NCERT Solutions for Class 8 Maths Ch 1 Rational Numbers

Here, we are providing Chapter 1 Rational Number Class 8 Maths NCERT Solutions which are effective in the preparation of examinations. These NCERT Solutions for Class 8 are very much helpful in increasing concertation among students. It will make students able to solve the difficult problems in a given in exercise. The numbers of the form p/q where p and q are integers and (q + 0), are called rational numbers. These are very helpful in getting good marks in the examinations.

NCERT Solutions for Class 8 Maths Ch 1 Rational Numbers

Page No: 14

Exercise 1.1

1. Using appropriate properties find.
(i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6   (ii) 2/5 × (-3/7) - 1/6 × 3/2 + 1/14 × 2/5

Answer

(i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6
= -2/3 × 3/5 - 3/5 × 1/6 + 5/2    (by commutativity)
= 3/5(-2/3 - 1/6) + 5/2
= 3/5{(-4 - 1)/6} + 5/2
= 3/5(-5/6) + 5/2    (by distributivity)
= -15/30 + 5/2
= -1/2 + 5/2
= 4/2 = 2

(ii) 2/5 × (-3/7) - 1/6 × 3/2 + 1/14 × 2/5
= 2/5 × (-3/7) + 1/14 × 2/5 - (1/6 × 3/2)    (by commutativity)
= 2/5(-3/7 + 1/14) - 1/4
= 2/5{(-6 + 1)/14} - 1/4    (by distributivity)
= 2/5(-5/14) - 1/4
= -1/7 - 1/4
= (-4-7)/28
= -11/28

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

Answer

(i) 2/8
Additive inverse = -2/8
(ii) -5/9
Additive inverse = 5/9
(iii) -6/-5 = 6/5
Additive inverse = -6/5
(iv) 2/-9 = -2/9
Additive inverse = 2/9
(v) 19/-6 = -19/6
Additive inverse = 19/6

3. Verify that : -(-x) = x for.
(i) x = 11/15   (ii) x = -13/17

Answer

(i) x = 11/15
The additive inverse of x = 11/15 is -x = -11/15 as 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) x = -13/17
The additive inverse of x = -13/17 is -x = 13/17 as (-13/17) + 13/17 = 0
The same equality 13/17 + (-13/17) = 0 , shows that the additive inverse of 13/17 is -13/17 or
-(13/17) = -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 × -3/7    (v) -1 × -2/5    (vi) -1

Answer

The multiplicative inverse of a number is the reciprocal of that number.

(i) -13
Multiplicative inverse = -1/13
(ii) -13/19
Multiplicative inverse = -19/13
(iii) 1/5
Multiplicative inverse = 5
(iv) -5/8 × -3/7 = 15/56
Multiplicative inverse = 56/15
(v) -1 × -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 × 1 = 1 × -4/5 = -4/5
(ii) -13/17 × -2/7 = -2/7 × -13/17
(iii) -19/29 × 29/-19 = 1

Answer

(i) -4/5 × 1 = 1 × -4/5 = -4/5
Here 1 is the multiplicative identity.
(ii) -13/17 × -2/7 = -2/7 × -13/17
Commutavity
(iii) -19/29 × 29/-19 = 1
Multiplicative inverse

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

Answer

Reciprocal of -7/16 = 16/-7
A/q,
6/13 × (Reciprocal of -7/16)
= 6/13 × 16/-7 = 96/-91 = -96/91

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

Answer

By the property of associativity.
8. Is 8/9 the multiplicative inverse of ? Why or why not?

Answer

If it will be the multiplicative inverse then their product will be 1.
= -7/8
A/q,
8/9 × -7/8 = -7/9 ≠ 1
Hence, 8/9 is not the multiplicative inverse.

9. Is 0.3 the multiplicative inverse of ? Why or why not?

Answer

If it will be the multiplicative inverse then their product will be 1.
= 10/3
also, 0.3 = 3/10
A/q,
3/10 × 10/3 = 1
Hence, 0.3 is the multiplicative inverse.

