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 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:

7a⁷ - 9a⁷
(7 - 9)a⁷
-2a⁷

The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.

To simplify a radical, factor out the perfect squares:

\( \sqrt{112} \)
\( \sqrt{16 \times 7} \)
\( \sqrt{4^2 \times 7} \)
4\( \sqrt{7} \)

Jennifer scored 75% on the test meaning she earned 75% of the possible points on the test. There were 400 possible points on the test so she earned 400 x 0.75 = 300 points. Each question is worth 4 points so she got \( \frac{300}{4} \) = 75 questions right.