NCERT Solutions Class 8 Mathematics Chapter 1 Rational Numbers

Q.2) Write the additive inverse of each of the following:
i) 2/8
ii) − 5/9
iii) −6/−5
iv) 2/−9
v) 19/−6
Sol.2) (i) 2/8 ,
Here, −2/8 is the additive inverse of 2/8 because − 2/8 + 2/8 = 0
(ii) − 5/9,
Here, 5/9 is the additive inverse of − 5/9 because − 5/9 + 5/9 = 0

Q.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.
Sol.10) (i) 0 is the rational number that does not have a reciprocal.
(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.

Q.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 1/𝑥 where 𝑥 ≠ 0 is _______________.
(v) The product of two rational numbers is always a _______________.
(vi) The reciprocal of a positive rational number is _______________
Sol.11) (i) Zero has no reciprocal.
(ii) The numbers 1 and -1 are their own reciprocals
(iii) The reciprocal of -5 is − (1/5).
(iv) Reciprocal of 1/𝑥, where 𝑥 ≠ 0 is 𝑥.
(v) The product of two rational numbers is always a rational number.
(vi) The reciprocal of a positive rational number is positive rational numbers.

Exercise 1.2

Q.1) Represent these numbers on the number line:
i) 7/4
ii) −5/6 
Sol.1) (i) 7/4 on the number line. Divide line between two natural number in 4 parts. Thus, the rational number 7/4 lies at a distance of 7 points from 0 towards positive number line.

(ii) -5/6 on the number line. Divide line between two natural number in 6 parts. Thus, the rational number -5/6 lies at a distance of 5 points from 0 towards negative number line.

Q.2) Represent −2/11, −5/11, −9/11 on the number line.
Sol.2) 2/11, -5/11, -9/11 on the number line.
Divide line between two natural number in 11 parts. Thus, the rational number -2/11, - 5/11, -9/11 lie at a distance of 2, 5, 9 points from 0 towards negative number line respectively.

Q.3) Write 5 rational numbers which are smaller than 2.
Sol.3) 2 can be written as 10/5.
Thus, 5 natural numbers smaller than 2 are: 
9/5, 8/5, 7/5, 6/5 and 5/5 .

Q.4) Find ten rational numbers between −2/5 and 1/2.
Sol.4) Given, rational numbers −2/5 and 1/2.
Here, L.C.M. of 5 and 2 is 10.