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:

\( \frac{6!}{3!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{6 \times 5 \times 4}{1} \)
\( 6 \times 5 \times 4 \)
120

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. 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 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

April scored 83% on the test meaning she earned 83% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.83 = 100 points. Each question is worth 2 points so she got \( \frac{100}{2} \) = 50 questions right.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-5c⁶ - 6c⁶
(-5 - 6)c⁶
-11c⁶

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.