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

If 64% of the town's 24,000 voters cast ballots the number of votes cast is:

(\( \frac{64}{100} \)) x 24,000 = \( \frac{1,536,000}{100} \) = 15,360

The mayor got 78% of the votes cast which is:

(\( \frac{78}{100} \)) x 15,360 = \( \frac{1,198,080}{100} \) = 11,981 votes.

The greatest common factor (GCF) is the greatest factor that divides two integers.

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 ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

32,000 fans x \( \frac{2}{3} \) = \( \frac{64000}{3} \) = 21,333 fans.