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 add the coefficients and retain the base and exponent:

8c⁶ + 2c⁶
(8 + 2)c⁶
10c⁶

The number of students taking German or Spanish is 6 + 10 = 16. Of that group of 16, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 16 - 2 = 14 who are taking at least one language. 20 - 14 = 6 students who are not taking either language.

To fill a 6 gallon tank exactly halfway you'll need 3 gallons of fuel. Each fuel can holds 1 gallons so:

cans = \( \frac{3 \text{ gallons}}{1 \text{ gallons}} \) = 3

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31