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. 9 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 9 x 3 = 27 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 27 - 12 = 15 new staff for the busy season.

You have 5 out of the total of 250 raffle tickets sold so you have a (\( \frac{5}{250} \)) x 100 = \( \frac{5 \times 100}{250} \) = \( \frac{500}{250} \) = 2% chance to win the raffle.

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

The number of students taking German or Spanish is 8 + 11 = 19. Of that group of 19, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 19 - 2 = 17 who are taking at least one language. 23 - 17 = 6 students who are not taking either language.

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.