To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{7} \) ÷ \( \frac{2}{7} \) = \( \frac{3}{7} \) x \( \frac{7}{2} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{7} \) x \( \frac{7}{2} \) = \( \frac{3 x 7}{7 x 2} \) = \( \frac{21}{14} \) = 1\(\frac{1}{2}\)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.

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

\( \frac{5 x 2}{8 x 2} \) + \( \frac{7 x 1}{16 x 1} \)

\( \frac{10}{16} \) + \( \frac{7}{16} \)

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

\( \frac{10 + 7}{16} \) = \( \frac{17}{16} \) = 1\(\frac{1}{16}\)

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

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.

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

3\( \sqrt{63} \) + 5\( \sqrt{7} \)
3\( \sqrt{9 \times 7} \) + 5\( \sqrt{7} \)
3\( \sqrt{3^2 \times 7} \) + 5\( \sqrt{7} \)
(3)(3)\( \sqrt{7} \) + 5\( \sqrt{7} \)
9\( \sqrt{7} \) + 5\( \sqrt{7} \)

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