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

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

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (5 + 3) ÷ 2 x 5 - 2²
P: 4 + (8) ÷ 2 x 5 - 2²
E: 4 + 8 ÷ 2 x 5 - 4
MD: 4 + \( \frac{8}{2} \) x 5 - 4
MD: 4 + \( \frac{40}{2} \) - 4
AS: \( \frac{8}{2} \) + \( \frac{40}{2} \) - 4
AS: \( \frac{48}{2} \) - 4
AS: \( \frac{48 - 8}{2} \)
\( \frac{40}{2} \)
20

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 \( \frac{\text{% made}}{100} \) = 15 x \( \frac{30}{100} \) = \( \frac{30 x 15}{100} \) = \( \frac{450}{100} \) = 4 shots

The center makes 25% 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 = \( \frac{4}{\frac{25}{100}} \) = 4 x \( \frac{100}{25} \) = \( \frac{4 x 100}{25} \) = \( \frac{400}{25} \) = 16 shots

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