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 absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

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:

\( \frac{4x^7}{8x^4} \)
\( \frac{4}{8} \) x^{(7 - 4)}
\(\frac{1}{2}\)x³

By buying two shirts, Roger will save $33 x \( \frac{50}{100} \) = \( \frac{$33 x 50}{100} \) = \( \frac{$1650}{100} \) = $16.50 on the second shirt.

So, his total cost will be
$33.00 + ($33.00 - $16.50)
$33.00 + $16.50
$49.50