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 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 + 9.2km
total distance = 49.5km

First, solve for \( \left|z + 0\right| \):

\( \left|z + 0\right| \) + 0 = -5
\( \left|z + 0\right| \) = -5 + 0
\( \left|z + 0\right| \) = -5

The value inside the absolute value brackets can be either positive or negative so (z + 0) must equal - 5 or --5 for \( \left|z + 0\right| \) to equal -5:

So, z = 5 or z = -5.

44% of the water consumption is industrial use and 11% is personal use so (44% - 11%) = 33% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{33}{100} \) x 10,000 gallons = 3,300 gallons.

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