A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

36,000 fans x \( \frac{2}{3} \) = \( \frac{72000}{3} \) = 24,000 fans.

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

7\( \sqrt{5} \) x 2\( \sqrt{4} \)
(7 x 2)\( \sqrt{5 \times 4} \)
14\( \sqrt{20} \)

Now we need to simplify the radical:

14\( \sqrt{20} \)
14\( \sqrt{5 \times 4} \)
14\( \sqrt{5 \times 2^2} \)
(14)(2)\( \sqrt{5} \)
28\( \sqrt{5} \)

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

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.