Operations On Rational Numbers (Exercise 5.5) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

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Exercise 5.5         Page No: 5.16 
 
1. Find six rational numbers between (-4/8) and (3/8) 
 
Solution: 
We know that between -4 and -8, below mentioned numbers will lie 
-3, -2, -1, 0, 1, 2. 
According to definition of rational numbers are in the form of (p/q) where q not equal to 
zero. 
Therefore six rational numbers between (-4/8) and (3/8) are  
(-3/8), (-2/8), (-1/8), (0/8), (1/8), (2/8), (3/8)  
 
2. Find 10 rational numbers between (7/13) and (- 4/13) 
 
Solution: 
We know that between 7 and -4, below mentioned numbers will lie 
-3, -2, -1, 0, 1, 2, 3, 4, 5, 6. 
According to definition of rational numbers are in the form of (p/q) where q not equal to 
zero. 
Therefore six rational numbers between (7/13) and (-4/13) are  
(-3/13), (-2/13), (-1/13), (0/13), (1/13), (2/13), (3/13), (4/13), (5/13), (6/13) 
 
3. State true or false: 
(i) Between any two distinct integers there is always an integer. 
(ii) Between any two distinct rational numbers there is always a rational number. 
(iii) Between any two distinct rational numbers there are infinitely many rational 
numbers. 
 
Solution: 
(i) False 
  
Explanation: 
Between any two distinct integers not necessary to be one integer. 
 
(ii) True 
 
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Exercise 5.5         Page No: 5.16 
 
1. Find six rational numbers between (-4/8) and (3/8) 
 
Solution: 
We know that between -4 and -8, below mentioned numbers will lie 
-3, -2, -1, 0, 1, 2. 
According to definition of rational numbers are in the form of (p/q) where q not equal to 
zero. 
Therefore six rational numbers between (-4/8) and (3/8) are  
(-3/8), (-2/8), (-1/8), (0/8), (1/8), (2/8), (3/8)  
 
2. Find 10 rational numbers between (7/13) and (- 4/13) 
 
Solution: 
We know that between 7 and -4, below mentioned numbers will lie 
-3, -2, -1, 0, 1, 2, 3, 4, 5, 6. 
According to definition of rational numbers are in the form of (p/q) where q not equal to 
zero. 
Therefore six rational numbers between (7/13) and (-4/13) are  
(-3/13), (-2/13), (-1/13), (0/13), (1/13), (2/13), (3/13), (4/13), (5/13), (6/13) 
 
3. State true or false: 
(i) Between any two distinct integers there is always an integer. 
(ii) Between any two distinct rational numbers there is always a rational number. 
(iii) Between any two distinct rational numbers there are infinitely many rational 
numbers. 
 
Solution: 
(i) False 
  
Explanation: 
Between any two distinct integers not necessary to be one integer. 
 
(ii) True 
 
 
 
 
 
 
 
 
Explanation: 
According to the properties of rational numbers between any two distinct rational 
numbers there is always a rational number. 
 
(iii) True  
 
Explanation: 
According to the properties of rational numbers between any two distinct rational 
numbers there are infinitely many rational numbers.