The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. 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 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:

39,000 fans x \( \frac{4}{5} \) = \( \frac{156000}{5} \) = 31,200 fans.

To simplify a radical, factor out the perfect squares:

\( \sqrt{50} \)
\( \sqrt{25 \times 2} \)
\( \sqrt{5^2 \times 2} \)
5\( \sqrt{2} \)

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

4\( \sqrt{27} \) + 3\( \sqrt{3} \)
4\( \sqrt{9 \times 3} \) + 3\( \sqrt{3} \)
4\( \sqrt{3^2 \times 3} \) + 3\( \sqrt{3} \)
(4)(3)\( \sqrt{3} \) + 3\( \sqrt{3} \)
12\( \sqrt{3} \) + 3\( \sqrt{3} \)

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