COMPARING RATIOS

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.  

Examples

Example 1 :

Compare 5 : 7 and 3 : 7. 

Solution :

Write the given ratios as fractions.

5 : 7  =  5/7

3 : 7  =  3/7

The fractions 5/7 and 3/7 have the same denominator '7'. 

Compare the numerators. 

5  >  7

Then, 

5/7  >  3/7

5 : 7  >  3 : 7

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

Example 2 :

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 3 :

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.

Example 4 :

Compare 2 ⅓ : 3 ⅓ and 3.6 : 4.8.

Solution :

Write the given ratios as fractions.

2 ⅓ : 3 ⅓  =  7/3 : 10/3

2 ⅓ : 3 ⅓  =  (7/3) ⋅ 3 : (10/3) ⋅ 3

2 ⅓ : 3 ⅓  =  7 : 10

2 ⅓ : 3 ⅓  =  7/10

3.6 : 4.8  =  3.6/4.8

3.6 : 4.8  =  (3.6 ⋅ 10) / (4.8 ⋅ 10)

3.6 : 4.8  =  36 / 48

3.6 : 4.8  =  3/4

The least common multiple of the denominators 10 and 4 is 20.

Make the denominators of the fractions as 20 using multiplication.

7/10  =  (7 ⋅ 2) / (10 ⋅ 2)  =  14/20

3/4  =  (3 ⋅ 5) / (4 ⋅ 5)  =  15/20

Compare the numerators. 

14  <  15

Then, 

14/20  <  15/20

2 ⅓ : 3 ⅓  <  3.6 : 4.8

So, 2 ⅓ : 3 ⅓ is less than 3.6 : 4.8. 

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