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

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 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 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.

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

\( \frac{2 x 5}{2 x 5} \) + \( \frac{9 x 1}{10 x 1} \)

\( \frac{10}{10} \) + \( \frac{9}{10} \)

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

\( \frac{10 + 9}{10} \) = \( \frac{19}{10} \) = 1\(\frac{9}{10}\)

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{14 + 8 + 15 + 7}{4} \) = \( \frac{44}{4} \) = 11

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{16}{4}} \)
\( \frac{\sqrt{16}}{\sqrt{4}} \)
\( \frac{\sqrt{4^2}}{\sqrt{2^2}} \)
\( \frac{4}{2} \)
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