# NCERT Solutions for Class 8 Maths Ch 1 Rational Numbers| PDF Download

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.

These solutions are as per the latest NCERT textbooks. These Chapter 1 NCERT solutions are prepared by faculty of Studyrankers who have provided step by step answers that will help you scoring more marks in the examinations. These can be used for completing your homework or understanding the basic concepts to solve problems. Study Materials for Class 8 Maths Chapter 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

(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

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

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

(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

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

(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.

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.

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

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?

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.

(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 ________.

(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

(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.

-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.

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.

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

(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.

-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.

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.

• Properties of Rational Numbers: We are going to study various properties of rational numbers such as closure, commutativity, associativity and also about reciprocal of rational numbers and distributivity of multiplication over addition for rational numbers.

• Representation of Rational Numbers on the Number Line: We will try to represent rational numbers on number line.

• Rational Numbers between Two Rational Numbers: Between any two given rational numbers there are countless rational numbers. We will find rational numbers between two rational numbers.

On this page, you will also get exercisewise Chapter 1 Rational Numbers NCERT Solutions through which you can be able to solve difficult questions given in a exercise.

Studyrankers experts have prepared these Class 8 Maths NCERT Solutions by focusing the needs of the students and detailed every questions that will solve your doubts quickly and easily.

### 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.