**Comparison of ratios :**

Here we are going to see how to compare two or more ratios.

To compare two ratios, we need to follow the steps given below.

**Step 1 :**

Consider the denominators of the given ratios. If they are not same, we have to convert the denominator as same by taking L.C.M

**Step 2 :**

After converting the denominators as same, we may decide that the ratio is greater which has greater numerator.

Let us look into some examples to understand the above concept.

**Example 1 :**

Compare 3:5 and 4:7

**Solution :**

We have to compare 3/5 and 4/7

The L.C.M of denominator 5 and 7 is 35.

(3/5) ⋅ (7/7) = 21/35

(4/7) ⋅ (5/5) = 28/35

By comparing the above fractions 28/35 and 21/35, 28 is greater.

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

4:7 > 3:5

**Example 2 :**

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) ⋅ (7/7) = 28/35

(5/7) ⋅(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 3 :**

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

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 4 and 5 is 20

(3/4) ⋅ (5/5) = 15/20

(4/5) ⋅ (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 4 :**

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

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 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 "Comparison of ratios"

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