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:

-8z⁵ - 7z⁵
(-8 - 7)z⁵
-15z⁵

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{3 x 4}{2 x 4} \) + \( \frac{3 x 1}{8 x 1} \)

\( \frac{12}{8} \) + \( \frac{3}{8} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{12 + 3}{8} \) = \( \frac{15}{8} \) = 1\(\frac{7}{8}\)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

April scored 80% on the test meaning she earned 80% of the possible points on the test. There were 160 possible points on the test so she earned 160 x 0.8 = 128 points. Each question is worth 4 points so she got \( \frac{128}{4} \) = 32 questions right.