At the end of this lesson, students should be able to compare fractions using the greater than, less than and the equal to sign.

NOTE:

In comparing fractions, we try to identify which fraction is greater, less or equal to the other. Therefore, we use the signs;

Greater than (>)

Less than (<)

Equal to (=)

There are several ways of comparing fractions. You can compare some fractions simply by observing the numerators and denominators.

Comparing fractions by simple observation

Example

Use >, < or = to compare 1/2 and 1/3 .

Solution

If you cut a piece of cake into 2 parts and cut another piece of cake of the same size into 3, the 1 part out of 2 will be bigger than 1 part out of 3. So

1/2 >1/3 .

Note:

The more parts you share the cake in, the smaller the piece. Therefore;

Also when the numerator is equal, the bigger the denominator the smaller the fraction. That is

Also

More than half or less than half

You can also compare fractions by checking if one of them is greater or less than 1/2.

Example

Use (>, < or =) to compare 4/5 and 3/5 and2/7

Double 4 is 8 so 4/8= 1/2.

Double 3 is 6 and 6 is more than 5.

So 3/5 is more than1/2 .

Double 2 is 4 and 4 is less than 7, so 2/7 is less than1/2 .

Therefore, 2/7 < 4/8 < 3/5 . OR 3/5 > 4/8 > 2/7.

3/5 is the largest of the three fractions.

Comparing fractions using the numerator and denominator.

When two fractions have the same numerator, we look at their denominators to compare. The one with the smaller denominator is greater.

Also when the numerator is equal, the bigger the denominator the smaller the fraction. That is

Also

When two fractions have the same denominator, we look at their numerators when comparing. The fraction with a bigger numerator is greater than the one with a smaller numerator.

Comparing fractions using the cross multiplication method (Butterfly method)

Fractions can also be compared using the cross multiplication or the butterfly method. By cross multiplication, we mean multiplying the denominator of the fraction on the left by the numerator of the fraction on the right and vice ver