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).

If 67% of the town's 27,000 voters cast ballots the number of votes cast is:

(\( \frac{67}{100} \)) x 27,000 = \( \frac{1,809,000}{100} \) = 18,090

The mayor got 82% of the votes cast which is:

(\( \frac{82}{100} \)) x 18,090 = \( \frac{1,483,380}{100} \) = 14,834 votes.

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{40}{48} \) = \( \frac{\frac{40}{8}}{\frac{48}{8}} \) = \( \frac{5}{6} \)

To subtract these radicals together their radicands must be the same:

7\( \sqrt{175} \) - 3\( \sqrt{7} \)
7\( \sqrt{25 \times 7} \) - 3\( \sqrt{7} \)
7\( \sqrt{5^2 \times 7} \) - 3\( \sqrt{7} \)
(7)(5)\( \sqrt{7} \) - 3\( \sqrt{7} \)
35\( \sqrt{7} \) - 3\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them: