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:

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

The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.

If 78% of the town's 45,000 voters cast ballots the number of votes cast is:

(\( \frac{78}{100} \)) x 45,000 = \( \frac{3,510,000}{100} \) = 35,100

The mayor got 64% of the votes cast which is:

(\( \frac{64}{100} \)) x 35,100 = \( \frac{2,246,400}{100} \) = 22,464 votes.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{49}{49}} \)
\( \frac{\sqrt{49}}{\sqrt{49}} \)
\( \frac{\sqrt{7^2}}{\sqrt{7^2}} \)
1

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).