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 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:

\( \sqrt{\frac{25}{16}} \)
\( \frac{\sqrt{25}}{\sqrt{16}} \)
\( \frac{\sqrt{5^2}}{\sqrt{4^2}} \)
\( \frac{5}{4} \)
1\(\frac{1}{4}\)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.

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

\( \frac{8 x 4}{6 x 4} \) - \( \frac{8 x 3}{8 x 3} \)

\( \frac{32}{24} \) - \( \frac{24}{24} \)

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

\( \frac{32 - 24}{24} \) = \( \frac{8}{24} \) = \(\frac{1}{3}\)

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.