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.

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:

\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

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:

7y⁶ - 5y⁶
(7 - 5)y⁶
2y⁶

Monica scored 87% on the test meaning she earned 87% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.87 = 104 points. Each question is worth 2 points so she got \( \frac{104}{2} \) = 52 questions right.