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.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 20mph \times 1h \)
20 miles

To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{10 \text{ gallons}}{2 \text{ gallons}} \) = 5

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{63\sqrt{15}}{9\sqrt{5}} \)
\( \frac{63}{9} \) \( \sqrt{\frac{15}{5}} \)
7 \( \sqrt{3} \)

Monica scored 81% on the test meaning she earned 81% of the possible points on the test. There were 400 possible points on the test so she earned 400 x 0.81 = 324 points. Each question is worth 4 points so she got \( \frac{324}{4} \) = 81 questions right.