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

\( \frac{3}{9} \) ÷ \( \frac{3}{6} \) = \( \frac{3}{9} \) x \( \frac{6}{3} \)

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

\( \frac{3}{9} \) x \( \frac{6}{3} \) = \( \frac{3 x 6}{9 x 3} \) = \( \frac{18}{27} \) = \(\frac{2}{3}\)

67% of the water consumption is industrial use and 34% is personal use so (67% - 34%) = 33% more water is used for industrial purposes. 15,000 gallons are consumed daily so industry consumes \( \frac{33}{100} \) x 15,000 gallons = 4,950 gallons.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{25\sqrt{16}}{5\sqrt{8}} \)
\( \frac{25}{5} \) \( \sqrt{\frac{16}{8}} \)
5 \( \sqrt{2} \)

To simplify a radical, factor out the perfect squares:

\( \sqrt{32} \)
\( \sqrt{16 \times 2} \)
\( \sqrt{4^2 \times 2} \)
4\( \sqrt{2} \)