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

\( \frac{4}{7} \) ÷ \( \frac{3}{9} \) = \( \frac{4}{7} \) x \( \frac{9}{3} \)

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

\( \frac{4}{7} \) x \( \frac{9}{3} \) = \( \frac{4 x 9}{7 x 3} \) = \( \frac{36}{21} \) = 1\(\frac{5}{7}\)

If 63% of the town's 10,000 voters cast ballots the number of votes cast is:

(\( \frac{63}{100} \)) x 10,000 = \( \frac{630,000}{100} \) = 6,300

The mayor got 61% of the votes cast which is:

(\( \frac{61}{100} \)) x 6,300 = \( \frac{384,300}{100} \) = 3,843 votes.

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{4!}{3!} \)
\( \frac{4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{4}{1} \)
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38% of the water consumption is industrial use and 26% is personal use so (38% - 26%) = 12% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{12}{100} \) x 20,000 gallons = 2,400 gallons.