Ratio, Proportion & Unitary Method (Exercise 9.2) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

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Exercise 9.2                                                                                  page: 9.9 
1. Which ratio is larger in the following pairs? 
(i) 3: 4 or 9: 16 
(ii) 15: 16 or 24: 25 
(iii) 4: 7 or 5: 8 
(iv) 9: 20 or 8: 13 
(v) 1: 2 or 13: 27 
Solution: 
 
(i) 3: 4 or 9: 16 
It can be written as 
3: 4 = 3/4 and 9: 16 = 9/16 
LCM of 4 and 16 is 16 
Multiplying both numerator and denominator of the term ¾ by 4 to make the denominator 16 
3/4 = (3/4) × (4/4) = 12/16 and 9/16 
We know that 12 > 9 
So we get 12/16 > 9/16 
We can write it as 
3/4 > 9/16 
 
Hence, 3: 4 > 9: 16. 
 
(ii) 15: 16 or 24: 25 
It can be written as 
15: 16 = 15/16 and 24: 25 = 24/25 
LCM of 16 and 25 is 400 
Multiplying both the terms by relevant numbers to make denominator as 400 
15/16 = (15/16) × (25/25) = 375/400 and 24/25 = (24/25) × (16/16) = 384/400 
We know that 384 > 375 
So we get 384/400 > 375/400 
We can write it as 24/25 > 15/16 
 
Hence, 24: 25 > 15: 16. 
 
(iii) 4: 7 or 5: 8 
It can be written as 
4: 7 = 4/7 and 5: 8 = 5/8 
LCM of 7 and 8 is 56 
Multiplying both the terms by relevant numbers to make denominator as 56 
4/7 = (4/7) × (8/8) = 32/56 and 5/8 = (5/8) × (7/7) = 35/56 
We know that 35 > 32 
So we get 35/56 > 32/56 
We can write it as 5/8 > 4/7 
 
Hence, 5: 8 > 4: 7. 
 
(iv) 9: 20 or 8: 13 
It can be written as 
9: 20 = 9/20 and 8: 13 = 8/13 
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Exercise 9.2                                                                                  page: 9.9 
1. Which ratio is larger in the following pairs? 
(i) 3: 4 or 9: 16 
(ii) 15: 16 or 24: 25 
(iii) 4: 7 or 5: 8 
(iv) 9: 20 or 8: 13 
(v) 1: 2 or 13: 27 
Solution: 
 
(i) 3: 4 or 9: 16 
It can be written as 
3: 4 = 3/4 and 9: 16 = 9/16 
LCM of 4 and 16 is 16 
Multiplying both numerator and denominator of the term ¾ by 4 to make the denominator 16 
3/4 = (3/4) × (4/4) = 12/16 and 9/16 
We know that 12 > 9 
So we get 12/16 > 9/16 
We can write it as 
3/4 > 9/16 
 
Hence, 3: 4 > 9: 16. 
 
(ii) 15: 16 or 24: 25 
It can be written as 
15: 16 = 15/16 and 24: 25 = 24/25 
LCM of 16 and 25 is 400 
Multiplying both the terms by relevant numbers to make denominator as 400 
15/16 = (15/16) × (25/25) = 375/400 and 24/25 = (24/25) × (16/16) = 384/400 
We know that 384 > 375 
So we get 384/400 > 375/400 
We can write it as 24/25 > 15/16 
 
Hence, 24: 25 > 15: 16. 
 
(iii) 4: 7 or 5: 8 
It can be written as 
4: 7 = 4/7 and 5: 8 = 5/8 
LCM of 7 and 8 is 56 
Multiplying both the terms by relevant numbers to make denominator as 56 
4/7 = (4/7) × (8/8) = 32/56 and 5/8 = (5/8) × (7/7) = 35/56 
We know that 35 > 32 
So we get 35/56 > 32/56 
We can write it as 5/8 > 4/7 
 
Hence, 5: 8 > 4: 7. 
 
(iv) 9: 20 or 8: 13 
It can be written as 
9: 20 = 9/20 and 8: 13 = 8/13 
 
 
 
 
 
 
LCM of 20 and 13 is 260 
Multiplying both the terms by relevant numbers to make denominator as 260 
9/20 = (9/20) × (13/13) = 117/260 and 8/13 = (8/13) × (20/20) = 160/260 
We know that 160 > 117 
So we get 160/260 > 117/260 
We can write it as 8/13 > 9/20 
 
Hence, 8: 13 > 9: 20. 
 
(v) 1: 2 or 13: 27 
It can be written as 
1: 2 = 1/2 and 13: 27 = 13/27 
LCM of 2 and 27 is 54 
Multiplying both the terms by relevant numbers to make denominator as 54 
1/2 = (1/2) × (27/27) = 27/54 and 13/27 = (13/27) × (2/2) = 26/54 
We know that 27 > 26 
So we get 27/54 > 26/54 
We can write it as 1/2 > 13/27 
 
Hence, 1: 2 > 13: 27. 
 
2. Give two equivalent ratios of 6: 8. 
Solution: 
 
The given ratio = 6: 8 
It can be written as = 6/8 
Dividing the fraction by 2 we get  
6/8 = (6/8) ÷ (2/2) = 3/4 
Hence, 3: 4 is an equivalent ratio of 6: 8 
 
Multiply the fraction by 2 we get 
6/8 = (6/8) × (2/2) = 12/16 
Hence, 12: 16 is an equivalent ratio of 6: 8 
 
So, 3: 4 and 12: 16 are the equivalent ratios of 6: 8. 
 
3. Fill in the following blanks: 
12/20 = ?/5 = 9/ ? 
Solution: 
 
It is given that  
12/20 = ?/5 = 9/ ? 
We know that LCM of 20 and 5 is 20 
It can be written as 20/4 = 5 
 
Dividing the fraction by 4 
12/20 = (12/20) × (4/4) = 3/5 
So the first number is 3 and the ratio is 3/5. 
 
In the same way, 
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Exercise 9.2                                                                                  page: 9.9 
1. Which ratio is larger in the following pairs? 
(i) 3: 4 or 9: 16 
(ii) 15: 16 or 24: 25 
(iii) 4: 7 or 5: 8 
(iv) 9: 20 or 8: 13 
(v) 1: 2 or 13: 27 
Solution: 
 
(i) 3: 4 or 9: 16 
It can be written as 
3: 4 = 3/4 and 9: 16 = 9/16 
LCM of 4 and 16 is 16 
Multiplying both numerator and denominator of the term ¾ by 4 to make the denominator 16 
3/4 = (3/4) × (4/4) = 12/16 and 9/16 
We know that 12 > 9 
So we get 12/16 > 9/16 
We can write it as 
3/4 > 9/16 
 
Hence, 3: 4 > 9: 16. 
 
(ii) 15: 16 or 24: 25 
It can be written as 
15: 16 = 15/16 and 24: 25 = 24/25 
LCM of 16 and 25 is 400 
Multiplying both the terms by relevant numbers to make denominator as 400 
15/16 = (15/16) × (25/25) = 375/400 and 24/25 = (24/25) × (16/16) = 384/400 
We know that 384 > 375 
So we get 384/400 > 375/400 
We can write it as 24/25 > 15/16 
 
Hence, 24: 25 > 15: 16. 
 
(iii) 4: 7 or 5: 8 
It can be written as 
4: 7 = 4/7 and 5: 8 = 5/8 
LCM of 7 and 8 is 56 
Multiplying both the terms by relevant numbers to make denominator as 56 
4/7 = (4/7) × (8/8) = 32/56 and 5/8 = (5/8) × (7/7) = 35/56 
We know that 35 > 32 
So we get 35/56 > 32/56 
We can write it as 5/8 > 4/7 
 
Hence, 5: 8 > 4: 7. 
 
(iv) 9: 20 or 8: 13 
It can be written as 
9: 20 = 9/20 and 8: 13 = 8/13 
 
 
 
 
 
 
LCM of 20 and 13 is 260 
Multiplying both the terms by relevant numbers to make denominator as 260 
9/20 = (9/20) × (13/13) = 117/260 and 8/13 = (8/13) × (20/20) = 160/260 
We know that 160 > 117 
So we get 160/260 > 117/260 
We can write it as 8/13 > 9/20 
 
Hence, 8: 13 > 9: 20. 
 
(v) 1: 2 or 13: 27 
It can be written as 
1: 2 = 1/2 and 13: 27 = 13/27 
LCM of 2 and 27 is 54 
Multiplying both the terms by relevant numbers to make denominator as 54 
1/2 = (1/2) × (27/27) = 27/54 and 13/27 = (13/27) × (2/2) = 26/54 
We know that 27 > 26 
So we get 27/54 > 26/54 
We can write it as 1/2 > 13/27 
 
Hence, 1: 2 > 13: 27. 
 
2. Give two equivalent ratios of 6: 8. 
Solution: 
 
The given ratio = 6: 8 
It can be written as = 6/8 
Dividing the fraction by 2 we get  
6/8 = (6/8) ÷ (2/2) = 3/4 
Hence, 3: 4 is an equivalent ratio of 6: 8 
 
Multiply the fraction by 2 we get 
6/8 = (6/8) × (2/2) = 12/16 
Hence, 12: 16 is an equivalent ratio of 6: 8 
 
So, 3: 4 and 12: 16 are the equivalent ratios of 6: 8. 
 
3. Fill in the following blanks: 
12/20 = ?/5 = 9/ ? 
Solution: 
 
It is given that  
12/20 = ?/5 = 9/ ? 
We know that LCM of 20 and 5 is 20 
It can be written as 20/4 = 5 
 
Dividing the fraction by 4 
12/20 = (12/20) × (4/4) = 3/5 
So the first number is 3 and the ratio is 3/5. 
 
In the same way, 
 
 
 
 
 
 
Consider 2/3 + 3/5 = 9/ ? 
We know that 9/3 = 3 
Multiply the fraction by 3 
3/5 = (3/5) × (3/3) = 9/15 
So the second number is 15 and the ratio is 9/15.