Lesson: What is a fraction? (part 1)

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Use this applet to explore the meaning of a fraction. Notice how the red arrow moves as your change the numerator and denominator.

Duane Habecker, Created with GeoGebra: https://www.geogebra.org/m/ZbtS3ufg

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A fraction is a number that describes part of a whole number. Because fractions are numbers just like 5, or 2, or 23, they live on a number line.

A fraction is made up of a numerator and a denominator:

$\huge\frac{numerator}{denominator}$

• The denominator tells how many parts each unit interval has been cut into.
• The numerator tells how many of those parts you have.

For example, in the fraction $\frac{5}{8}$ the denominator 8 means each unit interval has been cut into 8 parts. The numerator 5 means you want to start at 0 and move to the right five parts.

Similarly, the fraction $\frac{11}{8}$ means each whole step has been cut into 8 parts and you want to move to the right 11 parts.

This picture is also a visual representation that $\frac{11}{8}$ is equal to $~1\frac{3}{8}$.

To identify where $\frac{9}{4}$ lives on a number line, you need to recognize that each whole unit has been cut into 4 parts and you need to move to the right nine parts.

This is a good way to show that $\frac{9}{4}$ is equal to $~2\frac{1}{4}$.

Where is point Q located on the number line?

First count the number of parts the distance from 0 to 1 has been cut into: 8 parts

Secondly, count the number of parts Q is to the right of 0: 6 parts.

So, Q is located at $\frac{6}{8}$.

Where is point Q located on the number line?

There are two ways to think of where Q is on the number line.

The red arcs show that Q is located at $~1\frac{2}{5}$.

The green arc shows that Q is located at $\frac{7}{5}$$.