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Maths ·Class 6 Maths

The Other Side of Zero Class 6 Notes

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RBSEGuide
· Jul 01, 2026 · Reviewed & updated Sep 17, 2026 · 7 min read

The Other Side of Zero Class 6 Notes

The Other Side of Zero Class 6 Notes

1. Integer: A whole number that can be positive, negative, or zero. Integers do not include fractions or decimals.


2. Zero (0): A number that represents the absence of quantity. It is the integer that separates positive numbers from negative numbers on the number line.


3. Fraction: A numerical quantity that is not a whole number, represented as a ratio of two integers, where the numerator is divided by the denominator (e.g.,[latex]\frac{1}{2}[/latex], [latex]\frac{3}{4}[/latex] ).


4. Number Line: A visual representation of numbers arranged in a straight line, where each point corresponds to a number. It extends infinitely in both directions.


5. Number Ray: A part of a number line that starts at a specific point (like zero) and extends infinitely in one direction.


6. Negative Numbers: Numbers that are less than zero, represented on the left side of zero on the number line (e.g., -1, -2, -3).

7. Positive Numbers: Numbers that are greater than zero, represented on the right side of zero on the number line (e.g., 1, 2, 3).


8. Indian Numeral System: A numeral system that uses ten digits (0-9) to represent numbers, allowing for the expression of both large and small quantities.


9. Complete Number Line: A number line that includes both positive and negative numbers, as well as zero, providing a full representation of all integers.


Bela’s Building of Fun

Understanding the Building:

  1. Ground Floor (0): This is where we start. It represents zero.
  2. Positive Floors: Floors above the ground floor are positive numbers. For example :

First Floor : +1

Second Floor : +2

  1. Negative Floors : Floors below the ground floor are negative numbers. For example:

First Basement : -1

Second Basement : -2


Key Concepts :

1. Addition to Keep Track of Movement:

When you move up or down, you can think of it as adding or subtracting. For example, moving from 0 to +2 means you added 2.

2. Combining Button Presses is also Addition : If you press the V button twice to go from 0 to +2, you can think of it as :

  1. 0 + 1 + 1 = +2 ,

3. Back to Zero!: If you want to return to the ground floor after going up, you can press the button the same number of times you went up. For example, if you went to +2, pressing twice will bring you back to 0 : .

  1. +2 + (-2) = 0.

4. Comparing Numbers Using Floors: You can compare which floor is higher or lower. For example, +1 is higher than 0, and -1 is lower than 0. We can write :

  1. +1 > 0 and -1 < 0.

5. Subtraction to Find Which Button to Press: If you want to find out how many floors you need to go down from +2 to reach 0, you can subtract :

  1. 2 - 2 = 0 (You need to press '-'twice)

6. Adding and Subtracting Larger Numbers: You can also add or subtract larger numbers using the same concept. For example : If you start at +5 and go down to -3, you can think of it as :

  1. 5 + (-8) = -3

7. Adding, Subtracting, and Comparing Any Numbers: You can use these concepts with any numbers, not just floors. For example : If you have +3 and you want to compare it with -2, you can see that +3 is greater.

8. Converting Subtraction to Addition and Addition to Subtraction: Sometimes, it’s easier to think of subtraction as adding a negative number. For example :

Instead of thinking 5 -3, you can think of it as 5 + (- 3).


The Token Model

Tokens are like little counters that can represent positive and negative numbers. In this model, we use two types of tokens : positive tokens (let’s say green) and negative tokens (let’s say orange). This helps us see how numbers work together when we add or subtract them.

Understanding the Token Model:

  1. Positive Tokens: These represent positive numbers. For example, if you have 5 positive tokens, it means you have +5.
  2. Negative Tokens: These represent negative numbers. For example, if you have 3 negative tokens, it means you have - 3.

How It Works :

When you add or subtract using tokens, you can visualize the process.

