1.3: Why Fractions

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Fractions are very common in waterworks mathematics. You may not see them in their “typical” form, for example:

\[\dfrac{3}{4} \qquad \dfrac{2}{3} \qquad \dfrac{1}{5}\nonumber \]

You may see them as percentages:

\[75 \% \qquad 66 \% \qquad 20 \% \nonumber \]

Or you may see them as words:

Three quarters two thirds one fifth

However, these examples can also be expressed as fractions. We will discuss these later in the text. By understanding fractions, you can also understand how units are used to express things in terms of fractions. For example, if you drive a car at a velocity of 55 miles per hour, this is a form of a fraction.

\[\dfrac{55 \text { miles }}{\text { hour }}\nonumber \]

Fifty-five miles per hour is in fact a fraction. It is just expressed in a “per unit” example. It can be read as 55 miles per one unit of hour. What if you had an example of 110 miles per 2 hours? This could be written as:

\[\dfrac{110 \text { miles }}{2 \text { hours }}\nonumber \]

Similar to reducing fractions such as:

\[\dfrac{2}{4}=\dfrac{1}{2} \nonumber \]

The previous example of “55 miles per 2 hours” can be reduced as below:

\[\dfrac{110 \text { miles }}{2 \text { hours }}=\dfrac{55 \text { miles }}{1 \text { hour }} \text { or } \dfrac{55 \text { miles }}{h r} \nonumber \]

The concept of “units” will be discussed in more detail later in this text, but understanding the concept is important to learn the process of solving waterworks mathematics problems. Since “adding” and “subtracting” fractions is not a common process in water-related math problems we will skip directly to multiplication and division of fractions.