The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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).

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.

The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 16 are [1, 2, 4, 8, 16]. They share 5 factors [1, 2, 4, 8, 16] making 16 the greatest factor 32 and 16 have in common.

April scored 91% on the test meaning she earned 91% of the possible points on the test. There were 400 possible points on the test so she earned 400 x 0.91 = 364 points. Each question is worth 4 points so she got \( \frac{364}{4} \) = 91 questions right.