  1. Adding Tokens: When you add positive tokens, you simply count them together. If you have 3 positive tokens and you add 2 more, you have a total of 5 positive tokens. Example : +3 + (+2) = +5.
  2. Subtracting Tokens : When you subtract, you take away tokens. If you have 5 positive tokens and you take away 2 positive tokens, you are left with 3 positive tokens : Example : +5 - (+2) = +3.
  3. Combining Positive and Negative Tokens : When you have both positive and negative tokens, they can cancel each other out. One positive token and one negative token make a ‘zero pair’ because they balance each other out Example : +1 + (-1) = 0.


Integers in Other Places

  1. Positive Integers: These are numbers greater than zero, like +1, +2, +3, etc. They can represent things like money you earn or temperatures above freezing point.
  2. Negative Integers: These are numbers less than zero, like -1, -2, -3, etc. They can represent things like money you owe or temperatures below freezing point.
  3. Zero: This is a special number that represents nothing. It is neither positive nor negative.


1. Credits and Debits in Banking

Credits are amounts of money you earn or receive, represented by positive integers. Debits are amounts of money you spend or owe, represented by negative integers.

Example:

Imagine you have a bank account:

  1. Starting balance: You begin with ? 100 (Balance = +100).
  2. Credits: You earn ? 60 from your job (New Balance = +100 + (+60) = +160).
  3. Debits: You pay your electric bill of? 30 (New Balance = +160 - (+30) = +130).


2. Geographical Cross-sections

In geography, we often measure heights above and below sea level using integers.

  1. Above Sea Level: Heights like mountains are represented by positive integers. For example, a mountain that is 3000 metres high is + 3000.
  2. Below Sea Level: Depths like oceans or valleys are represented by negative integers. For example, the Dead Sea is about -430 metres below sea level.


Temperature

Temperature is another area where integers are used.

  1. Positive Temperatures: These are temperatures above freezing point, like + 25°C (warm day).
  2. Negative Temperatures: These are temperatures below freezing point, like - 5°C (cold day).


Explorations with Integers10.5 A Pinch of History


A Pinch of History

I. Who Was Brahmagupta?

Brahmagupta was a brilliant mathematician and astronomer. He wrote a famous book called the Brahma-sphuta-siddhanta, where he explained many mathematical concepts, including rules for adding and subtracting integers. His work was groundbreaking because it treated positive and negative numbers equally, which was not common at that time.


II. Brahmagupta’s Rules for Addition Brahmagupta provided clear rules for adding integers. Here are his rules simplified for you:

  1. Adding Two Positive Numbers: If you add two positive numbers, the result is positive. Example : 2 + 3 = 5.
  2. Adding Two Negative Numbers: If you add two negative numbers, the result is negative. You add the numbers without the signs and then put a minus sign in front. Example ; (— 2) + (— 3) = — 5.
  3. Adding a Positive and a Negative Number: If you add a positive number and a negative number, subtract the smaller number from the larger number and keep the sign of the larger number. Example : 3 + (- 5) = - 2 (because 5 is larger)
  4. Adding a Number and Its Inverse: If you add a number and its opposite (additive inverse), the result is zero.Example : 2 + (- 2) = 0.
  5. Adding Zero: If you add zero to any number, the result is the same number. Example : 5 + 0 = 5.


III. Brahmagupta’s Rules for Subtraction

Brahmagupta also explained how to subtract integers. Here are his rules:

  1. Subtracting a Smaller Positive from a Larger Positive: If you subtract a smaller positive number from a larger positive number, the result is positive. Example: 5 - 3 = 2.
  2. Subtracting a Larger Positive from a Smaller Positive: If you subtract a larger positive number from a smaller positive number, the result is negative. Example: 3 - 5 = -2.
  3. Subtracting a Negative Number: Subtracting a negative number is the same as adding the corresponding positive number. Example: 5 - (- 3) = 5 + 3 = 8.
  4. Subtracting a Number from Itself: If you subtract a number from itself, the result is zero. Example: 4 - 4 = 0.
  5. Subtracting Zero: If you subtract zero from a number, the result is the same number. Example: 7 - 0 = 7.