Important Formulas: The Other Side of Zero | Maths for Class 6 (Ganita Prakash) - New NCERT PDF Download

1. Positive Numbers are numbers with a ‘+’ sign in front, such as +1, +2, and +3. They represent numbers greater than zero.

2. Negative Numbers are numbers with a ‘–’ sign in front, such as –1, –2, and –3. They represent numbers less than zero.

3. Zero (0) is a number that comes before 1 and is neither positive nor negative. It represents nothing.

4. Inverse of a Number: The inverse of a number means its opposite sign. For example: Inverse of $+3+3$ is $-3-3$, and the inverse of $-3-3$ is $+3+3$.

5. Integers:

• Positive and negative whole numbers, including zero.
• Example: ..., –3, –2, –1, 0, 1, 2, 3, ...

6. Adding Integers:

• (+a) + (+b) = (+a + b): Adding two positive numbers results in a positive number.
• (–a) + (–b) = –(a + b): Adding two negative numbers results in a more negative number.
  

7. Subtracting Integers:

• Subtracting a positive number:
  $a-b$ = a+(−b)
• Subtracting a negative number:
  $a-(-b)$ = a+b  
• Subtracting a larger number from a smaller one:
  Result is negative.
  Example: $3-7=-(7-3)$= −4
  

8. Comparing Numbers:

• Positive numbers are greater than negative numbers.
• Numbers increase as you move to the right on the number line and decrease as you move to the left.

9. Number Line:

• A representation of numbers where positive numbers are on the right side of 0, and negative numbers are on the left side.
• Movement to the right represents addition, and movement to the left represents subtraction.

10. Key Operations on the Number Line:

• Starting Number + Movement = Target Number 
  Example: 5+4=9
• Target Number – Starting Number = Movement Needed 
  Example: $9\; –\; 5\; =\; 4$9–5=4

11. Unmarked Number Line (UNL) for Addition and Subtraction:

• The unmarked number line shows the position of zero, but other numbers are not marked.
• You can visualize the addition and subtraction of integers on this line by imagining the scale and the positions of numbers.

12. Addition Example on UNL:

Example: 85+(−60)

• Visualize starting at 85 and moving 60 steps backward.
• $85+(-60)=2585\; +\; (-60)\; =\; 25$

13. Subtraction Example on UNL:
Example: $-100\; -\; (+250)$−100−(+250)

• Visualize starting at -100 and moving backward by 250.
• $-100-250=$−350.

14. Converting Subtraction to Addition:

Subtraction can be converted to addition by replacing the number being subtracted with its inverse.

• Example: $(+7)\; -\; (+5)\; =\; (+7)\; +\; (-5)$(+7)−(+5)=(+7)+(−5).
• Similarly, addition can be converted to subtraction by replacing a number with its inverse.

15. Credits and Debits in Banking:

• Credit: A positive number representing a deposit into the account.
• Debit: A negative number representing a withdrawal from the account.
• Total bank balance = sum of all credits (positive) and debits (negative).
• Example: Start with ₹100, add a ₹60 credit, then subtract ₹30 debit. The balance is ₹130.

16. Geographical Cross-Sections:

Heights are measured from sea level.

• Heights above sea level are represented as positive numbers.
• Heights below sea level are represented as negative numbers.