Quick Revision Notes: Class 6 Mathematics

Chapter: Integers (पूर्णांक)

1. Introduction to Integers (परिचय)

• Natural Numbers (प्राकृतिक संख्याएँ): Counting numbers starting from 1.
  • Example: 1, 2, 3, 4, ...
• Whole Numbers (पूर्ण संख्याएँ): Natural numbers including zero.
  • Example: 0, 1, 2, 3, 4, ...
• Integers (पूर्णांक): The collection of whole numbers and negative numbers.
  • Example: ..., -3, -2, -1, 0, 1, 2, 3, ...

2. Types of Integers (पूर्णांकों के प्रकार)

• Positive Integers (धनात्मक पूर्णांक): Numbers greater than zero (+1, +2, +3, ...). They can be written without the plus sign (1, 2, 3).
• Negative Integers (ऋणात्मक पूर्णांक): Numbers less than zero (-1, -2, -3, ...). Note: Zero is neither positive nor negative.

3. Representation of Integers on a Number Line (संख्या रेखा पर निरूपण)

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

  <---|---|---|---|---|---|---|---|---|--->
     -4  -3  -2  -1   0  +1  +2  +3  +4

• To the right of zero: Positive integers (values increase as we move right).
• To the left of zero: Negative integers (values decrease as we move left).

4. Ordering and Comparison of Integers (पूर्णांकों की तुलना)

• Every positive integer is greater than every negative integer.
• Zero is less than every positive integer and greater than every negative integer.
• On the number line, a number to the right is always greater than the number to its left.
• Absolute Value (निरपेक्ष मान): The numerical value of an integer regardless of its sign. It is denoted by | |.
  • Example: |-5| = 5 and |+5| = 5

5. Addition and Subtraction of Integers (पूर्णांकों का जोड़ और घटाव)

Rules of Addition:

1. Same Signs: Add the absolute values and give the common sign.
   • (+a) + (+b) = +(a + b) (Example: (+5) + (+3) = +8)
   • (-a) + (-b) = -(a + b) (Example: (-5) + (-3) = -8)
2. Different Signs: Subtract the smaller absolute value from the larger one and give the sign of the integer with the larger absolute value.
   • (+a) + (-b) = Sign of the larger number of (a - b)
   • Example: (+8) + (-3) = +5
   • Example: (-8) + (+3) = -5

Rules of Subtraction:

To subtract an integer from another, change the sign of the integer being subtracted and add it to the first integer.

• a - (+b) = a - b
• a - (-b) = a + b (Minus multiplied by minus becomes plus)
  • Example: (+7) - (+3) = 7 - 3 = 4
  • Example: (+7) - (-3) = 7 + 3 = 10

6. Important Points to Remember (महत्वपूर्ण बिंदु)

• The sum of an integer and its opposite is always zero (a + (-a) = 0).
• Additive inverse (योज्य प्रतिलोम) of an integer a is -a, and of -a is a.
  • Example: Additive inverse of +7 is -7, and of -12 is 12.