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).

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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 share.

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

\( \frac{8 x 2}{4 x 2} \) + \( \frac{6 x 1}{8 x 1} \)

\( \frac{16}{8} \) + \( \frac{6}{8} \)

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

\( \frac{16 + 6}{8} \) = \( \frac{22}{8} \) = 2\(\frac{3}{4}\)

The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

1

50% of the water consumption is industrial use and 22% is personal use so (50% - 22%) = 28% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{28}{100} \) x 30,000 gallons = 8,400 gallons.