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 + 40.7km + 13.600000000000001km
total distance = 54.7km

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

9\( \sqrt{4} \) x 4\( \sqrt{4} \)
(9 x 4)\( \sqrt{4 \times 4} \)
36\( \sqrt{16} \)

Now we need to simplify the radical:

36\( \sqrt{16} \)
36\( \sqrt{4^2} \)
(36)(4)
144

Jennifer scored 83% on the test meaning she earned 83% of the possible points on the test. There were 90 possible points on the test so she earned 90 x 0.83 = 75 points. Each question is worth 3 points so she got \( \frac{75}{3} \) = 25 questions right.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

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

\( \frac{8 x 3}{2 x 3} \) + \( \frac{7 x 1}{6 x 1} \)

\( \frac{24}{6} \) + \( \frac{7}{6} \)

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

\( \frac{24 + 7}{6} \) = \( \frac{31}{6} \) = 5\(\frac{1}{6}\)