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.

To multiply terms with the same base, multiply the coefficients and add the exponents. To divide terms with the same base, divide the coefficients and subtract the exponents. For example, 3x² x 2x² = 6x⁴ and \({8x^5 \over 4x^2} \) = 2x^(5-2) = 2x³.

To multiply fractions, multiply the numerators together and then multiply the denominators together. To divide fractions, invert the second fraction (get the reciprocal) and multiply it by the first.

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.

Fractions are generally presented with the numerator and denominator as small as is possible meaning there is no number, except one, that can be divided evenly into both the numerator and the denominator. To reduce a fraction to lowest terms, divide the numerator and denominator by their greatest common factor (GCF).