The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

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 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.

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.