To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.1km + 40.8km + 9.3km
total distance = 50.2km

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:

\( \sqrt{\frac{49}{49}} \)
\( \frac{\sqrt{49}}{\sqrt{49}} \)
\( \frac{\sqrt{7^2}}{\sqrt{7^2}} \)
1

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 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 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.

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

\( \frac{9 x 7}{6 x 7} \) - \( \frac{6 x 3}{14 x 3} \)

\( \frac{63}{42} \) - \( \frac{18}{42} \)

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

\( \frac{63 - 18}{42} \) = \( \frac{45}{42} \) = 1\(\frac{1}{14}\)

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{3!} \)
\( \frac{2 \times 1}{3 \times 2 \times 1} \)
\( \frac{1}{3} \)
\( \frac{1}{3} \)