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**NCERT Solutions for Class 8 Maths Chapter 1: **The NCERT Class 8 Maths chapter 1 is Rational Numbers. In this chapter, students will learn about properties of natural numbers, representation of rational numbers on the number lines, rational numbers between two rational numbers, etc. The NCERT Solutions Class 8 Maths chapter 1 are designed by subject matter experts at Embibe so that students can easily understand complex topics.

Exercises 1.1 and 1.2 are slightly more difficult than the ones in other other units. However, students do not need to worry about anything because this article provides free NCERT solutions for Class 8 Maths chapter 1 PDF to help them overcome their challenges. Continue to read the article to learn more about chapter 1 Maths Class 8 NCERT solutions in detail.

Before getting into the details of NCERT solutions for Class 8 Maths chapter 1 PDF, here is a look at the list of topics and sub-topics covered in the Rational Numbers chapter from the table below:

Particulars | Details |
---|---|

1.1 | Introduction |

1.2 | Properties of Rational Numbers |

1.3 | Representation of Rational Numbers on the Number Line |

1.4 | Rational Numbers between Two Rational Numbers |

Experts have taken into consideration the CBSE guidelines and marking scheme while preparing the solutions. The language used in these solutions can be easily understood by a Class 8 student:

Here are a few questions and their answers which students can use as they prepare for their examinations:

**Q.1. Represent this number on the number line.**

**Solution: **The given number is 74.

74=134

Divide the line between the whole numbers into four parts. For example, divide the line between 0 and 1 to 4 parts, 1 and 2 to 4 parts and so on. Thus, the rational number 74 lies at a distance of 7 points away from 0 towards positive number line. This number is represented on the number line as shown in the figure. The circled position is the required one.

**Q.2. Represent the following number on the number line.**

**Solution:** The given number is -56.

Divide the line between the integers into 6 parts. For example, divide the line between 0 and 1 to 6 parts, -1 and -2 to 6 parts and so on. Therefore, the rational number -56 lies at a distance of 5 points away from 0, on negative number line. The number is represented on the number line as shown in the figure. M represents the required number.

**Q.3. Represent -211,-511,-911 on the number line.**

**Solution:** The given numbers are -211, -511, -911.

Divide the line between the integers into 11 parts.

Thus, the rational numbers -211, -511, -911 lies at a distance of 2, 5, 9 points away from 0, towards negative number line respectively. These numbers are represented on the number line as -211=C, -511=B and -911=A.

**DOWNLOAD SOLUTIONS FOR CLASS 8 MATHS CHAPTER 1 PDF**

In earlier classes, students must have studied various numbers like natural numbers, whole numbers, integers, fractions, etc. Here in this chapter, they will learn about Rational Numbers. A rational number is expressed in p/q, where p and q are integers and q≠0. The concept of rational numbers is pivotal in Class 8 Maths, as well as for several important mathematical concepts that come after it.

Any fraction with a non-zero denominator is said to be a rational number. A rational number can be represented on a number line by simplifying them first. In this chapter students will also study various properties of rational numbers like closure, commutativity, associativity, the role of zero, the role of 1, negative of a number, reciprocal, distributivity of multiplication over addition for rational numbers, representation of rational numbers on the number line and rational numbers between two rational numbers.

Here is an overview of some of the concepts that are being discussed in this chapter.

- Rational numbers are closed during operations such as addition, subtraction and multiplication.
- The operations of addition and multiplication are
- commutative for rational numbers &
- associative for rational numbers.

- Zero (0) is the additive identity for rational numbers.
- One (1) is the multiplicative identity for rational numbers.
- The law of distributivity of rational numbers: For all rational numbers a, b and c, a(b + c) = ab + ac and a(b – c) = ab – ac
- All rational numbers can be represented along a number line.
- There are countless rational numbers between any two given rational numbers. We use the concept of mathematical mean to find rational numbers between two rational numbers.

The difference between a rational number and a fraction is tabulated below:

Rational Number | Fraction |
---|---|

These are the numbers which are written in the form p/q, where p and q are integers and q≠0. | These are the numbers which are written in the form p/q, where p and q are whole numbers and q≠0. |

They can be positive or negative numbers. | Fraction cannot be negative. |

For example: 12/7, 2/-8, -22/-56/ -1/22 | For example: 10/12, 15/76, 55/98, 12/9 |

So, we can say that a fractional number can always be a rational number, but a rational number may or may not be a fractional number.

