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.

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

3 + (5 + 3) ÷ 3 x 5 - 5²
P: 3 + (8) ÷ 3 x 5 - 5²
E: 3 + 8 ÷ 3 x 5 - 25
MD: 3 + \( \frac{8}{3} \) x 5 - 25
MD: 3 + \( \frac{40}{3} \) - 25
AS: \( \frac{9}{3} \) + \( \frac{40}{3} \) - 25
AS: \( \frac{49}{3} \) - 25
AS: \( \frac{49 - 75}{3} \)
\( \frac{-26}{3} \)
-8\(\frac{2}{3}\)

If 55% of the town's 34,000 voters cast ballots the number of votes cast is:

(\( \frac{55}{100} \)) x 34,000 = \( \frac{1,870,000}{100} \) = 18,700

The mayor got 88% of the votes cast which is:

(\( \frac{88}{100} \)) x 18,700 = \( \frac{1,645,600}{100} \) = 16,456 votes.

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,300
i = 0.08 x $1,300

No payments were made so the total amount due is the original amount + the accumulated interest:

First, solve for \( \left|a + 9\right| \):

\( \left|a + 9\right| \) - 5 = -7
\( \left|a + 9\right| \) = -7 + 5
\( \left|a + 9\right| \) = -2

The value inside the absolute value brackets can be either positive or negative so (a + 9) must equal - 2 or --2 for \( \left|a + 9\right| \) to equal -2:

So, a = -7 or a = -11.