The greatest common factor (GCF) is the greatest factor that divides two integers.

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:

\( \frac{-7a^9}{4a^4} \)
\( \frac{-7}{4} \) a^{(9 - 4)}
-1\(\frac{3}{4}\)a⁵

If 88% of the town's 31,000 voters cast ballots the number of votes cast is:

(\( \frac{88}{100} \)) x 31,000 = \( \frac{2,728,000}{100} \) = 27,280

The mayor got 84% of the votes cast which is:

(\( \frac{84}{100} \)) x 27,280 = \( \frac{2,291,520}{100} \) = 22,915 votes.

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{56} \) = \( \frac{\frac{36}{4}}{\frac{56}{4}} \) = \( \frac{9}{14} \)

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.