HOW TO COMPARE TWO RATIOS

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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