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:

43,000 fans x \( \frac{4}{5} \) = \( \frac{172000}{5} \) = 34,400 fans.

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 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:

\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)

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

5\( \sqrt{80} \) - 3\( \sqrt{5} \)
5\( \sqrt{16 \times 5} \) - 3\( \sqrt{5} \)
5\( \sqrt{4^2 \times 5} \) - 3\( \sqrt{5} \)
(5)(4)\( \sqrt{5} \) - 3\( \sqrt{5} \)
20\( \sqrt{5} \) - 3\( \sqrt{5} \)

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

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