How to Plot Fractions on the Real Number Line

Graphing Fractions

Fractions (and mixed numbers), are numbers which contain a fractional component. Fractions cannot be described by whole units alone, the fractional component describes the part of the value which is not whole. A fractional component is made up of a numerator and a denominator (^NUM⁄_DEN). To graph a fractional component on the number line, we split the unit up into multiple parts (which is described by the denominator); then, we move the coordinate the number of parts equal to the numerator.

Example 1

- For example, say we ordered a mini pizza from a local restaurant. It was quite small, and we ate the entire pie; so, we order another. Each pizza is cut-up into 4 slices, and this time we're only able to eat 3 of the 4 slices of pie. Describe the amount of pie that we ate using a whole number and a fraction; then, graph that value onto the real number line.

- We ate one whole (mini) pizza, so the whole number is 1. Now, the second pizza is split-up into 4 parts, which represents the denominator of the fraction. We ate 3 of parts, which is the numerator. The ratio between the numerator and denominator is our fraction, that combined with the whole number gives us the amount of pizza we ate as a mixed number.

To plot this mixed number on the real number line, we equate each pizza that we've eaten with a unit on the line. We begin by moving right by the whole number part. We ate one entire (mini) pizza, so we move right 1 unit. Now, we need to include the fractional part. We do this by dividing the next unit up into a number of parts equal to the denominator. The pizza is cut into 4 pieces, so we split the next unit up into 4 parts. Finally, we move forward the number of parts equal to that of the numerator. We ate 3 of the 4 slices of pizza, so we move forward 3 of the 4 parts (each step represents a slice of pizza). The final location is the coordinate of the mixed number.