What is a third?
A third is when something has been split into three equal parts.
You can find a third of a shape, measure or a quantity.
There are three thirds in a whole.
Quiz
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Writing a third
A third is a fraction. A fraction is part of a whole.
This is how you write one third as a fraction: \(\frac{1}{3} \)
There are 3 thirds in one whole and each third must be equal.
\(\frac{1}{3} \) + \(\frac{1}{3} \) + \(\frac{1}{3} \) = 1 whole
Look at these two bar models. Which one do you think shows thirds?
The first bar model does not show thirds. One of the parts is smaller than the other two. There are 3 parts, but they are not equal, so you would not call them thirds.
The second bar model does show thirds. All three parts are equal and together they make up the whole.
Finding a third of a set of objects
Here are 6 raspberries.
To find a third you need to divide the raspberries into 3 equal groups.
A bar model is helpful for this. First, you divide your bottom bar into 3 equal parts.
Next you divide the raspberries into the 3 equal parts. Each of these parts represents one third.
\( \frac{1}{3} \) of the 6 raspberries is 2 raspberries.
Finding a third of a number
You can find a third of a number in the same way.
Let's find \(\frac{1}{3} \) of 24.
First, you divide your bar model into 3 equal parts.
Then you use your times table and division table knowledge to help calculate the answer.
You divide 24 by 3 because you are finding thirds.
24 ÷ 3 = 8
You know this because 3 × 8 = 24 and 8 × 3 = 24
\( \frac{1}{3} \) of 24 = 8
Example 1
Find \(\frac{1}{3} \) of 12 pears.
You could draw a bar model to help you.
✓ First draw a bar model with three equal parts.
Divide the pears into the parts, making sure there is an equal number of pears in each part.
You are finding one third, so you count the number of pears in one of the parts.
There will be four pears in each part.
So:
\( \frac{1}{3} \) of 12 = 4
Example 2
Let's make a bar model to show \(\frac{2}{3} \) of 18.
Your bar model would need three equal parts
Find \( \frac{2}{3} \) of 18.
✓ To find the answer, you need to divide 18 by 3.
Our number sentence would start with 18 ÷ 3
Therefore:
18 ÷ 3 = 6
You know this because 3 x 6 = 18 and 6 x 3 = 18.
So 6 is one third of 18. However, you need to find two thirds, so you need to add two of our thirds together.
6 + 6 = 12
\(\frac{2}{3} \) of 18 = 12
Example 3
Let's draw a bar model to find \(\frac{2}{3} \) of 36.
Draw a bar model with 3 equal parts because we are finding thirds.
What is \( \frac{2}{3} \) of 36?
✓ Divide 36 by 3 because we are finding thirds.
36 ÷ 3 = 12
We know this because 3 × 12 = 36 and 12 × 3 = 36.
\(\frac{1}{3} \) of 36 = 12
We are finding \(\frac{2}{3} \), so:
12 × 2 = 24
Therefore, \(\frac{2}{3} \) of 36 = 24.
More on Fractions
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