How to Divide Integers in Class 7?

Dividing integers involves understanding a few key rules and concepts, which are detailed below and based on provided references.

Understanding Integer Division

Integer division, much like regular division, determines how many times one number (the divisor) fits into another (the dividend). However, with integers, we also need to consider positive and negative signs.

Basic Rules of Integer Division

Here are the fundamental rules you'll need to know, based on the provided references:

• Dividing an Integer by Itself (Except Zero): Any non-zero integer divided by itself equals 1.
  • Reference: (1)
  • Example: 5 ÷ 5 = 1, (-3) ÷ (-3) = 1
• Dividing an Integer by 1: Any integer divided by 1 equals the integer itself.
  • Reference: (2)
  • Example: 7 ÷ 1 = 7, (-4) ÷ 1 = -4
• Dividing Zero by a Non-Zero Integer: Zero divided by any non-zero integer always equals 0.
  • Reference: (3)
  • Example: 0 ÷ 6 = 0, 0 ÷ (-2) = 0
• Dividing by Zero: Dividing any integer by zero is not defined, and therefore, is not a valid operation.
  • Reference: (4)
  • Example: 5 ÷ 0 is not valid.

Rules Involving Signs

The rules for multiplying and dividing integers regarding signs are the same.

• Positive ÷ Positive = Positive: Example: 10 ÷ 2 = 5
• Negative ÷ Negative = Positive: Example: (-12) ÷ (-3) = 4
• Positive ÷ Negative = Negative: Example: 15 ÷ (-5) = -3
• Negative ÷ Positive = Negative: Example: (-20) ÷ 4 = -5

Important Note on Order of Operations

When you have more than one division operation, the order matters:

• Non-Associative Property: If you have three non-zero integers, x, y, and z, then (x ÷ y) ÷ z is not the same as x ÷ (y ÷ z), except when z = 1.
  • Reference: (5)
  • Example:
    • (12 ÷ 2) ÷ 3 = 6 ÷ 3 = 2
    • 12 ÷ (2 ÷ 3) = 12 ÷ (2/3) = 18.

Step-by-Step Process

To divide integers effectively:

1. Ignore the signs: Perform the division as if all numbers are positive.
2. Determine the sign of the answer:
   • Same signs result in a positive answer.
   • Different signs result in a negative answer.

Examples

Let's look at a few examples:

• Example 1: (-21) ÷ (-7)
  1. 21 ÷ 7 = 3
  2. Negative ÷ Negative = Positive
  3. Answer: 3
• Example 2: 36 ÷ (-4)
  1. 36 ÷ 4 = 9
  2. Positive ÷ Negative = Negative
  3. Answer: -9
• Example 3: (-48) ÷ 6
  1. 48 ÷ 6 = 8
  2. Negative ÷ Positive = Negative
  3. Answer: -8

Practice

Practice is key to mastering integer division. Use the above rules and examples to solve different types of problems.