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.

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.

A number with an exponent (b^e) consists of 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).

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{8} \) x \( \frac{1}{9} \) = \( \frac{2 x 1}{8 x 9} \) = \( \frac{2}{72} \) = \(\frac{1}{36}\)

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{5} \) ÷ \( \frac{3}{9} \) = \( \frac{2}{5} \) x \( \frac{9}{3} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{5} \) x \( \frac{9}{3} \) = \( \frac{2 x 9}{5 x 3} \) = \( \frac{18}{15} \) = 1\(\frac{1}{5}\)