A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

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 8 workers at the company now and that's enough to staff 4 crews so there are \( \frac{8}{4} \) = 2 workers on a crew. 7 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 7 x 2 = 14 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 14 - 8 = 6 new staff for the busy season.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-6a^5}{9a^2} \)
\( \frac{-6}{9} \) a^{(5 - 2)}
-\(\frac{2}{3}\)a³

To subtract these radicals together their radicands must be the same:

8\( \sqrt{75} \) - 5\( \sqrt{3} \)
8\( \sqrt{25 \times 3} \) - 5\( \sqrt{3} \)
8\( \sqrt{5^2 \times 3} \) - 5\( \sqrt{3} \)
(8)(5)\( \sqrt{3} \) - 5\( \sqrt{3} \)
40\( \sqrt{3} \) - 5\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them: