Ratio & Proportion (Exercise 9.2) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

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Exercise 9.2        Page No: 9.10 
 
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) Given 3: 4 or 9: 16 
LCM for 4 and 16 is 16 
3: 4 can be written as = 3/4 
3/4 × (4/4) = 12/16 
And we have 9/16 
Clearly 12 > 9 
Therefore 3: 4 > 9: 16 
 
(ii) Given 15: 16 or 24: 25 
LCM for 16 and 25 is 400 
15: 16 can be written as = 15/16 
15/16 × (25/25) = 375/400 
And we have 24/25 
24/25 × (16/16) = 384/400 
Clearly 384 > 375 
Therefore 15: 16 < 24: 25 
 
(iii) Given 4: 7 or 5: 8 
LCM for 7 and 8 is 56 
4: 7 can be written as = 4/7 
4/7 × (8/8) = 32/56 
And we have 5/8 
5/8 × (7/7) = 35/56 
Clearly 35 > 32 
Therefore 4: 7 < 5: 8 
 
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Exercise 9.2        Page No: 9.10 
 
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) Given 3: 4 or 9: 16 
LCM for 4 and 16 is 16 
3: 4 can be written as = 3/4 
3/4 × (4/4) = 12/16 
And we have 9/16 
Clearly 12 > 9 
Therefore 3: 4 > 9: 16 
 
(ii) Given 15: 16 or 24: 25 
LCM for 16 and 25 is 400 
15: 16 can be written as = 15/16 
15/16 × (25/25) = 375/400 
And we have 24/25 
24/25 × (16/16) = 384/400 
Clearly 384 > 375 
Therefore 15: 16 < 24: 25 
 
(iii) Given 4: 7 or 5: 8 
LCM for 7 and 8 is 56 
4: 7 can be written as = 4/7 
4/7 × (8/8) = 32/56 
And we have 5/8 
5/8 × (7/7) = 35/56 
Clearly 35 > 32 
Therefore 4: 7 < 5: 8 
 
  
 
 
 
 
  
 
(iv) Given 9: 20 or 8: 13 
LCM for 20 and 13 is 260 
9: 20 can be written as = 9/20 
9/20 × (13/13) = 117/260 
And we have 8/13 
8/13 × (20/20) = 160/260 
Clearly 160 > 117 
Therefore 9: 20 < 8: 13 
 
(v) Given 1: 2 or 13: 27 
LCM for 2 and 27 is 54 
1: 2 can be written as = 1/2 
1/2 × (27/27) = 27/54 
And we have 13/27 
13/27 × (2/2) = 26/54 
Clearly 27 > 26 
Therefore 1: 2 > 13: 27 
 
2. Give the equivalent ratios of 6: 8. 
 
Solution: 
Given 6: 8 
By multiplying both numerator and denominator by 2 we equivalent ratios 
6/8 × (2/2) = 12/16 
And also by dividing both numerator and denominator by 2 we equivalent ratios 
(6/2)/ (8/2) = 3/4 
Two equivalent ratios are 3: 4 = 12: 16 
 
3.  Fill in the following blanks: 
12/20 = …. /5 = 9/…. 
 
Solution: 
12/20 = 3/5 = 9/15 
 
Explanation: 
Consider 12/20 = …. /5 
Let unknown value be x 
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Exercise 9.2        Page No: 9.10 
 
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) Given 3: 4 or 9: 16 
LCM for 4 and 16 is 16 
3: 4 can be written as = 3/4 
3/4 × (4/4) = 12/16 
And we have 9/16 
Clearly 12 > 9 
Therefore 3: 4 > 9: 16 
 
(ii) Given 15: 16 or 24: 25 
LCM for 16 and 25 is 400 
15: 16 can be written as = 15/16 
15/16 × (25/25) = 375/400 
And we have 24/25 
24/25 × (16/16) = 384/400 
Clearly 384 > 375 
Therefore 15: 16 < 24: 25 
 
(iii) Given 4: 7 or 5: 8 
LCM for 7 and 8 is 56 
4: 7 can be written as = 4/7 
4/7 × (8/8) = 32/56 
And we have 5/8 
5/8 × (7/7) = 35/56 
Clearly 35 > 32 
Therefore 4: 7 < 5: 8 
 
  
 
 
 
 
  
 
(iv) Given 9: 20 or 8: 13 
LCM for 20 and 13 is 260 
9: 20 can be written as = 9/20 
9/20 × (13/13) = 117/260 
And we have 8/13 
8/13 × (20/20) = 160/260 
Clearly 160 > 117 
Therefore 9: 20 < 8: 13 
 
(v) Given 1: 2 or 13: 27 
LCM for 2 and 27 is 54 
1: 2 can be written as = 1/2 
1/2 × (27/27) = 27/54 
And we have 13/27 
13/27 × (2/2) = 26/54 
Clearly 27 > 26 
Therefore 1: 2 > 13: 27 
 
2. Give the equivalent ratios of 6: 8. 
 
Solution: 
Given 6: 8 
By multiplying both numerator and denominator by 2 we equivalent ratios 
6/8 × (2/2) = 12/16 
And also by dividing both numerator and denominator by 2 we equivalent ratios 
(6/2)/ (8/2) = 3/4 
Two equivalent ratios are 3: 4 = 12: 16 
 
3.  Fill in the following blanks: 
12/20 = …. /5 = 9/…. 
 
Solution: 
12/20 = 3/5 = 9/15 
 
Explanation: 
Consider 12/20 = …. /5 
Let unknown value be x 
  
 
 
 
 
  
 
Therefore 12/20 = x/5 
On cross multiplying 
x = 60/20 
x = 3 
Consider 12/20 = 9/…. 
Let the unknown value be y 
Therefore 12/20 = 9/y 
On cross multiplying we get 
y = 180/12 
y = 15