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NCERT Solutions for Class 8 Maths Maths – NCERT Solution Chapter 1- Rational Numbers


Exercise 1.1 : Solutions of Questions on Page Number : 14


Q1 : Using appropriate properties find:
(i)
(ii)
Answer :
(i)

(ii)
(By commutativity)


Q2 : Write the additive inverse of each of the following:
(i) (ii) (iii) (iv) (v)
Answer :
(i)
Additive inverse =
(ii)
Additive inverse =
(iii)
Additive inverse =
(iv)
Additive inverse
(v)
Additive inverse


Q3 : Verify that – ( – x) = x for.
(i) (ii)
Answer :
(i)
The additive inverse of is  as
This equality represents that the additive inverse of is or it can be said that i.e., – ( – x) = x
(ii)
The additive inverse of is as
This equality represents that the additive inverse of is- i.e., – ( – x) = x


Q4 : Find the multiplicative inverse of the following.
(i) (ii) (iii)
(iv) (v) (vi) – 1
Answer :
(i) – 13
Multiplicative inverse = –
(ii)
Multiplicative inverse =
(iii)
Multiplicative inverse = 5
(iv)
Multiplicative inverse
(v)
Multiplicative inverse
(vi) – 1
Multiplicative inverse = – 1


Q5 : Name the property under multiplication used in each of the following:
(i)
(ii)
(iii)
Answer :
(i)
1 is the multiplicative identity.
(ii) Commutativity
(iii) Multiplicative inverse


Q6 : Multiply by the reciprocal of.
Answer :


Q7 : Tell what property allows you to compute.
Answer :
Associativity


Q8 : Is the multiplicative inverse of? Why or why not?
Answer :
If it is the multiplicative inverse, then the product should be 1.
However, here, the product is not 1 as


Q9 : Is 0.3 the multiplicative inverse of? Why or why not?
Answer :


0.3 × = 0.3 ×
Here, the product is 1. Hence, 0.3 is the multiplicative inverse of.


Q10 : 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 is a rational number but its reciprocal is not defined.
(ii) 1 and -1 are the rational numbers that are equal to their reciprocals.
(iii) 0 is the rational number that is equal to its negative.


Q11 : 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 is __________.
(v) The product of two rational numbers is always a __________.
(vi) The reciprocal of a positive rational number is __________.
Answer :
(i) No
(ii) 1, – 1
(iii)
(iv) x
(v) Rational number
(vi) Positive rational number


Exercise 1.2 : Solutions of Questions on Page Number : 20


Q1 : Represent these numbers on the number line.
(i) (ii)
Answer :
(i) can be represented on the number line as follows.

(ii) can be represented on the number line as follows.


Q2 : Represent on the number line.
Answer :
can be represented on the number line as follows.


Q3 : Write five rational numbers which are smaller than 2.
Answer :
2 can be represented as.
Therefore, five rational numbers smaller than 2 are


Q4 : Find ten rational numbers between and.
Answer :
and can be represented as respectively.
Therefore, ten rational numbers between and are


Q5 : Find five rational numbers between
(i)
(ii)
(iii)
Answer :
(i) can be represented as respectively.
Therefore, five rational numbers between are
(ii) can be represented as respectively.
Therefore, five rational numbers between are
(iii) can be represented as respectively.
Therefore, five rational numbers between are


Q6 : Write five rational numbers greater than – 2.
Answer :
– 2 can be represented as – .
Therefore, five rational numbers greater than – 2 are


Q7 : Find ten rational numbers between and.
Answer :
and can be represented as respectively.
Therefore, ten rational numbers between and are


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