The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{45}{100} \) = \( \frac{45 x 20}{100} \) = \( \frac{900}{100} \) = 9 shots

The center makes 35% 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 = \( \frac{9}{\frac{35}{100}} \) = 9 x \( \frac{100}{35} \) = \( \frac{9 x 100}{35} \) = \( \frac{900}{35} \) = 26 shots

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

April scored 95% on the test meaning she earned 95% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.95 = 114 points. Each question is worth 2 points so she got \( \frac{114}{2} \) = 57 questions right.

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.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).