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:

\( \frac{2!}{4!} \)
\( \frac{2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4 \times 3} \)
\( \frac{1}{12} \)

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:

7y⁷ + 2y⁷
(7 + 2)y⁷
9y⁷

42% of the water consumption is industrial use and 30% is personal use so (42% - 30%) = 12% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{12}{100} \) x 40,000 gallons = 4,800 gallons.

To add these radicals together their radicands must be the same:

4\( \sqrt{75} \) + 2\( \sqrt{3} \)
4\( \sqrt{25 \times 3} \) + 2\( \sqrt{3} \)
4\( \sqrt{5^2 \times 3} \) + 2\( \sqrt{3} \)
(4)(5)\( \sqrt{3} \) + 2\( \sqrt{3} \)
20\( \sqrt{3} \) + 2\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 have in common.