March 09, 2026

NCERT Class 6 Maths Chapter 10: The Other Side of Zero – Complete Explanation with Step-by-Step Solutions

NCERT Class 6 Maths Chapter 10

The Other Side of Zero

Introduction

In earlier chapters, students learned about whole numbers starting from 0 and moving to the right side of the number line.

But have you ever wondered:

What happens on the left side of zero?

For example:

Temperature in winter can be below 0°C
Bank balance can go below zero
Some floors in buildings are below ground level

To represent such situations, mathematics introduces numbers smaller than zero, called negative numbers.

This chapter explains how numbers exist on both sides of zero.

This is Bela's fun building.A lift is used to go up and down between the floors. It has two
buttons: ‘+’ to go up and ‘–’ to go down. Can you spot the lift?
To go to the Art Centre from the ‘Welcome Hall’, you
must press the ‘+’ button twice.
We say that the button press is + + or + 2.
To go down two floors, you must press the ‘–’
button twice, which we write as – – or – 2.
So if you press + 1 (i.e., if you press the ‘+’
button once), then you will go up one floor and if
you press – 1 (i.e., if you press the ‘–’ button
once), then you will go down 1 floor.
Understanding the Number Line

A number line is a straight line where numbers are placed at equal intervals.

Important observations:

• Numbers increase as we move right
• Numbers decrease as we move left
• Zero lies in the middle

Example representation

-3 -2 -1 0 1 2 3

Numbers on the left side are negative numbers.

Numbers on the right side are positive numbers.

Key Terms and Definitions

1 Positive Numbers

Numbers greater than zero are called positive numbers.

Examples

1, 2, 5, 10, 100

2 Negative Numbers

Numbers smaller than zero are called negative numbers.

Examples

-1, -2, -5, -10

These are written with a minus sign (-).

3 Integers

Numbers that include negative numbers, zero, and positive numbers are called integers.

Examples

-3, -2, -1, 0, 1, 2, 3

4 Opposite Numbers

Two numbers that lie at the same distance from zero but on opposite sides are called opposite numbers.

Examples

3 and -3
5 and -5

Real Life Examples of Negative Numbers

Temperature

Winter temperatures sometimes fall below zero.

Example:

Shimla temperature = –3°C

Elevation

Places below sea level use negative numbers.

Example

Dead Sea = –430 meters

Bank Balance

If someone withdraws more money than available:

Balance = –₹500

Representing Integers on Number Line

Example:

Represent –4 on the number line.

Step 1
Draw a number line.

Step 2
Mark zero.

Step 3
Move 4 steps to the left of zero.

So the point represents –4.

Section Questions with Step-by-Step Solutions

Question 1

Write the integers between

a) -3 and 3

Solution

Numbers between -3 and 3 are

-2, -1, 0, 1, 2

Question 2

Write the opposite of the following numbers

a) 5
b) -7
c) 10

Solution

Opposite numbers lie at equal distance from zero.

a) Opposite of 5 = -5

b) Opposite of -7 = 7

c) Opposite of 10 = -10

Question 3

Which number is smaller?

a) -2 or 1

Solution

On a number line:

Numbers on the left are smaller.

-2 is on the left of 1

Therefore

-2 < 1

So -2 is smaller.

Question 4

Arrange the numbers in ascending order

3, -1, 0, -5, 2

Solution

Step 1 Identify smallest number

-5

Step 2 Next numbers

-1, 0, 2, 3

Final order

-5, -1, 0, 2, 3

Quick Practice Questions for Students

1 Write integers between -5 and 2

2 Write opposite numbers of
-8, 6, -10

3 Arrange in descending order
-3, 4, -1, 0, 2

4 Which is greater?
-4 or -1

Learning Summary

In this chapter students learned

• Numbers exist on both sides of zero

• Numbers less than zero are negative numbers
• Numbers greater than zero are positive numbers
• Negative numbers, zero and positive numbers together form integers
• Integers can be represented on a number line

This chapter builds the foundation of integer mathematics used in higher classes.