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Exercise 5.2         Page No: 5.7 
 
1. Subtract the first rational number from the second in each of the following: 
(i) (3/8), (5/8) 
(ii) (-7/9), (4/9) 
(iii) (-2/11), (-9/11) 
(iv) (11/13), (-4/13) 
 
Solution: 
(i) Given (3/8), (5/8) 
(5/8) – (3/8) = (5 – 3)/8 
= (2/8) 
= (1/4) 
 
(ii) Given (-7/9), (4/9) 
(4/9) – (-7/9) = (4/9) + (7/9) 
= (4 + 7)/9 
= (11/9) 
 
(iii) Given (-2/11), (-9/11) 
(-9/11) – (-2/11) = (-9/11) + (2/11) 
= (-9 + 2)/ 11 
= (-7/11) 
 
(iv) Given (11/13), (-4/13) 
(-4/13) – (11/13) = (-4 – 11)/13 
= (-15/13) 
 
2. Evaluate each of the following: 
(i) (2/3) – (3/5) 
(ii) (-4/7) – (2/-3) 
(iii) (4/7) – (-5/-7) 
(iv) -2 – (5/9) 
 
Solution: 
(i) Given (2/3) – (3/5) 
The LCM of 3 and 5 is 15 
Page 2


 
 
 
 
 
 
 
Exercise 5.2         Page No: 5.7 
 
1. Subtract the first rational number from the second in each of the following: 
(i) (3/8), (5/8) 
(ii) (-7/9), (4/9) 
(iii) (-2/11), (-9/11) 
(iv) (11/13), (-4/13) 
 
Solution: 
(i) Given (3/8), (5/8) 
(5/8) – (3/8) = (5 – 3)/8 
= (2/8) 
= (1/4) 
 
(ii) Given (-7/9), (4/9) 
(4/9) – (-7/9) = (4/9) + (7/9) 
= (4 + 7)/9 
= (11/9) 
 
(iii) Given (-2/11), (-9/11) 
(-9/11) – (-2/11) = (-9/11) + (2/11) 
= (-9 + 2)/ 11 
= (-7/11) 
 
(iv) Given (11/13), (-4/13) 
(-4/13) – (11/13) = (-4 – 11)/13 
= (-15/13) 
 
2. Evaluate each of the following: 
(i) (2/3) – (3/5) 
(ii) (-4/7) – (2/-3) 
(iii) (4/7) – (-5/-7) 
(iv) -2 – (5/9) 
 
Solution: 
(i) Given (2/3) – (3/5) 
The LCM of 3 and 5 is 15 
 
 
 
 
 
 
 
Consider (2/3) = (2/3) × (5/5) = (10/15) 
Now again (3/5) = (3/5) × (3/3) = (9/15) 
(2/3) – (3/5) = (10/15) – (9/15) 
= (1/15) 
 
(ii) Given (-4/7) – (2/-3) 
The LCM of 7 and 3 is 21 
Consider (-4/7) = (-4/7) × (3/3) = (-12/21) 
Again (2/-3) = (-2/3) × (7/7) = (-14/21) 
(-4/7) – (2/-3) = (-12/21) – (-14/21) 
= (-12 + 14)/21 
= (2/21) 
 
(iii) Given (4/7) – (-5/-7) 
(4/7) – (5/7) = (4 -5)/7 
= (-1/7) 
 
(iv) Given -2 – (5/9) 
Consider (-2/1) = (-2/1) × (9/9) = (-18/9) 
-2 – (5/9) = (-18/9) – (5/9) 
= (-18 -5)/9 
= (-23/9) 
 
3. The sum of the two numbers is (5/9). If one of the numbers is (1/3), find the other. 
 
Solution: 
Given sum of two numbers is (5/9) 
And one them is (1/3) 
Let the unknown number be x 
x + (1/3) = (5/9) 
x = (5/9) – (1/3) 
LCM of 3 and 9 is 9 
Consider (1/3) = (1/3) × (3/3) = (3/9) 
On substituting we get 
x = (5/9) – (3/9) 
x = (5 – 3)/9 
x = (2/9) 
Page 3


