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

\( \frac{4}{7} \) x \( \frac{1}{9} \) = \( \frac{4 x 1}{7 x 9} \) = \( \frac{4}{63} \) = \(\frac{4}{63}\)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 share.

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

\( \frac{2 x 3}{4 x 3} \) - \( \frac{4 x 1}{12 x 1} \)

\( \frac{6}{12} \) - \( \frac{4}{12} \)

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

\( \frac{6 - 4}{12} \) = \( \frac{2}{12} \) = \(\frac{1}{6}\)

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

\( \frac{1}{7} \) ÷ \( \frac{4}{5} \) = \( \frac{1}{7} \) x \( \frac{5}{4} \)

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

\( \frac{1}{7} \) x \( \frac{5}{4} \) = \( \frac{1 x 5}{7 x 4} \) = \( \frac{5}{28} \) = \(\frac{5}{28}\)

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 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.5km + 30.6km + 3.3km
total distance = 34.4km

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (3 + 4) ÷ 4 x 5 - 3²
P: 5 + (7) ÷ 4 x 5 - 3²
E: 5 + 7 ÷ 4 x 5 - 9
MD: 5 + \( \frac{7}{4} \) x 5 - 9
MD: 5 + \( \frac{35}{4} \) - 9
AS: \( \frac{20}{4} \) + \( \frac{35}{4} \) - 9
AS: \( \frac{55}{4} \) - 9
AS: \( \frac{55 - 36}{4} \)
\( \frac{19}{4} \)
4\(\frac{3}{4}\)