Comparison of Fraction:

To identify which fraction is greater or smaller we go through the comparison. The basic way to identify the fraction is greater or the smaller is cross multiplication. But there is more 2 ways by which we can identify this easily. Those are:

• Type 1: Cross multiplication.
• Type 2: Common difference method.
• Type 3: Easy decimal method.

Type 1: 

In this section we do cross multiplication. We multiply one’s numerator  with another denominator. Which numerator multiplication will be greater that fraction will be greater.

Example:

Suppose, 1/2 and 4/6 are two fractions, If we multiply 1st one numerator with the 2nd one’s denominator then we get; 1 x 6 = 6 and If we multiply 2nd one’s numerator with the 1st one’s denominator then we get; 2 x 4 = 8. Here 2nd numerator’s multiplication is greater. So the 2nd fraction, 4/6 is greater. 

Type 2:
Suppose some fractions are,

5/16, 3/14, 8/19, 13/24

Step 1: Find the  difference of numerator and denominator.

In 5/16 the difference is; 16 – 5 = 11

In 3/14 the difference is; 14 – 3 = 11

In 8/19 the difference is; 19 – 8= 11

In 13/24 the difference is; 24 – 13 = 11

Step 2: If the difference is same then which numerator is greater that will be the greater fraction.

Here, 13>8>5>3, the 13 is the greater numerator.

So, 13/24 is the greater fraction and 3/14 is the smallest fraction.

Type 3:

We can find the decimal of a fraction by dividing the numerator by denominator. But when the number is so big then it is quite hard to do so. There we can do a short trick.

1. We can calculate the difference of the numerator and denominator of a fraction.
2. Then we will divide the numerator by that number.
3. Then we will get some decimal number. From those which one will be the greater that correspond fraction will be the greater.

Example:

Suppose some fractions are;

25/27, 31/37, 81/89, 21/25

Step 1:

Here, the difference of numerator and denominator of fraction 25/27 is 2

The difference of numerator and denominator of fraction 31/37 is 6

The difference of numerator and denominator of fraction 81/89 is 8

the difference of numerator and denominator of fraction 21/25 is 4

Step 2:

25 ÷ 2 = 12.5

31 ÷ 6 = 5.167

81 ÷ 8 = 10.125

21 ÷ 4 = 5.25

Here, 12.5 > 10.125 > 5.25 > 5.167

So, 25/27 > 81/89 > 21/25 > 31/27