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 terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-5a^8}{2a^2} \)
\( \frac{-5}{2} \) a^{(8 - 2)}
-2\(\frac{1}{2}\)a⁶

By buying two shirts, Monty will save $31 x \( \frac{50}{100} \) = \( \frac{$31 x 50}{100} \) = \( \frac{$1550}{100} \) = $15.50 on the second shirt.

To multiply terms with radicals, multiply the coefficients and radicands separately:

5\( \sqrt{9} \) x 2\( \sqrt{2} \)
(5 x 2)\( \sqrt{9 \times 2} \)
10\( \sqrt{18} \)

Now we need to simplify the radical:

10\( \sqrt{18} \)
10\( \sqrt{2 \times 9} \)
10\( \sqrt{2 \times 3^2} \)
(10)(3)\( \sqrt{2} \)
30\( \sqrt{2} \)

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.