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:

\( \sqrt{\frac{16}{25}} \)
\( \frac{\sqrt{16}}{\sqrt{25}} \)
\( \frac{\sqrt{4^2}}{\sqrt{5^2}} \)
\(\frac{4}{5}\)

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (4 + 4) ÷ 5 x 4 - 3²
P: 2 + (8) ÷ 5 x 4 - 3²
E: 2 + 8 ÷ 5 x 4 - 9
MD: 2 + \( \frac{8}{5} \) x 4 - 9
MD: 2 + \( \frac{32}{5} \) - 9
AS: \( \frac{10}{5} \) + \( \frac{32}{5} \) - 9
AS: \( \frac{42}{5} \) - 9
AS: \( \frac{42 - 45}{5} \)
\( \frac{-3}{5} \)
-\(\frac{3}{5}\)

If 52% of the town's 48,000 voters cast ballots the number of votes cast is:

(\( \frac{52}{100} \)) x 48,000 = \( \frac{2,496,000}{100} \) = 24,960

The mayor got 77% of the votes cast which is:

(\( \frac{77}{100} \)) x 24,960 = \( \frac{1,921,920}{100} \) = 19,219 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.