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:

\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60

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.

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

3\( \sqrt{5} \) x 8\( \sqrt{7} \)
(3 x 8)\( \sqrt{5 \times 7} \)
24\( \sqrt{35} \)

To divide fractions, invert the second fraction and then multiply:

\( \frac{4}{6} \) ÷ \( \frac{2}{6} \) = \( \frac{4}{6} \) x \( \frac{6}{2} \)

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

\( \frac{4}{6} \) x \( \frac{6}{2} \) = \( \frac{4 x 6}{6 x 2} \) = \( \frac{24}{12} \) = 2

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