A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

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

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:

\( \sqrt{\frac{64}{16}} \)
\( \frac{\sqrt{64}}{\sqrt{16}} \)
\( \frac{\sqrt{8^2}}{\sqrt{4^2}} \)
\( \frac{8}{4} \)
2

The number of students taking German or Spanish is 15 + 12 = 27. Of that group of 27, 9 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 27 - 9 = 18 who are taking at least one language. 27 - 18 = 9 students who are not taking either language.