guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{65}{100} \) = \( \frac{65 x 15}{100} \) = \( \frac{975}{100} \) = 9 shots

The center makes 50% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{9}{\frac{50}{100}} \) = 9 x \( \frac{100}{50} \) = \( \frac{9 x 100}{50} \) = \( \frac{900}{50} \) = 18 shots

to make the same number of shots as the guard and thus score the same number of points.

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:

\( \sqrt{\frac{36}{64}} \)
\( \frac{\sqrt{36}}{\sqrt{64}} \)
\( \frac{\sqrt{6^2}}{\sqrt{8^2}} \)
\(\frac{3}{4}\)

If 77% of the town's 43,000 voters cast ballots the number of votes cast is:

(\( \frac{77}{100} \)) x 43,000 = \( \frac{3,311,000}{100} \) = 33,110

The mayor got 61% of the votes cast which is:

(\( \frac{61}{100} \)) x 33,110 = \( \frac{2,019,710}{100} \) = 20,197 votes.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)