Class 6 Maths Chapter 10 The Other Side of Zero NCERT Solutions (Complete Explanation, Step-by-Step Answers & Examples | Ganita Prakash)
Class 6 Maths Chapter 10 The Other Side of Zero NCERT Solutions (Complete Explanation, Step-by-Step Answers & Examples | Ganita Prakash)
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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.
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
This chapter builds the foundation of integer mathematics used in higher classes.
Final Tip from FUZY MATH ACADEMY
Students often get confused between which negative number is larger.
Remember this simple rule:
The number closer to zero is greater.
Example
-2 > -5
Because -2 is closer to zero.
Fuzymath Academy
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