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.

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

If 52% of the town's 20,000 voters cast ballots the number of votes cast is:

(\( \frac{52}{100} \)) x 20,000 = \( \frac{1,040,000}{100} \) = 10,400

The mayor got 67% of the votes cast which is:

(\( \frac{67}{100} \)) x 10,400 = \( \frac{696,800}{100} \) = 6,968 votes.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{5 x 5}{4 x 5} \) + \( \frac{8 x 2}{10 x 2} \)

\( \frac{25}{20} \) + \( \frac{16}{20} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{25 + 16}{20} \) = \( \frac{41}{20} \) = 2\(\frac{1}{20}\)

52% of the water consumption is industrial use and 34% is personal use so (52% - 34%) = 18% more water is used for industrial purposes. 15,000 gallons are consumed daily so industry consumes \( \frac{18}{100} \) x 15,000 gallons = 2,700 gallons.