The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

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:

\( \frac{2z^9}{6z^2} \)
\( \frac{2}{6} \) z^{(9 - 2)}
\(\frac{1}{3}\)z⁷

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

By buying two shirts, Bob will save $13 x \( \frac{45}{100} \) = \( \frac{$13 x 45}{100} \) = \( \frac{$585}{100} \) = $5.85 on the second shirt.

So, his total cost will be
$13.00 + ($13.00 - $5.85)
$13.00 + $7.15
$20.15