A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

37,000 fans x \( \frac{3}{4} \) = \( \frac{111000}{4} \) = 27,750 fans.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{8b^7}{5b^3} \)
\( \frac{8}{5} \) b^{(7 - 3)}
1\(\frac{3}{5}\)b⁴

To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{80} \) = \( \frac{\frac{16}{16}}{\frac{80}{16}} \) = \( \frac{1}{5} \)

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

\( \frac{1}{7} \) x \( \frac{4}{9} \) = \( \frac{1 x 4}{7 x 9} \) = \( \frac{4}{63} \) = \(\frac{4}{63}\)

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $800
i = 0.05 x $800

No payments were made so the total amount due is the original amount + the accumulated interest: