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:

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

\( \frac{16}{24} \) - \( \frac{9}{24} \)

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

\( \frac{16 - 9}{24} \) = \( \frac{7}{24} \) = \(\frac{7}{24}\)

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).

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 4 workers at the company now and that's enough to staff 2 crews so there are \( \frac{4}{2} \) = 2 workers on a crew. 6 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 6 x 2 = 12 total workers to staff the crews during the busy season. The company already employs 4 workers so they need to add 12 - 4 = 8 new staff for the busy season.

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

5\( \sqrt{8} \) x 2\( \sqrt{9} \)
(5 x 2)\( \sqrt{8 \times 9} \)
10\( \sqrt{72} \)

Now we need to simplify the radical:

10\( \sqrt{72} \)
10\( \sqrt{2 \times 36} \)
10\( \sqrt{2 \times 6^2} \)
(10)(6)\( \sqrt{2} \)
60\( \sqrt{2} \)

The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 the greatest factor 36 and 76 have in common.