The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

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 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 3 workers on a crew. 7 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 7 x 3 = 21 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 21 - 6 = 15 new staff for the busy season.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{9 x 5}{9 x 5} \) - \( \frac{7 x 3}{15 x 3} \)

\( \frac{45}{45} \) - \( \frac{21}{45} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{45 - 21}{45} \) = \( \frac{24}{45} \) = \(\frac{8}{15}\)