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.

By buying two shirts, Charlie will save $14 x \( \frac{20}{100} \) = \( \frac{$14 x 20}{100} \) = \( \frac{$280}{100} \) = $2.80 on the second shirt.

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 16 workers at the company now and that's enough to staff 4 crews so there are \( \frac{16}{4} \) = 4 workers on a crew. 7 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 7 x 4 = 28 total workers to staff the crews during the busy season. The company already employs 16 workers so they need to add 28 - 16 = 12 new staff for the busy season.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{49}{64}} \)
\( \frac{\sqrt{49}}{\sqrt{64}} \)
\( \frac{\sqrt{7^2}}{\sqrt{8^2}} \)
\(\frac{7}{8}\)

The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.