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

\( \frac{2}{7} \) x \( \frac{1}{8} \) = \( \frac{2 x 1}{7 x 8} \) = \( \frac{2}{56} \) = \(\frac{1}{28}\)

The factors of 16 are [1, 2, 4, 8, 16] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 the greatest factor 16 and 52 have in common.

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 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 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.4km + 50.2km + 14.3km
total distance = 64.9km

If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 22 large cakes are needed for the party so \( \frac{22}{10} \) = 2\(\frac{1}{5}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 16 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 16 x 2 = 32 small cakes during that time. 380 small cakes are needed for the party so \( \frac{380}{32} \) = 11\(\frac{7}{8}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 12 = 15 cooks.