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.

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

\( \frac{4}{8} \) ÷ \( \frac{4}{9} \) = \( \frac{4}{8} \) x \( \frac{9}{4} \)

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

\( \frac{4}{8} \) x \( \frac{9}{4} \) = \( \frac{4 x 9}{8 x 4} \) = \( \frac{36}{32} \) = 1\(\frac{1}{8}\)

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

5x⁷ + 3x⁷
(5 + 3)x⁷
8x⁷

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 50% the radius (and, consequently, the total area) increases by \( \frac{50\text{%}}{2} \) = 25%

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.