Comparing fractions | Year 3 Mathematics PDF Download

Why do you compare fractions?

• When we compare fractions, we are essentially looking at how much of the whole is represented within each fraction. This is crucial when dividing or sharing something like a cake, ensuring that each share is fair and equal.
• Imagine cutting a cake where everyone should get an equal slice. By visually comparing fractions, we ensure that each portion is proportionate.
  
• Two main types of fractions for comparison are unit fractions and fractions with the same denominator.

Comparing Unit Fractions

A unit fraction has a numerator of 1, while the denominator can be any other whole number. For example, 1/4.
Since the numerator stays constant with unit fractions, we compare them based on the denominator. The larger the denominator, the smaller the fraction, as it signifies the number of parts the whole has been divided into.
Both are unit fractions, so we focus on their denominators to determine which is bigger. Using bar models can assist in visual comparison.

Solved Example

Example: Which is bigger, 1/6 or 1/3?
Since both fractions are unit fractions, you need to look at the denominator to determine which fraction is larger. Bar models can also assist in comparing them.

You can see that 1/3 is the bigger fraction because it has been split up into fewer parts.
If we used the greater than and less than signs, we would write:

Comparing fractions with the same denominator

• It is easy to compare fractions with the same denominator. You only have to focus on the numerator.
• The fraction is larger if the numerator is a bigger number. That’s because you are talking about more parts of the whole.

Solved Example

Example: Luke and Khadija cut a pizza into 6 slices. Luke ate 2/6 of the pizza and Khadija ate 3/6. Who ate more pizza?
The two fractions you need to look at are 3/6 and 2/6. Which has the bigger numerator?
The larger the numerator, the larger the fraction.
It can also help to draw each fraction to understand which one is larger.
You can see that 3/6 is larger than 2/6, so Khadija ate more pizza!
Using the greater than and less than signs, you would write it as: