If 42% of the town's 33,000 voters cast ballots the number of votes cast is:

(\( \frac{42}{100} \)) x 33,000 = \( \frac{1,386,000}{100} \) = 13,860

The mayor got 53% of the votes cast which is:

(\( \frac{53}{100} \)) x 13,860 = \( \frac{734,580}{100} \) = 7,346 votes.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{44} \) = \( \frac{\frac{20}{4}}{\frac{44}{4}} \) = \( \frac{5}{11} \)

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.