 
 
 
 
 
 
 
Exercise 5.2         Page No: 5.7 
 
1. Subtract the first rational number from the second in each of the following: 
(i) (3/8), (5/8) 
(ii) (-7/9), (4/9) 
(iii) (-2/11), (-9/11) 
(iv) (11/13), (-4/13) 
 
Solution: 
(i) Given (3/8), (5/8) 
(5/8) – (3/8) = (5 – 3)/8 
= (2/8) 
= (1/4) 
 
(ii) Given (-7/9), (4/9) 
(4/9) – (-7/9) = (4/9) + (7/9) 
= (4 + 7)/9 
= (11/9) 
 
(iii) Given (-2/11), (-9/11) 
(-9/11) – (-2/11) = (-9/11) + (2/11) 
= (-9 + 2)/ 11 
= (-7/11) 
 
(iv) Given (11/13), (-4/13) 
(-4/13) – (11/13) = (-4 – 11)/13 
= (-15/13) 
 
2. Evaluate each of the following: 
(i) (2/3) – (3/5) 
(ii) (-4/7) – (2/-3) 
(iii) (4/7) – (-5/-7) 
(iv) -2 – (5/9) 
 
Solution: 
(i) Given (2/3) – (3/5) 
The LCM of 3 and 5 is 15 
 
 
 
 
 
 
 
Consider (2/3) = (2/3) × (5/5) = (10/15) 
Now again (3/5) = (3/5) × (3/3) = (9/15) 
(2/3) – (3/5) = (10/15) – (9/15) 
= (1/15) 
 
(ii) Given (-4/7) – (2/-3) 
The LCM of 7 and 3 is 21 
Consider (-4/7) = (-4/7) × (3/3) = (-12/21) 
Again (2/-3) = (-2/3) × (7/7) = (-14/21) 
(-4/7) – (2/-3) = (-12/21) – (-14/21) 
= (-12 + 14)/21 
= (2/21) 
 
(iii) Given (4/7) – (-5/-7) 
(4/7) – (5/7) = (4 -5)/7 
= (-1/7) 
 
(iv) Given -2 – (5/9) 
Consider (-2/1) = (-2/1) × (9/9) = (-18/9) 
-2 – (5/9) = (-18/9) – (5/9) 
= (-18 -5)/9 
= (-23/9) 
 
3. The sum of the two numbers is (5/9). If one of the numbers is (1/3), find the other. 
 
Solution: 
Given sum of two numbers is (5/9) 
And one them is (1/3) 
Let the unknown number be x 
x + (1/3) = (5/9) 
x = (5/9) – (1/3) 
LCM of 3 and 9 is 9 
Consider (1/3) = (1/3) × (3/3) = (3/9) 
On substituting we get 
x = (5/9) – (3/9) 
x = (5 – 3)/9 
x = (2/9) 
 
 
 
 
 
 
 
4. The sum of two numbers is (-1/3). If one of the numbers is (-12/3), find the other. 
 
Solution: 
Given sum of two numbers = (-1/3) 
One of them is (-12/3) 
Let the required number be x 
x + (-12/3) = (-1/3) 
x = (-1/3) – (-12/3) 
x = (-1/3) + (12/3) 
x = (-1 + 12)/3 
x = (11/3) 
 
5. The sum of two numbers is (– 4/3). If one of the numbers is -5, find the other. 
 
Solution: 
Given sum of two numbers = (-4/3) 
One of them is -5 
Let the required number be x 
x + (-5) = (-4/3) 
LCM of 1 and 3 is 3 
(-5/1) = (-5/1) × (3/3) = (-15/3) 
On substituting 
x + (-15/3) = (-4/3) 
x = (-4/3) – (-15/3) 
x = (-4/3) + (15/3) 
x = (-4 + 15)/3 
x = (11/3) 
 
6. The sum of two rational numbers is - 8. If one of the numbers is (-15/7), find the 
other. 
 
Solution: 
Given sum of two numbers is -8 
One of them is (-15/7) 
Let the required number be x 
x + (-15/7) = -8 
The LCM of 7 and 1 is 7 
Page 4


