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 divide fractions, invert the second fraction and then multiply:

\( \frac{3}{8} \) ÷ \( \frac{1}{6} \) = \( \frac{3}{8} \) x \( \frac{6}{1} \)

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

\( \frac{3}{8} \) x \( \frac{6}{1} \) = \( \frac{3 x 6}{8 x 1} \) = \( \frac{18}{8} \) = 2\(\frac{1}{4}\)

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

41,000 fans x \( \frac{3}{4} \) = \( \frac{123000}{4} \) = 30,750 fans.

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

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.