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:

\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60

If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 29 large cakes are needed for the party so \( \frac{29}{16} \) = 1\(\frac{13}{16}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 19 x 4 = 76 small cakes during that time. 370 small cakes are needed for the party so \( \frac{370}{76} \) = 4\(\frac{33}{38}\) 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 + 5 = 7 cooks.

If 64% of the town's 40,000 voters cast ballots the number of votes cast is:

(\( \frac{64}{100} \)) x 40,000 = \( \frac{2,560,000}{100} \) = 25,600

The mayor got 66% of the votes cast which is:

(\( \frac{66}{100} \)) x 25,600 = \( \frac{1,689,600}{100} \) = 16,896 votes.

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 $1,300
i = 0.05 x $1,300
i = $65

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

\( \frac{4}{5} \) x \( \frac{1}{5} \) = \( \frac{4 x 1}{5 x 5} \) = \( \frac{4}{25} \) = \(\frac{4}{25}\)