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 simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{60} \) = \( \frac{\frac{16}{4}}{\frac{60}{4}} \) = \( \frac{4}{15} \)

If 71% of the town's 42,000 voters cast ballots the number of votes cast is:

(\( \frac{71}{100} \)) x 42,000 = \( \frac{2,982,000}{100} \) = 29,820

The mayor got 75% of the votes cast which is:

(\( \frac{75}{100} \)) x 29,820 = \( \frac{2,236,500}{100} \) = 22,365 votes.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Diane scored 76% on the test meaning she earned 76% of the possible points on the test. There were 320 possible points on the test so she earned 320 x 0.76 = 244 points. Each question is worth 4 points so she got \( \frac{244}{4} \) = 61 questions right.