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## NCERT Class 7 Maths Textbook Chapter 9 With Answer PDF Free Download

### Chapter 9: Rational Numbers

Given below are some of the concepts present in this chapter.

- Need For Rational Numbers
- What Are Rational Numbers
- Positive And Negative Rational Numbers
- Rationals Numbers On a Number Line
- Rational Numbers in Standard Form
- Comparison of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Operations On Rational Numbers
- Addition of Rational Numbers
- Subtraction of Rational Numbers
- Multiplication of Rational Numbers
- Division of Rational Numbers

#### 9.1 INTRODUCTION

You began your study of numbers by counting objects around you. The numbers used for this purpose were called counting numbers or natural numbers.

They are 1, 2, 3, 4, … By including 0 to natural numbers, we got the whole numbers, i.e., 0, 1, 2, 3, …

The negatives of natural numbers were then put together with whole numbers to make up integers. Integers are …, –3, –2, –1, 0, 1, 2, 3, ….

We, thus, extended the number system, from natural numbers to whole numbers and from whole numbers to integers.

You were also introduced to fractions. These are numbers of the form numerator denominator where the numerator is either 0 or a positive integer and the denominator, a positive integer.

You compared two fractions, found their equivalent forms, and studied all the four basic operations of addition, subtraction, multiplication, and division on them.

In this Chapter, we shall extend the number system further. We shall introduce the concept of rational numbers along with their addition, subtraction, multiplication, and division operations.

Author | NCERT |

Language | English |

No. of Pages | 20 |

PDF Size | 1536 KB |

Category | Mathematics |

Source/ Credits | ncert.nic.in |

### NCERT Solutions Class 7 Maths Chapter 8 Comparing Quantities

Exercise 9.1 Page: 182

**1. List five rational numbers between:**

**(i) -1 and 0**

**Solution:-**

The five rational numbers between -1 and 0 are,

-1< (-2/3) < (-3/4) < (-4/5) < (-5/6) < (-6/7) < 0

**(ii) -2 and -1**

**Solution:-**

The five rational numbers between -2 and -1 are,

-2 < (-8/7) < (-9/8) < (-10/9) < (-11/10) < (-12/11) < -1

**(iii) -4/5 and -2/3**

**Solution:-**

The five rational numbers between -4/5 and -2/3 are,

-4/5 < (-13/12) < (-14/13) < (-15/14) < (-16/15) < (-17/16) < -2/3

**(iv) -1/2 and 2/3**

**Solution:-**

The five rational numbers between -1/2 and 2/3 are,

-1/2 < (-1/6) < (0) < (1/3) < (1/2) < (20/36) < 2/3

**2. Write four more rational numbers in each of the following patterns:**

**(i) -3/5, -6/10, -9/15, -12/20, …..**

**Solution:-**

In the above question, we can observe that the numerator and denominator are the multiples of 3 and 5.

= (-3 × 1)/ (5 × 1), (-3 × 2)/ (5 × 2), (-3 × 3)/ (5 × 3), (-3 × 4)/ (5 × 4)

Then, next four rational numbers in this pattern are,

= (-3 × 5)/ (5 × 5), (-3 × 6)/ (5 × 6), (-3 × 7)/ (5 × 7), (-3 × 8)/ (5 × 8)

= -15/25, -18/30, -21/35, -24/40 ….

**(ii) -1/4, -2/8, -3/12, …..**

**Solution:-**

In the above question, we can observe that the numerator and denominator are the multiples of 1 and 4.

= (-1 × 1)/ (4 × 1), (-1 × 2)/ (4 × 2), (-1 × 3)/ (1 × 3)

Then, next four rational numbers in this pattern are,

= (-1 × 4)/ (4 × 4), (-1 × 5)/ (4 × 5), (-1 × 6)/ (4 × 6), (-1 × 7)/ (4 × 7)

= -4/16, -5/20, -6/24, -7/28 ….

NCERT Class 7 Maths Textbook Chapter 9 With Answer PDF Free Download