To divide fractions, invert the second fraction and then multiply:

\( \frac{4}{8} \) ÷ \( \frac{3}{9} \) = \( \frac{4}{8} \) x \( \frac{9}{3} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{8} \) x \( \frac{9}{3} \) = \( \frac{4 x 9}{8 x 3} \) = \( \frac{36}{24} \) = 1\(\frac{1}{2}\)

50% of the water consumption is industrial use and 31% is personal use so (50% - 31%) = 19% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{19}{100} \) x 25,000 gallons = 4,750 gallons.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-3a⁴ + 4a⁴
(-3 + 4)a⁴
a⁴

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:

\( \frac{7 x 2}{4 x 2} \) + \( \frac{9 x 1}{8 x 1} \)

\( \frac{14}{8} \) + \( \frac{9}{8} \)

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

\( \frac{14 + 9}{8} \) = \( \frac{23}{8} \) = 2\(\frac{7}{8}\)

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.