The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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

-3y⁶ - 9y⁶
(-3 - 9)y⁶
-12y⁶

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

\( \frac{2}{7} \) ÷ \( \frac{4}{7} \) = \( \frac{2}{7} \) x \( \frac{7}{4} \)

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

\( \frac{2}{7} \) x \( \frac{7}{4} \) = \( \frac{2 x 7}{7 x 4} \) = \( \frac{14}{28} \) = \(\frac{1}{2}\)

By buying two shirts, Roger will save $42 x \( \frac{25}{100} \) = \( \frac{$42 x 25}{100} \) = \( \frac{$1050}{100} \) = $10.50 on the second shirt.

So, his total cost will be
$42.00 + ($42.00 - $10.50)
$42.00 + $31.50
$73.50

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{3!} \)
\( \frac{2 \times 1}{3 \times 2 \times 1} \)
\( \frac{1}{3} \)
\( \frac{1}{3} \)