = \frac{35 - \left(32 + 70\right)}{40}$

Now we can apply PEMDAS.

• Parentheses first: $32 + 70 = 102$
$\frac{35 - 102}{40}$
• Now subtract:
$- \frac{67}{40}$