Page No: 15

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 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.

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 ________.

Answer

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

Page No: 20

Exercise 1.2

1. Represent these numbers on the number line. (i) 7/4   (ii) -5/6

Answer

(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.
 

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

Answer

-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.


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

Answer

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

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

Answer

The numbers -2/5 and 1/2 can be written as -8/20 and 10/20
Thus, ten rational numbers between -2/5 and 1/2 are:
-7/20, -6/20, -5/20, -4/20, -3/20, -2/20, -1/20, 0, 1/20 and 2/20

5. Find five rational numbers between.
(i) 2/3 and 4/5    (ii) -3/2 and 5/3    (iii) 1/4 and 1/2

Answer

(i) Five rational numbers between 2/3 and 4/5
The numbers 2/3 and 4/5 can be written as 30/45 and 36/45
Thus, five rational numbers are:
31/45, 32/45, 33/45, 34/45 and 35/45

(ii) Five rational numbers between -3/2 and 5/3
The numbers -3/2 and 5/3 can be written as -9/6 and 10/6
Thus, five rational numbers are:
-8/6, -5/6, -2/6, 0 and 2/6

(iii) Five rational numbers between 1/4 and 1/2
The numbers 1/4 and 1/2 can be written as 7/28 and 14/28
Thus, five rational numbers are:
8/28, 9/28, 10/28, 11/28 and 12/28

6. Write five rational numbers greater than -2.

Answer

-2 can be written as -16/8.
Five rational numbers greater than -2 are:
-15/8, -14/8, -13/8, -12/8 and -11/8

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

Answer

The numbers 3/5 and 3/4 can be written as 48/80 and 60/80
Thus, ten rational numbers between 3/5 and 3/4 are:
49/80, 50/80, 51/80, 52/80, 53/80, 54/80, 55/80, 56/80, 57/80 and 58/80.


NCERT Solutions for Class 8 Maths Ch 1 Rational Numbers


You can find accurate detailed NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers which are prepared by Studyrankers experts who have in depth knowledge of the topics. These NCERT Solutions will improve the learning behaviour of the students. In this chapter, we are going to study various properties of rational numbers such as closure, commutativity, associativity. We will also study study about reciprocal of rational numbers and distributivity of multiplication over addition for rational
numbers. We will also try to represent rational numbers on number line and find rational numbers between two rational numbers.

NCERT Solutions for Class 8 Maths Chapters:

Chapter 2 Linear Equations in One Variable
Chapter 3 Understanding Quadrilaterals
Chapter 4 Practical Geometry
Chapter 5 Data Handling
Chapter 6 Square and Square Roots
Chapter 7 Cube and Cube Roots
Chapter 8 Comparing Quantities 
Chapter 9 Algebraic Expressions and Identities
Chapter 10 Visualizing Solid Shapes
Chapter 11 Mensuration
Chapter 12 Exponents and Powers
Chapter 13 Direct and Inverse Proportions
Chapter 14 Factorization
Chapter 15 Introduction to Graphs
Chapter 16 Playing with Numbers

FAQ on Chapter 1 Rational Numbers

How many exercises in Chapter 1 Rational Numbers

There are total 2 exercise in the Chapter 1 Rational Numbers which are very much helpful in understand the basic concepts of the chapter and knowing properties of rational numbers.

What do you mean by Natural Numbers?

The counting numbers 1, 2, 3, 4, 5, … are called ‘natural numbers’. The smallest natural number is 1, but there is no last (or the greatest) natural number. 

What is Commutative Property of Rational Numbers?

When two rational numbers are swapped between one operator and still their result does not change then we say that the rational numbers follow the commutative property for that operation. 

What is Associative Property of Rational Numbers?

When rational numbers are rearranged among two or more same operations and still their result does not change then we say that the rational numbers follow the associative property for that operation.
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