**Compare rational numbers :**

In this section, we are going to see, how to compare rational numbers.

Let us see the steps involved in comparing two rational numbers.

Whenever we want to compare two rational numbers in the form a/b, first we have to check the denominators.

**Case 1 :**

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

**Case 2 :**

**If the denominators are different then we have to convert each fraction into equivalent fraction with the common denominator.**

**By finding the least common multiple, we can make the denominators same.**

**After converting both fractions with common denominators, we can compare and decide which fraction is greater and which is smaller.**

**Let us see some examples based on the above concept.**

**Example 1 :**

**Compare the fractions, and write >, < or = in the box.**

**Solution :**

To compare the above two fractions, first we have to consider the denominators.Since the denominators are not same, we have to take L.C.M.

L.C.M = 3 x 3 x 4 = 36

- In order to make the denominator of the first fraction as 36, we have to multiply both numerator and denominator of the first fraction by 4.
- In order to make the denominator of the second fraction as 36, we have to multiply both numerator and denominator of the first fraction by 9.

(4/9) x (4/4) = 16/36

(7/12) x (3/3) = 21/36

By comparing the numerators, we come to know that the fraction 16/36 is lesser than 21/36.

Hence, the answer is

**Example 2 :**

**Compare the fractions, and write >, < or = in the box.**

**Solution :**

To compare the above two fractions, first we have to consider the denominators.Since the denominators are not same, we have to take L.C.M.

L.C.M = 14 x 5 = 60

- In order to make the denominator of the first fraction as 60, we have to multiply both numerator and denominator of the first fraction by 5.
- In order to make the denominator of the second fraction as 36, we have to multiply both numerator and denominator of the first fraction by 36.

(7/14) x (5/5) = 35/60

(1/5) x (14/14) = 14/60

By comparing the numerators, we come to know that the fraction 35/60 is greater than 14/60.

Hence, the answer is

**Example 3 :**

**Compare the fractions, and write >, < or = in the box.**

**Solution :**

To compare the above two fractions, first we have to consider the denominators.Since the denominators are not same, we have to take L.C.M.

L.C.M = 2 x 8 x 7 = 112

- In order to make the denominator of the first fraction as 112, we have to multiply both numerator and denominator of the first fraction by 7.
- In order to make the denominator of the second fraction as 112, we have to multiply both numerator and denominator of the first fraction by 8.

(8/16) x (7/7) = 56/112

(13/14) x (8/8) = 104/112

By comparing the numerators, we come to know that the fraction 104/112 is greater than 56/112.

Hence, the answer is

**Example 4 :**

**Compare the fractions, and write >, < or = in the box.**

**Solution :**

L.C.M = 2 x 9 = 18

- In order to make the denominator of the first fraction as 18, we have to multiply both numerator and denominator of the first fraction by 9.
- In order to make the denominator of the second fraction as 18, we have to multiply both numerator and denominator of the first fraction by 2.

(1/2) x (9/9) = 9/18

(4/9) x (2/2) = 8/18

By comparing the numerators, we come to know that the fraction 9/18 is greater than 8/18.

Hence, the answer is

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