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.

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

\( \frac{3}{5} \) ÷ \( \frac{1}{6} \) = \( \frac{3}{5} \) x \( \frac{6}{1} \)

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

\( \frac{3}{5} \) x \( \frac{6}{1} \) = \( \frac{3 x 6}{5 x 1} \) = \( \frac{18}{5} \) = 3\(\frac{3}{5}\)

There are 4 4-passenger taxis available so that's 4 x 4 = 16 total seats. There are 19 people needing transportation leaving 19 - 16 = 3 who will have to find other transportation.

The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 32 are [1, 2, 4, 8, 16, 32]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 40 and 32 have in common.

If 45% of the town's 40,000 voters cast ballots the number of votes cast is:

(\( \frac{45}{100} \)) x 40,000 = \( \frac{1,800,000}{100} \) = 18,000

The mayor got 75% of the votes cast which is:

(\( \frac{75}{100} \)) x 18,000 = \( \frac{1,350,000}{100} \) = 13,500 votes.