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

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{50}{100} \) = \( \frac{50 x 25}{100} \) = \( \frac{1250}{100} \) = 12 shots

The center makes 30% 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 = \( \frac{12}{\frac{30}{100}} \) = 12 x \( \frac{100}{30} \) = \( \frac{12 x 100}{30} \) = \( \frac{1200}{30} \) = 40 shots

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

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $900
i = 0.02 x $900
i = $18

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.