 
 
 
 
 
 
 
Exercise 5.2         Page No: 5.7 
 
1. Subtract the first rational number from the second in each of the following: 
(i) (3/8), (5/8) 
(ii) (-7/9), (4/9) 
(iii) (-2/11), (-9/11) 
(iv) (11/13), (-4/13) 
 
Solution: 
(i) Given (3/8), (5/8) 
(5/8) – (3/8) = (5 – 3)/8 
= (2/8) 
= (1/4) 
 
(ii) Given (-7/9), (4/9) 
(4/9) – (-7/9) = (4/9) + (7/9) 
= (4 + 7)/9 
= (11/9) 
 
(iii) Given (-2/11), (-9/11) 
(-9/11) – (-2/11) = (-9/11) + (2/11) 
= (-9 + 2)/ 11 
= (-7/11) 
 
(iv) Given (11/13), (-4/13) 
(-4/13) – (11/13) = (-4 – 11)/13 
= (-15/13) 
 
2. Evaluate each of the following: 
(i) (2/3) – (3/5) 
(ii) (-4/7) – (2/-3) 
(iii) (4/7) – (-5/-7) 
(iv) -2 – (5/9) 
 
Solution: 
(i) Given (2/3) – (3/5) 
The LCM of 3 and 5 is 15 
 
 
 
 
 
 
 
Consider (2/3) = (2/3) × (5/5) = (10/15) 
Now again (3/5) = (3/5) × (3/3) = (9/15) 
(2/3) – (3/5) = (10/15) – (9/15) 
= (1/15) 
 
(ii) Given (-4/7) – (2/-3) 
The LCM of 7 and 3 is 21 
Consider (-4/7) = (-4/7) × (3/3) = (-12/21) 
Again (2/-3) = (-2/3) × (7/7) = (-14/21) 
(-4/7) – (2/-3) = (-12/21) – (-14/21) 
= (-12 + 14)/21 
= (2/21) 
 
(iii) Given (4/7) – (-5/-7) 
(4/7) – (5/7) = (4 -5)/7 
= (-1/7) 
 
(iv) Given -2 – (5/9) 
Consider (-2/1) = (-2/1) × (9/9) = (-18/9) 
-2 – (5/9) = (-18/9) – (5/9) 
= (-18 -5)/9 
= (-23/9) 
 
3. The sum of the two numbers is (5/9). If one of the numbers is (1/3), find the other. 
 
Solution: 
Given sum of two numbers is (5/9) 
And one them is (1/3) 
Let the unknown number be x 
x + (1/3) = (5/9) 
x = (5/9) – (1/3) 
LCM of 3 and 9 is 9 
Consider (1/3) = (1/3) × (3/3) = (3/9) 
On substituting we get 
x = (5/9) – (3/9) 
x = (5 – 3)/9 
x = (2/9) 
 
 
 
 
 
 
 
4. The sum of two numbers is (-1/3). If one of the numbers is (-12/3), find the other. 
 
Solution: 
Given sum of two numbers = (-1/3) 
One of them is (-12/3) 
Let the required number be x 
x + (-12/3) = (-1/3) 
x = (-1/3) – (-12/3) 
x = (-1/3) + (12/3) 
x = (-1 + 12)/3 
x = (11/3) 
 
5. The sum of two numbers is (– 4/3). If one of the numbers is -5, find the other. 
 
Solution: 
Given sum of two numbers = (-4/3) 
One of them is -5 
Let the required number be x 
x + (-5) = (-4/3) 
LCM of 1 and 3 is 3 
(-5/1) = (-5/1) × (3/3) = (-15/3) 
On substituting 
x + (-15/3) = (-4/3) 
x = (-4/3) – (-15/3) 
x = (-4/3) + (15/3) 
x = (-4 + 15)/3 
x = (11/3) 
 
6. The sum of two rational numbers is - 8. If one of the numbers is (-15/7), find the 
other. 
 
Solution: 
Given sum of two numbers is -8 
One of them is (-15/7) 
Let the required number be x 
x + (-15/7) = -8 
The LCM of 7 and 1 is 7 
 
