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:

44,000 fans x \( \frac{5}{6} \) = \( \frac{220000}{6} \) = 36,667 fans.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.

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

\( \frac{7 x 3}{8 x 3} \) + \( \frac{7 x 2}{12 x 2} \)

\( \frac{21}{24} \) + \( \frac{14}{24} \)

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

\( \frac{21 + 14}{24} \) = \( \frac{35}{24} \) = 1\(\frac{11}{24}\)

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{16}{16}} \)
\( \frac{\sqrt{16}}{\sqrt{16}} \)
\( \frac{\sqrt{4^2}}{\sqrt{4^2}} \)
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The greatest common factor (GCF) is the greatest factor that divides two integers.