NCERT Solutions for Class 8 Maths: Chapter 1 Rational Numbers

Check NCERT Solutions for Class 8 Maths, Chapter 1 Rational Numbers. This is the first and basic chapter of CBSE Class 8 Maths NCERT Textbook. Here, we have also provided the PDF of this chapter. Link to download the PDF is given at the end of this article. 

Chapter – 1

Rational Numbers

EXERCISE 1.1

1. Using appropriate properties find.

Solution:

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

Solution:

We obtain the additive

(i) - 2/8

(ii) -5/9

(iii) -6/-5 = 6/5. So, additive inverse = -6/5

(iv) 2/-9 = -2/9. So, additive inverse = 2/9

(v) 19/6

3. Verify that – (– x) = x for.

(i) x = 11/15

(ii) x = -13/17

Solution:

(i) We have, x = 11/15

The additive inverse of x = 11/15 is -x = -11/15 since 11/15 + (-11/15) = 0

The same equality (11/15) + (- 11/15) = 0, shows that the additive inverse of -11/15 is 11/15 or  - (-11/15) = 11/15 i.e., − (−x) = x

(ii) We have, x = - 13/17

The additive inverse of x = -13/17 is –x = 13/17, since, (-13/17) + (13/17) = 0

The same equality (-13/17) + (13/17) = 0, shows that the  additive inverse of 13/17 is -13/17 i.e., − (−x) = x

4. Find the multiplicative inverse of the following.

(i) -13

(ii) -13/19

(iii) 1/5

(iv) (-5/8) X (-3/7)

(v) (-1) X (-2/5)

(vi) -1

Solutions:

(i) Multiplicative inverse of −13= −1/13

(ii) Multiplicative inverse of -13/19= -19/13

(iii) Multiplicative inverse of 1/5 = 5

(iv) Simplifying, (-5/8) x (-3/7) = 15/56

Multiplicative inverse of 15/56= 56/15

(v) (-1) X (-2/5) = 2/5

Multiplicative inverse = 5/2

(vi) −1

Multiplicative inverse = −1

5. Name the property under multiplication used in each of the following.

(i) (-4/5 x 1) = 1 x (-4/5) = -4/5

(ii) (-13/17) x (-2/7) = (-2/7) x (-13/17)

(iii) (-19/29) x (29/-19) = 1

Solutions:

So, 1 is the multiplicative identity.

(ii) Commutativity.

(iii) Multiplicative inverse.

6. Multiply 6/13 by the reciprocal of -7/16.

Solutions:

Reciprocal of -7/16 of - 16/6.

7. Tell what property allows you to compute 1/3 x (6 x 4/3) as (1/3 x 6) x 4/3.

Solutions: Associativity.

8.

Solutions: If 8/9 is the multiplicative of the given fractions then their product should be equal to 1.

On multiplying both fractions, we have

Here, the product is not 1 so 8/9 is not the multiplicative inverse.

9.

Solutions:

As the product is 1, so, clearly  0.3 is the multiplicative inverse of the given fraction.

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.

Solutions:

(i) 0 is a rational number and it does not have a reciprocal as its reciprocal is not defined.

(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 1/x, where x¹ 0 is ________.

(v) The product of two rational numbers is always a _______.

(vi) The reciprocal of a positive rational number is ________.

Solutions:

(i) No

(ii) −1, 1

(iii) -1/5

(iv) x

(v) Rational number

EXERCISE 1.2

1. Represent these numbers on the number line.

(i) 7/4

(ii) 5/6

Solutions:

(i)

(ii)

2. Represent -2/11, -5/11, -9/11 on the number line.

Solutions:

3. Write five rational numbers which are smaller than 2.

Solutions:

Some of the rational numbers are,  –1,–1/2, 0,1,1/2,

4. Find ten rational numbers between -2/5 and 1/2.

Solutions:

-2/5 and 1/2 can be written as -8/20 as 10/20 respectively.

Now, ten rational numbers between -2/5 and 1/2 or  -8/20 and 10/20 are,

-7/20, -6/20, -5/20, -4/20, -3/20, -2/20, 0, -1/20, 0, 1/20, 2/20 (There can be many more such rational numbers)

5. Find five rational numbers between.

(i) 2/3 and 4/5

(ii) -3/2 and 5/3

(iii) 1/4 and 1/2

Solutions:

(i) 2/3 and 4/5 can be written as40/60 and48/60 respectively.

Now, five rational numbers between 2/3 and 4/5 or  40/60and48/60 are

41/60, 42/60, 43/60, 44/60, 45/60

(ii) -3/2 and 5/3 can be written as -9/6 and 10/6 respectively.

Now, five rational numbers between -3/2 and 5/3 or  -9/6 and 10/6 are -8/6, -7/6, 0, 1/6, 2/6

(iii) 1/4 and 1/2 can be written as 8/32 and 16/32 respectively.

Now, five rational numbers between 1/4 and 1/2 are9/32, 10/32, 11/32, 12/32, 13/32.

6. Write five rational numbers greater than –2.

Solutions:

Five rational numbers greater than 2 are, -3/2, - 1, -1/2, 0, 1/2.

7. Find ten rational numbers between 3/5 and 3/4.

Solutions:

3/5 and 3/4 can be  written as (3 x 32)/(5 x 32) and  (3 x 40)/(4 x 40) or 96/160 or 120/160 respectively.

Now, ten rational numbers between 3/5 and 3/4 or 96/160 or 120/160 are

97/160, 98/160, 99/160, 100/160, 101/160, 102/160, 103/160, 104/160, 105/169, 106/160.