To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

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

\( \frac{4 x 2}{2 x 2} \) + \( \frac{5 x 1}{4 x 1} \)

\( \frac{8}{4} \) + \( \frac{5}{4} \)

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

\( \frac{8 + 5}{4} \) = \( \frac{13}{4} \) = 3\(\frac{1}{4}\)

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

7b⁵ + 3b⁵
(7 + 3)b⁵
10b⁵

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

\( \frac{3}{8} \) x \( \frac{4}{6} \) = \( \frac{3 x 4}{8 x 6} \) = \( \frac{12}{48} \) = \(\frac{1}{4}\)

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 4 workers at the company now and that's enough to staff 2 crews so there are \( \frac{4}{2} \) = 2 workers on a crew. 5 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 5 x 2 = 10 total workers to staff the crews during the busy season. The company already employs 4 workers so they need to add 10 - 4 = 6 new staff for the busy season.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.