To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.

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

\( \frac{9 x 9}{5 x 9} \) - \( \frac{4 x 5}{9 x 5} \)

\( \frac{81}{45} \) - \( \frac{20}{45} \)

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

\( \frac{81 - 20}{45} \) = \( \frac{61}{45} \) = 1\(\frac{16}{45}\)

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).

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 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

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

\( \frac{8 x 3}{2 x 3} \) + \( \frac{6 x 1}{6 x 1} \)

\( \frac{24}{6} \) + \( \frac{6}{6} \)

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

\( \frac{24 + 6}{6} \) = \( \frac{30}{6} \) = 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 = \( \frac{55mi}{55mph} \)
1 hour

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

\( \frac{6\sqrt{25}}{3\sqrt{5}} \)
\( \frac{6}{3} \) \( \sqrt{\frac{25}{5}} \)
2 \( \sqrt{5} \)