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

\( \frac{1}{7} \) x \( \frac{4}{7} \) = \( \frac{1 x 4}{7 x 7} \) = \( \frac{4}{49} \) = \(\frac{4}{49}\)

The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. 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 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

If a single cook can bake 5 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 5 x 4 = 20 large cakes during that time. 35 large cakes are needed for the party so \( \frac{35}{20} \) = 1\(\frac{3}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 13 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 13 x 4 = 52 small cakes during that time. 350 small cakes are needed for the party so \( \frac{350}{52} \) = 6\(\frac{19}{26}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 7 = 9 cooks.

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:

\( \frac{-2b^5}{b^4} \)
\( \frac{-2}{1} \) b^{(5 - 4)}
-2b

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

38,000 fans x \( \frac{3}{4} \) = \( \frac{114000}{4} \) = 28,500 fans.