# COMPARING AND ORDERING FRACTIONS

Comparing and Ordering Fractions :

In this section, you will learn, how to compare and order fractions.

## Comparing Fractions - Different Cases

Whenever we compare two fractions, first we have to check the denominators.

Case 1 :

If the denominators are same, then we can decide that the fraction which is having the greater numerator is greater.

Case 2 :

If the denominators are different, then we have to make the denominators same and compare the fractions as said in case 1.

To make the denominator same, we have to apply the concept of least common multiple.

## Ordering Fractions - Different Cases

To order fractions from least to greatest or greatest to least, first we have to check the denominators.

Case 1 :

If the denominators are same, then we can compare the values of the numerators and order the fractions.

Case 2 :

If the denominators are different, then we have to make the denominators same and order the fractions as said in case 1.

## Comparing and Ordering Fractions - Examples

Example 1 :

Find which fraction is greater :

6/19  and  16/19

Solution :

Because the denominators of the above fractions are same, we can compare the numerators and decide which fraction is greater as shown below. So,

16/19 is greater than 6/19

Example 2 :

Find which fraction is greater :

1/2  and  3/5

Solution : Here, the denominators are different.

So, we have to find the least common multiple (LCM) of the denominators.

Now, we have to make the denominators of the fractions same using LCM as shown below. Now we can compare the numerators and decide which fraction is greater.

Then, we have

6/10 is greater than 5/10

So,

3/5 is greater than 1/2

Example 3 :

Order the fractions from least to greatest :

5/19, 7/19, 2/19, 3/19

Solution :

Because the denominators of the above fractions are same, we can compare the numerators and order the fractions from least to greatest as shown below.

2/19, 3/19, 5/19, 7/19

Example 4 :

Order the fractions from least to greatest :

3/4, 2/5, 1/8

Solution :

Here, the denominators are different.

So, we have to find the least common multiple (LCM) of the denominators. LCM of (4, 5 and 8)  =  40.

Now we have to make the denominator of each fraction as 40 using multiplication.

Multiply both numerator and denominator of the first fraction by 10

Multiply both numerator and denominator of the second fraction by 8

Multiply both numerator and denominator of the third fraction by 5 Now we can compare the numerators and order the fractions from least to greatest.

5/40, 16/40, 30/40

Therefore, order of the given fractions from least to greatest is

1/8, 2/5, 3/4

Example 5 :

Order the fractions from greatest to least :

5/6, 3/8, 1/4

Solution :

Here, the denominators are different.

So, we have to find the least common multiple (LCM) of the denominators. LCM of (6, 8 and 4)  =  24.

Now we have to make the denominator of each fraction as 24 using multiplication.

Multiply both numerator and denominator of the first fraction by 4

Multiply both numerator and denominator of the second fraction by 3

Multiply both numerator and denominator of the third fraction by 6 Now we can compare the numerators and order the fractions from least to greatest.

20/24, 9/24, 6/24

Therefore, order of the given fractions from least to greatest is

5/6, 3/8, 1/4 After having gone through the stuff given above, we hope that the students would have understood, how to compare and order fractions.

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