Math > Year 3

Comparing & Ordering Fractions with the same denominator


What is a fraction?
A fraction is a part of a whole. It tells us how many parts of a whole we have.


For example, out of four parts of a watermelon, you get one part, and the fraction you have is one quarter i.e., ¼ (one out of four).

 

 




The top part of the fraction is called the numerator. It shows the number of parts that you have.

The bottom part of the fraction is called the denominator. It shows the total number of parts the whole is divided into.


Comparing Fractions

Comparing fractions means finding out which fraction is bigger or smaller.

 

How to compare fractions?

To compare fractions, we can use diagrams and number lines.
 

Example 1
 

 

As  \frac{4}{5}  has more shaded region than \frac{3}{5}, \frac{4}{5} is bigger than \frac{3}{5}

When the denominators are the same, the fraction with a higher numerator is the bigger fraction.


 

Example 2
 

Find which fraction is smaller. 

\frac{2}{4}  or  \frac{3}{4}
 

For comparing fractions, we can use a number line. We can mark the fractions on the number line.
 



 


The fraction on the right-hand side is always bigger than the one on the left-hand side.

 

Thus,  \frac{2}{4} is smaller than  \frac{3}{4}.
 


Symbols

We use 3 symbols to compare numbers.

 

 

Ordering Fractions

Ordering fractions means arranging fractions in a sequence.
 

There are two ways of ordering:

Ascending: Smallest to biggest

Descending: Biggest to Smallest

 

When ordering fractions with the same denominator, we compare the numerator. The fraction with a higher numerator will be the bigger one.
 

Example:
 

Order the given fraction in ascending order.


 

As the denominators are the same, we will compare the numerators.

\frac{1}{7} has the smallest numerator.

Then it's \frac{3}{7}

Then \frac{4}{7}

The highest one is \frac{5}{7}

So, the ascending order is \frac{1}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}


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