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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

The greatest common factor (GCF) is the greatest factor that divides two integers.

The equation for this sequence is:

a_n = a_n-1 + 9

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 9
a₆ = 37 + 9
a₆ = 46

By buying two shirts, Roger will save $38 x \( \frac{20}{100} \) = \( \frac{$38 x 20}{100} \) = \( \frac{$760}{100} \) = $7.60 on the second shirt.

So, his total cost will be
$38.00 + ($38.00 - $7.60)
$38.00 + $30.40
$68.40

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

\( \frac{1}{5} \) ÷ \( \frac{3}{7} \) = \( \frac{1}{5} \) x \( \frac{7}{3} \)

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

\( \frac{1}{5} \) x \( \frac{7}{3} \) = \( \frac{1 x 7}{5 x 3} \) = \( \frac{7}{15} \) = \(\frac{7}{15}\)