 
 
 
 
 
 
Consider (-8/1) = (-8/1) × (7/7) = (-56/7) 
On substituting  
x + (-15/7) = (-56/7) 
x = (-56/7) – (-15/7) 
x = (-56/7) + (15/7) 
x = (-56 + 15)/7 
x = (-41/7) 
 
7. What should be added to (-7/8) so as to get (5/9)? 
 
Solution: 
Given (-7/8) 
Let the required number be x 
x + (-7/8) = (5/9) 
The LCM of 8 and 9 is 72 
x = (5/9) – (-7/8) 
x = (5/9) + (7/8) 
Consider (5/9) = (5/9) × (8/8) = (40/72) 
Again (7/8) = (7/8) × (9/8) = (63/72) 
On substituting 
x = (40/72) + (63/72) 
x = (40 + 63)/72 
x = (103/72)  
 
8. What number should be added to (-5/11) so as to get (26/33)? 
 
Solution: 
Given (-5/11) 
Let the required number be x 
x + (-5/11) = (26/33) 
x = (26/33) – (-5/11) 
x = (26/33) + (5/11) 
Consider (5/11) = (5/11) × (3/3) = (15/33) 
On substituting 
x = (26/33) + (15/33) 
x = (41/33) 
 
Page 5


 
 
 
 
 
 
 
Exercise 5.2         Page No: 5.7 
 
1. Subtract the first rational number from the second in each of the following: 
(i) (3/8), (5/8) 
(ii) (-7/9), (4/9) 
(iii) (-2/11), (-9/11) 
(iv) (11/13), (-4/13) 
 
Solution: 
(i) Given (3/8), (5/8) 
(5/8) – (3/8) = (5 – 3)/8 
= (2/8) 
= (1/4) 
 
(ii) Given (-7/9), (4/9) 
(4/9) – (-7/9) = (4/9) + (7/9) 
= (4 + 7)/9 
= (11/9) 
 
(iii) Given (-2/11), (-9/11) 
(-9/11) – (-2/11) = (-9/11) + (2/11) 
= (-9 + 2)/ 11 
= (-7/11) 
 
(iv) Given (11/13), (-4/13) 
(-4/13) – (11/13) = (-4 – 11)/13 
= (-15/13) 
 
2. Evaluate each of the following: 
(i) (2/3) – (3/5) 
(ii) (-4/7) – (2/-3) 
(iii) (4/7) – (-5/-7) 
(iv) -2 – (5/9) 
 
Solution: 
(i) Given (2/3) – (3/5) 
The LCM of 3 and 5 is 15 
 
 
 
 
 
 
 
Consider (2/3) = (2/3) × (5/5) = (10/15) 
Now again (3/5) = (3/5) × (3/3) = (9/15) 
(2/3) – (3/5) = (10/15) – (9/15) 
= (1/15) 
 
(ii) Given (-4/7) – (2/-3) 
The LCM of 7 and 3 is 21 
Consider (-4/7) = (-4/7) × (3/3) = (-12/21) 
Again (2/-3) = (-2/3) × (7/7) = (-14/21) 
(-4/7) – (2/-3) = (-12/21) – (-14/21) 
= (-12 + 14)/21 
= (2/21) 
 
(iii) Given (4/7) – (-5/-7) 
(4/7) – (5/7) = (4 -5)/7 
= (-1/7) 
 
(iv) Given -2 – (5/9) 
Consider (-2/1) = (-2/1) × (9/9) = (-18/9) 
-2 – (5/9) = (-18/9) – (5/9) 
= (-18 -5)/9 
= (-23/9) 
 
3. The sum of the two numbers is (5/9). If one of the numbers is (1/3), find the other. 
 
Solution: 
Given sum of two numbers is (5/9) 
And one them is (1/3) 
Let the unknown number be x 
x + (1/3) = (5/9) 
x = (5/9) – (1/3) 
LCM of 3 and 9 is 9 
Consider (1/3) = (1/3) × (3/3) = (3/9) 
On substituting we get 
x = (5/9) – (3/9) 
x = (5 – 3)/9 
x = (2/9) 
 
