There are 2 4-passenger taxis available so that's 2 x 4 = 8 total seats. There are 10 people needing transportation leaving 10 - 8 = 2 who will have to find other transportation.

If a single cook can bake 3 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 3 x 2 = 6 large cakes during that time. 34 large cakes are needed for the party so \( \frac{34}{6} \) = 5\(\frac{2}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 10 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 10 x 2 = 20 small cakes during that time. 460 small cakes are needed for the party so \( \frac{460}{20} \) = 23 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 6 + 23 = 29 cooks.

If 72% of the town's 13,000 voters cast ballots the number of votes cast is:

(\( \frac{72}{100} \)) x 13,000 = \( \frac{936,000}{100} \) = 9,360

The mayor got 65% of the votes cast which is:

(\( \frac{65}{100} \)) x 9,360 = \( \frac{608,400}{100} \) = 6,084 votes.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.