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 simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{76} \) = \( \frac{\frac{20}{4}}{\frac{76}{4}} \) = \( \frac{5}{19} \)

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

7\( \sqrt{6} \) x 4\( \sqrt{8} \)
(7 x 4)\( \sqrt{6 \times 8} \)
28\( \sqrt{48} \)

Now we need to simplify the radical:

28\( \sqrt{48} \)
28\( \sqrt{3 \times 16} \)
28\( \sqrt{3 \times 4^2} \)
(28)(4)\( \sqrt{3} \)
112\( \sqrt{3} \)

By buying two shirts, Charlie will save $28 x \( \frac{10}{100} \) = \( \frac{$28 x 10}{100} \) = \( \frac{$280}{100} \) = $2.80 on the second shirt.

So, his total cost will be
$28.00 + ($28.00 - $2.80)
$28.00 + $25.20
$53.20

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 16 workers at the company now and that's enough to staff 4 crews so there are \( \frac{16}{4} \) = 4 workers on a crew. 7 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 7 x 4 = 28 total workers to staff the crews during the busy season. The company already employs 16 workers so they need to add 28 - 16 = 12 new staff for the busy season.