Because a ratio can be expressed as a fraction, we can compare the two ratios using fractions.

We can follow the steps given below to compare two ratios.

**Step 1 :**

Write the given two ratios as fractions.

**Step 2 :**

Find the least common multiple of the denominators of both the fractions (if the denominators are not same).

**Step 3 :**

Make the denominators of both the fractions same as the value of least common multiple found in step 1 using multiplication.

**Step 4 :**

After getting same denominator for both the fractions, compare the numerators and decide which fraction is greater.

The fraction which has larger numerator is greater in value.

**Example 1 :**

Compare 3 : 5 and 4 : 7.

**Solution :**

Write the given ratios as fractions.

3 : 5 = 3/5

4 : 7 = 4/7

The least common multiple of the denominators 5 and 7 is 35.

Make the denominators of the fractions as 35 using multiplication.

3/5 = (3 ⋅ 7) / (5 ⋅ 7) = 21/35

4/7 = (3 ⋅ 5) / (7 ⋅ 5) = 20/35

Compare the numerators.

21 > 20

Then,

21/35 > 20/35

3 : 5 > 4 : 7

So, 3 : 5 is greater than 4 : 7.

**Example 2 :**

Compare 2 : 3 and 3 : 4.

**Solution :**

Write the given ratios as fractions.

2 : 3 = 2/3

3 : 4 = 3/4

The least common multiple of the denominators 3 and 4 is 12.

Make the denominators of the fractions as 12 using multiplication.

2/3 = (2 ⋅ 4) / (3 ⋅ 4) = 8/12

3/4 = (3 ⋅ 3) / (4 ⋅ 3) = 9/12

Compare the numerators.

8 < 9

Then,

8/12 < 9/12

2 : 3 < 3 : 4

So, 2 : 3 is less than 3 : 4.

**Example 3 :**

Compare 4 : 5 and 5 : 7.

**Solution :**

Write the given ratios as fractions.

4 : 5 = 4/5

5 : 7 = 5/7

The least common multiple of the denominators 5 and 7 is 35.

Make the denominators of the fractions as 35 using multiplication.

4/5 = (4 ⋅ 7) / (5 ⋅ 7) = 28/35

5/7 = (5 ⋅ 5) / (7 ⋅ 5) = 25/35

Compare the numerators.

28 > 25

Then,

28/35 > 25/35

4 : 5 > 5 : 7

So, 4 : 5 is greater than 5 : 7.

**Example 4 :**

Compare 3 : 4 and 4 : 5.

**Solution :**

Write the given ratios as fractions.

3 : 4 = 3/4

4 : 5 = 4/5

The least common multiple of the denominators 4 and 5 is 20.

Make the denominators of the fractions as 20 using multiplication.

3/4 = (3 ⋅ 5) / (4 ⋅ 5) = 15/20

4/5 = (4 ⋅ 4) / (5 ⋅ 4) = 16/20

Compare the numerators.

15 < 16

Then,

15/20 < 16/20

3 : 4 < 4 : 5

So, 3 : 4 is greater than 4 : 5.

**Example 5 :**

Compare 5 : 12 and 7 : 18.

**Solution :**

Write the given ratios as fractions.

5 : 12 = 5/12

7 : 18 = 7/18

The least common multiple of the denominators 12 and 18 is 36.

Make the denominators of the fractions as 36 using multiplication.

5/12 = (5 ⋅ 3) / (12 ⋅ 3) = 15/36

7/18 = (7 ⋅ 2) / (18 ⋅ 2) = 14/36

Compare the numerators.

15 < 14

Then,

15/36 < 14/36

5 : 12 < 7 : 18

So, 5 : 12 is less than 7 : 18.

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