Fractions must share a common denominator in order to be added or subtracted. The common denominator is the least common multiple of all the denominators.

To add or subtract radicals, the degree and radicand must be the same. For example, \(2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}\) but \(2\sqrt{2} + 2\sqrt{3}\) cannot be added because they have different radicands.

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.

An exponent (cb^e) consists of coefficient (c) and a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

A negative exponent indicates the number of times that the base is divided by itself. To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal: \(b^{-e} = { 1 \over b^e }\). For example, \(3^{-2} = {1 \over 3^2} = {1 \over 9}\)

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

A proportion is a statement that two ratios are equal: a:b = c:d, \({a \over b} = {c \over d}\). To solve proportions with a variable term, cross-multiply: \({a \over 8} = {3 \over 6} \), 6a = 24, a = 4.

A rate is a ratio that compares two related quantities. Common rates are speed = \({distance \over time}\), flow = \({amount \over time}\), and defect = \({errors \over units}\).

A sequence is a group of ordered numbers. An arithmetic sequence is a sequence in which each successive number is equal to the number before it plus some constant number.