The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

3 + (5 + 3) ÷ 4 x 2 - 3²
P: 3 + (8) ÷ 4 x 2 - 3²
E: 3 + 8 ÷ 4 x 2 - 9
MD: 3 + \( \frac{8}{4} \) x 2 - 9
MD: 3 + \( \frac{16}{4} \) - 9
AS: \( \frac{12}{4} \) + \( \frac{16}{4} \) - 9
AS: \( \frac{28}{4} \) - 9
AS: \( \frac{28 - 36}{4} \)
\( \frac{-8}{4} \)
-2

1

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 12 workers at the company now and that's enough to staff 4 crews so there are \( \frac{12}{4} \) = 3 workers on a crew. 8 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 8 x 3 = 24 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 24 - 12 = 12 new staff for the busy season.

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{6} \) ÷ \( \frac{3}{5} \) = \( \frac{2}{6} \) x \( \frac{5}{3} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{6} \) x \( \frac{5}{3} \) = \( \frac{2 x 5}{6 x 3} \) = \( \frac{10}{18} \) = \(\frac{5}{9}\)