If 35% of the town's 20,000 voters cast ballots the number of votes cast is:

(\( \frac{35}{100} \)) x 20,000 = \( \frac{700,000}{100} \) = 7,000

The mayor got 73% of the votes cast which is:

(\( \frac{73}{100} \)) x 7,000 = \( \frac{511,000}{100} \) = 5,110 votes.

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

\( \frac{4}{9} \) x \( \frac{3}{9} \) = \( \frac{4 x 3}{9 x 9} \) = \( \frac{12}{81} \) = \(\frac{4}{27}\)

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:

\( \frac{6!}{3!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{6 \times 5 \times 4}{1} \)
\( 6 \times 5 \times 4 \)
120

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 simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 6 factors [1, 2, 4, 7, 14, 28] making 28 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{56} \) = \( \frac{\frac{28}{28}}{\frac{56}{28}} \) = \( \frac{1}{2} \)