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

\( \frac{1}{9} \) x \( \frac{2}{9} \) = \( \frac{1 x 2}{9 x 9} \) = \( \frac{2}{81} \) = \(\frac{2}{81}\)

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. 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 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 12 workers at the company now and that's enough to staff 3 crews so there are \( \frac{12}{3} \) = 4 workers on a crew. 8 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 8 x 4 = 32 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 32 - 12 = 20 new staff for the busy season.

To fill a 4 gallon tank exactly halfway you'll need 2 gallons of fuel. Each fuel can holds 1 gallons so:

cans = \( \frac{2 \text{ gallons}}{1 \text{ gallons}} \) = 2

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

6\( \sqrt{20} \) - 4\( \sqrt{5} \)
6\( \sqrt{4 \times 5} \) - 4\( \sqrt{5} \)
6\( \sqrt{2^2 \times 5} \) - 4\( \sqrt{5} \)
(6)(2)\( \sqrt{5} \) - 4\( \sqrt{5} \)
12\( \sqrt{5} \) - 4\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them: