1. Rational Numbers – Class 8 Mathematics NCERT Chapter 1 Complete Guide (CBSE)
NCERT Class 8 Mathematics Chapter 1: Rational Numbers – All Exercise Solutions | CBSE Board
Chapter 1: Rational Numbers
Exercise 1.1
1. Using appropriate properties find.
(i) 
(ii) 
Solution: (i) We have, 
(ii) We have, 
2. Write the additive inverse of each of the following.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
Solution : (i) 
The additive inverse of 
(ii)
The additive inverse of 
(iii) 
The additive inverse of 
(iv)
The additive inverse of 
(v)
The additive inverse of 
3. Verify that 
for.
(i) 
(ii) 
Solution : (i)
We have, 
verified .
(ii)
We have , 
verified .
4. Find the multiplicative inverse of the following.
(i) – 13 (ii) 
(iii) 
(iv) 
(v) 
(vi) – 1
Solution : (i) We have, the multiplicative inverse of 
(ii) We have, the multiplicative inverse of 
(iii) We have , the multiplicative inverse of 
(iv) We have, the multiplicative inverse of 
(v) We have , the multiplicative inverse of 
(vi) We have , the multiplicative inverse of 
5. Name the property under multiplication used in each of the following.
(i) 
(ii) 
(iii) 
Solution : (i) 
This is the multiplicative identity Property . Because , 1 is the multiplicative identity .
(ii) 
The multiplication is commutative .
(iii) 
This is the multiplicative inverse .
6. Multiply 
by the reciprocal of 
.
Solution: We have , the reciprocal of 
is 
7. Tell what property allows you to compute 
Solution: The multiplication is associative . [Because, 
]
8. Is 
the multiplicative inverse of 
? Why or why not?
Solution: We have , 
is not the multiplicative inverse of 
, Because the product is not 1 .
9. Is 0.3 the multiplicative inverse of 
? Why or why not ?
Solution: We have , 
The multiplicative inverse of 
is 
Yes , 0.3 is the multiplicative inverse of 
.
10. Write.
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Answer: (i) 0 . (ii) 1 and – 1 . (iii) 0 .
11. Fill in the blanks.
(i) Zero has ________ reciprocal.
(ii) The numbers ________ and ________ are their own reciprocals
(iii) The reciprocal of – 5 is ________.
(iv) Reciprocal of 
, where x ≠ 0 is ________.
(v) The product of two rational numbers is always a _______.
(vi) The reciprocal of a positive rational number is ________.
Answer : (i) Zero has 
reciprocal.
(ii) The numbers 
and 
are their own reciprocals
(iii) The reciprocal of – 5 is 
(iv) Reciprocal of , where 
is 
.
(v) The product of two rational numbers is always a 
.
(vi) The reciprocal of a positive rational number is 
.
Exercise 1.2
1. Represent these numbers on the number line. (i) 
(ii) 
Solution: (i) We draw the number line ,
(ii) We draw the number line,
2. Represent
on the number line.
Solution: We draw the number line ,
3. Write five rational numbers which are smaller than 2.
Solution: The five rational numbers which are smaller than 2 are : – 4 , – 3 , – 2 , – 1 and 1 .
4. Find ten rational numbers between 
and 
Solution: We have , 
and 
Therefore , the ten rational numbers between and are : 
and 
.
5. Find five rational numbers between.
(i) 
(ii) 
(iii) 
Solution : (i) 
We have , 
Therefore ,the five rational numbers between are : 
(ii)
We have , 
Therefore ,the five rational numbers between are : 
(iii)
We have , 
Therefore ,the five rational numbers between are : 
6. Write five rational numbers greater than –2.
Solution: The five rational numbers greater than –2 are : – 1 , 1 , 2 , 3 and 4 [There are infinitely many rational between two rational numbers .]
7. Find ten rational numbers between 
and 
.
Solution: We have , 
and 
The rational numbers are : 
The ten rational numbers between and are 
and 
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