The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.

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

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

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

\( \frac{3}{7} \) x \( \frac{7}{1} \) = \( \frac{3 x 7}{7 x 1} \) = \( \frac{21}{7} \) = 3

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

-9b³ x 5b⁶
(-9 x 5)b^{(3 + 6)}
-45b⁹

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

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $500
i = 0.01 x $500
i = $5