What are fractions?

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 $\LARGE\frac{5}{8}$ 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 $\large\frac{11}{8}$ 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 $\large\frac{11}{8}$ is equal to $\large~1\frac{3}{8}$.

To identify where $\LARGE\frac{9}{4}$ 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 $\large\frac{9}{4}$ is equal to $\large~2\frac{1}{4}$.

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 $\LARGE\frac{6}{8}$.

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 $\large~1\frac{2}{5}$.

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

Duane Habecker, Created with GeoGebra

Self-Check

 Question 1 Where is Q on the number line? [show answer] $\Huge\frac{7}{12}$

 Question 2 Where is Q on the number line? [show answer] $\Huge\frac{3}{8}$

 Question 3 Where is Q on the number line? [show answer] $\Huge\frac{9}{5}$ which is also equal to $\Huge~1\frac{4}{5}$