To fill a 8 gallon tank exactly halfway you'll need 4 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{4 \text{ gallons}}{2 \text{ gallons}} \) = 2

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. 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 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

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

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

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

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

8\( \sqrt{7} \) x 4\( \sqrt{5} \)
(8 x 4)\( \sqrt{7 \times 5} \)
32\( \sqrt{35} \)

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

\( \frac{42\sqrt{10}}{6\sqrt{5}} \)
\( \frac{42}{6} \) \( \sqrt{\frac{10}{5}} \)
7 \( \sqrt{2} \)