Below are a few solved examples that can help in getting a better idea of the chapter:

**1. Using appropriate properties find.**

(i) -2/3 × 3/5 + 5/2 – 3/5 × 1/6

**Solution:**

-2/3 × 3/5 + 5/2 – 3/5 × 1/6

= -2/3 × 3/5– 3/5 × 1/6+ 5/2 (by law of commutativity)

= 3/5 (-2/3 – 1/6)+ 5/2 = 3/5 ((- 4 – 1)/6)+ 5/2

= 3/5 ((–5)/6)+ 5/2 (by law of 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**

**Solution:**

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 law of commutativity)

= 2/5 × (- 3/7 + 1/14) – 3/12

= 2/5 × ((- 6 + 1)/14) – 3/12

= 2/5 × ((- 5)/14)) – 1/4 = (-10/70) – 1/4

= – 1/7 – 1/4 = (– 4– 7)/28

= – 11/28

**2. Write the additive inverse of each of the following**

**Solution:**

(i) 2/8

The additive inverse of 2/8 is – 2/8

(ii) -5/9

The additive inverse of -5/9 is 5/9

(iii) -6/-5 = 6/5

The additive inverse of 6/5 is -6/5

(iv) 2/-9 = -2/9

The additive inverse of -2/9 is 2/9

(v) 19/-16 = -19/16

The additive inverse of -19/16 is 19/16

**3. Verify that: -(-x) = x for.**

**(i) x = 11/15**

**(ii) x = -13/17**

**Solution:**

(i) x = 11/15

We know that, x = 11/15

The additive inverse of x is – x (because x + (-x) = 0)

and the additive inverse of 11/15 is – 11/15 (because 11/15 + (-11/15) = 0)

The same logic is applied to 11/15 + (-11/15) = 0, to conclude that the additive inverse of -11/15 is 11/15.

Or, – (-11/15) = 11/15

i.e., -(-x) = x

(ii) -13/17

We have, x = -13/17

The additive inverse of x is – x (as x + (-x) = 0)

Then, the additive inverse of -13/17 is 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**

**(i) -13 (ii) -13/19 (iii) 1/5 (iv) -5/8 × (-3/7) (v) -1 × (-2/5) (vi) -1**

**Solution:**

(i) -13

The multiplicative inverse of -13 is -1/13

(ii) -13/19

The multiplicative inverse of -13/19 is -19/13

(iii) 1/5

The multiplicative inverse of 1/5 is 5

(iv) -5/8 × (-3/7) = 15/56

The multiplicative inverse of 15/56 is 56/15

(v) -1 × (-2/5) = 2/5

The multiplicative inverse of 2/5 is 5/2

(vi) -1

The multiplicative inverse of -1 is -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**

**Solution:**

(i) -4/5 × 1 = 1 × (-4/5) = -4/5

Here 1 is used as the multiplicative identity.

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

The law of commutativity is used in this equation

(iii) -19/29 × 29/-19 = 1

The property of multiplicative inverse is used in this equation.

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

**Solution:**

1/3 × (6 × 4/3) = (1/3 × 6) × 4/3

The way in which numbers are grouped in a multiplication problem does not change the product. Therefore, the Associativity Property is used here.

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

**Solution:**

Reciprocal of -7/16 = 16/-7 = -16/7

According to the question,

6/13 × (Reciprocal of -7/16)

6/13 × (-16/7) = -96/91

**Ans:** The important topics in Class 8 Maths chapter 1 are as follows:

1.1 Introduction

1.2 Properties of Rational Numbers

1.2.1 Closure

1.2.2 Commutativity

1.2.3 Associativity

1.2.4 The role of zero

1.2.5 The role of 1

1.2.6 Negative of a number

1.2.7 Reciprocal

1.2.8 Distributivity of multiplication over addition for rational numbers.

1.3 Representation of Rational Numbers on the Number Line

1.4 Rational Numbers between Two Rational Numbers

**Ans:** Yes, Embibe provides accurate and detailed solutions for all questions provided in the NCERT Class 8 Maths book. We bring you NCERT solutions for Class 8 Maths, designed by our subject experts to facilitate an easy and clear understanding of the fundamental concepts.

**Ans: **A number that is represented in p/q form is called rational numbers where q is not equal to zero. A rational number is also a type of real number. Any fraction with non-zero denominators is a rational number.

**Ans: **Yes, the NCERT solutions for all the Maths chapters on Embibe are available for free.

**Ans: **Yes, the NCERT solutions for chapter 1 Maths are available in PDF format on this page.

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