A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

41,000 fans x \( \frac{5}{6} \) = \( \frac{205000}{6} \) = 34,167 fans.

The factors of a number are all positive integers that divide evenly into the number. The factors of 64 are 1, 2, 4, 8, 16, 32, 64.

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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

6\( \sqrt{80} \) - 7\( \sqrt{5} \)
6\( \sqrt{16 \times 5} \) - 7\( \sqrt{5} \)
6\( \sqrt{4^2 \times 5} \) - 7\( \sqrt{5} \)
(6)(4)\( \sqrt{5} \) - 7\( \sqrt{5} \)
24\( \sqrt{5} \) - 7\( \sqrt{5} \)

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

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 2}{4 x 2} \) + \( \frac{4 x 1}{8 x 1} \)

\( \frac{8}{8} \) + \( \frac{4}{8} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{8 + 4}{8} \) = \( \frac{12}{8} \) = 1\(\frac{1}{2}\)