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 subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

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

\( \frac{7 x 5}{3 x 5} \) - \( \frac{8 x 3}{5 x 3} \)

\( \frac{35}{15} \) - \( \frac{24}{15} \)

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

\( \frac{35 - 24}{15} \) = \( \frac{11}{15} \) = \(\frac{11}{15}\)

To fill a 16 gallon tank exactly halfway you'll need 8 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{8 \text{ gallons}}{2 \text{ gallons}} \) = 4

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:

9c⁴ + 2c⁴
(9 + 2)c⁴
11c⁴

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.