Skill: Identify thirds

To identify thirds, check that a whole is split into 3 equal parts.

• Each equal part is called one third, written $\frac{1}{3}$.
• The three parts together make one whole:

$$\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=1$$

Example: What fraction of this rectangle is shaded?

Shaded	Not shaded	Not shaded
$\frac{1}{3}$	$\frac{1}{3}$	$\frac{1}{3}$

1. Count the parts. There are 3 parts.
2. Check their sizes. The parts are equal.
3. Therefore, the rectangle is divided into thirds.
4. One part is shaded, so the shaded part is $\frac{1}{3}$.

On a number line, thirds divide the distance from $0$ to $1$ into 3 equal spaces:

$$0 \quad\text{—}\quad \frac{1}{3} \quad\text{—}\quad \frac{2}{3} \quad\text{—}\quad 1$$

The points $\frac{1}{3}$ and $\frac{2}{3}$ make three equal sections. If the three parts were different sizes, they would not be thirds.