KNOW INTEGERS

Integers are whole numbers, including positive numbers, negative numbers, and zero.

 They do not include fractions or decimals. 

For 7th-grade CBSE students, understanding integers involves learning how to represent them on a number line, performing basic operations (addition, subtraction, multiplication, and division), and recognizing their properties. 

Here's a breakdown of key concepts:

1. Definition and Representation: 

• Integers are whole numbers, both positive and negative, and zero.
• They can be represented on a number line, with zero as the center, positive integers to the right, and negative integers to the left.
• Examples: -5, 0, 3, 12, -100.
• . Definition and Representation:
  • Integers: Whole numbers, both positive and negative, including zero. Examples: -3, -2, -1, 0, 1, 2, 3. 
  • Positive Integers: Numbers greater than zero (1, 2, 3, ...). Also known as natural numbers. 
  • Negative Integers: Numbers less than zero (-1, -2, -3, ... ). 
  • Zero: Neither positive nor negative. 
  • Number Line: Integers can be visually represented on a number line, with zero in the center, positive integers to the right, and negative integers to the left. 
  2. Operations on Integers: 

• Addition
•  

  • Addition:

    • a
    • involves combining their values. When adding integers with the sa

    Adding integers sign, add their absolute values and keep the sign.
  •  When adding integers with different signs,
  •  subtract the smaller absolute value from the larger and keep the sign of the number with the larger absolute value.
  • Subtraction:

    Subtracting an integer is the same as adding its additive inverse (opposite). For example, 5 - 3 is the same as 5 + (-3).
  • Multiplication:

    Multiplying integers follows specific sign rules:

    • Positive x Positive = Positive
    • Positive x Negative = Negative
    • Negative x Positive = Negative
    • Negative x Negative = Positive.
  • Division:

    Similar to multiplication, division of integers also follows sign rules:

    • Positive / Positive = Positive
    • Positive / Negative = Negative
    • Negative / Positive = Negative
    • Negative / Negative = Positive.

  3. Properties of Integers:
• 3.3. Properties of Integers:

  • Commutative Property:

    The order of addition or multiplication does not change the result (e.g., a + b = b + a, and a * b = b * a). 
  • Associative Property:

    How numbers are grouped in addition or multiplication does not change the result (e.g., (a + b) + c = a + (b + c), and (a * b) * c = a * (b * c)). 
  • Identity Property:

    Zero is the additive identity (a + 0 = a), and one is the multiplicative identity (a * 1 = a). 
  • Distributive Property:

    Relates multiplication and addition (or subtraction) (e.g., a * (b + c) = a * b + a * c). 
  • 
    
  • .4. Order of Operations (BODMAS/PEMDAS):
    • B: rackets / Parentheses
    • O: f / Exponents
    • D: ivision and Multiplication (from left to right)
    • A: ddition and Subtraction (from left to right). 
    5. Real-World Applications:
    • Integers are used in everyday situations, such as calculating temperature changes,
    •  financial transactions (gains and losses), 
    • and measuring altitudes. 
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    • https://ncert.nic.in/textbook/pdf/gemh101.