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.

A factor is a positive integer that divides evenly into a given number. The factors of 8 are 1, 2, 4, and 8. A multiple is a number that is the product of that number and an integer. The multiples of 8 are 0, 8, 16, 24, ...

Percentages are ratios of an amount compared to 100. The percent change of an old to new value is equal to 100% x \({ new - old \over old }\).

Ratios relate one quantity to another and are presented using a colon or as a fraction. For example, 2:3 or \({2 \over 3}\) would be the ratio of red to green marbles if a jar contained two red marbles for every three green marbles.

The radicand of a simplified radical has no perfect square factors. A perfect square is the product of a number multiplied by itself (squared). To simplify a radical, factor out the perfect squares by recognizing that \(\sqrt{a^2} = a\). For example, \(\sqrt{64} = \sqrt{16 \times 4} = \sqrt{4^2 \times 2^2} = 4 \times 2 = 8\).