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 + 40.2km + 14.0km
total distance = 54.3km

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

The greatest common factor (GCF) is the greatest factor that divides two integers.

To add these radicals together their radicands must be the same:

7\( \sqrt{45} \) + 5\( \sqrt{5} \)
7\( \sqrt{9 \times 5} \) + 5\( \sqrt{5} \)
7\( \sqrt{3^2 \times 5} \) + 5\( \sqrt{5} \)
(7)(3)\( \sqrt{5} \) + 5\( \sqrt{5} \)
21\( \sqrt{5} \) + 5\( \sqrt{5} \)

Now that the radicands are identical, you can add them together:

To simplify a radical, factor out the perfect squares:

\( \sqrt{45} \)
\( \sqrt{9 \times 5} \)
\( \sqrt{3^2 \times 5} \)
3\( \sqrt{5} \)