If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 20 large cakes are needed for the party so \( \frac{20}{12} \) = 1\(\frac{2}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 20 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 20 x 4 = 80 small cakes during that time. 490 small cakes are needed for the party so \( \frac{490}{80} \) = 6\(\frac{1}{8}\) 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.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 30mph \times 7h \)
210 miles

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

\( \frac{4}{9} \) ÷ \( \frac{4}{9} \) = \( \frac{4}{9} \) x \( \frac{9}{4} \)

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

\( \frac{4}{9} \) x \( \frac{9}{4} \) = \( \frac{4 x 9}{9 x 4} \) = \( \frac{36}{36} \) = 1

If 44% of the town's 22,000 voters cast ballots the number of votes cast is:

(\( \frac{44}{100} \)) x 22,000 = \( \frac{968,000}{100} \) = 9,680

The mayor got 52% of the votes cast which is:

(\( \frac{52}{100} \)) x 9,680 = \( \frac{503,360}{100} \) = 5,034 votes.

To fill a 25 gallon tank exactly halfway you'll need 12\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{12\frac{1}{2} \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 5