 
 
 
 
 
 
4. The sum of two numbers is (-1/3). If one of the numbers is (-12/3), find the other. 
 
Solution: 
Given sum of two numbers = (-1/3) 
One of them is (-12/3) 
Let the required number be x 
x + (-12/3) = (-1/3) 
x = (-1/3) – (-12/3) 
x = (-1/3) + (12/3) 
x = (-1 + 12)/3 
x = (11/3) 
 
5. The sum of two numbers is (– 4/3). If one of the numbers is -5, find the other. 
 
Solution: 
Given sum of two numbers = (-4/3) 
One of them is -5 
Let the required number be x 
x + (-5) = (-4/3) 
LCM of 1 and 3 is 3 
(-5/1) = (-5/1) × (3/3) = (-15/3) 
On substituting 
x + (-15/3) = (-4/3) 
x = (-4/3) – (-15/3) 
x = (-4/3) + (15/3) 
x = (-4 + 15)/3 
x = (11/3) 
 
6. The sum of two rational numbers is - 8. If one of the numbers is (-15/7), find the 
other. 
 
Solution: 
Given sum of two numbers is -8 
One of them is (-15/7) 
Let the required number be x 
x + (-15/7) = -8 
The LCM of 7 and 1 is 7 
 
 
 
 
 
 
 
Consider (-8/1) = (-8/1) × (7/7) = (-56/7) 
On substituting  
x + (-15/7) = (-56/7) 
x = (-56/7) – (-15/7) 
x = (-56/7) + (15/7) 
x = (-56 + 15)/7 
x = (-41/7) 
 
7. What should be added to (-7/8) so as to get (5/9)? 
 
Solution: 
Given (-7/8) 
Let the required number be x 
x + (-7/8) = (5/9) 
The LCM of 8 and 9 is 72 
x = (5/9) – (-7/8) 
x = (5/9) + (7/8) 
Consider (5/9) = (5/9) × (8/8) = (40/72) 
Again (7/8) = (7/8) × (9/8) = (63/72) 
On substituting 
x = (40/72) + (63/72) 
x = (40 + 63)/72 
x = (103/72)  
 
8. What number should be added to (-5/11) so as to get (26/33)? 
 
Solution: 
Given (-5/11) 
Let the required number be x 
x + (-5/11) = (26/33) 
x = (26/33) – (-5/11) 
x = (26/33) + (5/11) 
Consider (5/11) = (5/11) × (3/3) = (15/33) 
On substituting 
x = (26/33) + (15/33) 
x = (41/33) 
 
 
 
 
 
 
 
 
9. What number should be added to (-5/7) to get (-2/3)? 
 
Solution: 
Given (-5/7) 
Let the required number be x 
x + (-5/7) = (-2/3) 
x = (-2/3) – (-5/7) 
x = (-2/3) + (5/7) 
LCM of 3 and 7 is 21 
Consider (-2/3) = (-2/3) × (7/7) = (-14/21) 
Again (5/7) = (5/7) × (3/3) = (15/21) 
On substituting 
x = (-14/21) + (15/21) 
x = (-14 + 15)/21 
x = (1/21) 
 
10. What number should be subtracted from (-5/3) to get (5/6)? 
 
Solution: 
Given (-5/3) 
Let the required number be x 
(-5/3) – x = (5/6) 
- x = (5/6) – (-5/3) 
- x = (5/6) + (5/3) 
Consider (5/3) = (5/3) × (2/2) = (10/6) 
On substituting 
- x = (5/6) + (10/6) 
- x = (15/6) 
x = (-15/6) 
 
11. What number should be subtracted from (3/7) to get (5/4)? 
 
Solution: 
Given (3/7) 
Let the required number be x 
(3/7) – x = (5/4) 
- x = (5/4) – (3/7)

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RD Sharma Solutions: Operations On Rational Numbers (Exercise 5.2) Class 7 Questions

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