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.

The amount of flour you need is (2\(\frac{1}{4}\) - \(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{18}{8} \) - \( \frac{1}{8} \)) cups
\( \frac{17}{8} \) cups
2\(\frac{1}{8}\) cups

To add these radicals together their radicands must be the same:

2\( \sqrt{20} \) + 6\( \sqrt{5} \)
2\( \sqrt{4 \times 5} \) + 6\( \sqrt{5} \)
2\( \sqrt{2^2 \times 5} \) + 6\( \sqrt{5} \)
(2)(2)\( \sqrt{5} \) + 6\( \sqrt{5} \)
4\( \sqrt{5} \) + 6\( \sqrt{5} \)

Now that the radicands are identical, you can add them together:

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

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

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{210mi}{30mph} \)
7 hours