**How to compare two ratios :**

Since we can express ratios as a fraction ,so any given ratios can be compared by the method used for fractions.

Let us recall when we had to compare fractions we converted the fractions to have the same denominator.

Let us see some example problems based on the above concept.

**Example 1 :**

Compare 3:5 and 4:7

**Solution :**

To compare the above ratios, let us write each ratio in the fractional form

That is,

3:5 = 3/5

4:7 = 4/7

Since the denominators are not same, we have to take L.C.M in order to make the denominators as same.

L.C.M of 5 and 7 is 35

(3/5) x (7/7) = 21/35

(4/7) x (5/5) = 20/35

21/35 is greater than 20/35.That is 3/5 is greater than 4/7.

Hence the ratio 3:5 is greater than the ratio 4:7.

3:5 > 4:7

**Example 2 :**

Compare 2:3 and 3:4

**Solution :**

To compare the above ratios, let us write each ratio in the fractional form

That is,

2:3 = 2/3

3:4 = 3/4

Since the denominators are not same, we have to take L.C.M in order to make the denominators as same.

L.C.M of 3 and 4 is 12

(2/3) x (4/4) = 8/12

(3/4) x (3/3) = 9/12

9/12 is greater than 8/12.That is 3/4 is greater than 2/3.

Hence the ratio 3:4 is greater than the ratio 2:3.

3:4 > 2:3

**Example 3 :**

Compare 4:5 and 5:7

**Solution :**

To compare the above ratios, let us write each ratio in the fractional form

That is,

4:5 = 4/5

5:7 = 5/7

Since the denominators are not same, we have to take L.C.M in order to make the denominators as same.

L.C.M of 5 and 7 is 35

(4/5) x (7/7) = 28/35

(5/7) x (5/5) = 25/35

28/35 is greater than 25/35.That is, 4/5 is greater than 5/7.

Hence the ratio 4:5 is greater than the ratio 5:7.

4:5 > 5:7

**Example 4 :**

Compare 3:4 and 4:5

**Solution :**

To compare the above ratios, let us write each ratio in the fractional form

That is,

3:4 = 3/4

4:5 = 4/5

L.C.M of 4 and 5 is 20

(3/4) x (5/5) = 15/20

(4/5) x (4/4) = 16/20

16/20 is greater than 15/20.That is, 4/5 is greater than 3/4.

Hence the ratio 4:5 is greater than the ratio 3:4.

4:5 > 3:4

**Example 5 :**

Compare 3:7 and 7:9

**Solution :**

To compare the above ratios, let us write each ratio in the fractional form

That is,

3:7 = 3/7

7:9 = 7/9

L.C.M of 7 and 9 is 63

(3/7) x (9/9) = 27/63

(7/9) x (7/7) = 49/63

49/63 is greater than 27/63.That is, 7/9 is greater than 3/7.

Hence the ratio 7:9 is greater than the ratio 3:7.

4:5 > 3:4

After having gone through the stuff given above, we hope that the students would have understood "How to compare two ratios".

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