Division of Integers Lecture Notes

Overview

• This lecture covers the basic rules for dividing integers and provides several practical examples.
• The rules for dividing integers are the same as those for multiplying integers.
• More detailed explanations of these rules can be found in another video.

Rules for Dividing Integers

• Same Signs:
  • If the signs are the same, the quotient is positive.
  • Example:
    • Positive ÷ Positive = Positive
    • Negative ÷ Negative = Positive
• Different Signs:
  • If the signs are different, the quotient is negative.
  • Example:
    • Positive ÷ Negative = Negative
    • Negative ÷ Positive = Negative

Examples

1. Positive 36 ÷ Positive 4

   • Result: Positive 9
   • Rule: Positive ÷ Positive = Positive

2. Negative 35 ÷ Negative 7

   • Result: Positive 5
   • Rule: Negative ÷ Negative = Positive
   • Check: 5 × (-7) = -35

3. Negative 56 ÷ Positive 7

   • Result: Negative 8
   • Rule: Negative ÷ Positive = Negative
   • Check: -8 × 7 = -56

4. Positive 27 ÷ Negative 3

   • Result: Negative 9
   • Rule: Positive ÷ Negative = Negative
   • Check: -9 × (-3) = 27

Division by Zero

• Division by Zero:

  • Example: 12 ÷ 0 is undefined.
  • Reason: Cannot divide items into 0 groups.

• Zero Divided by Constant:

  • Example: 0 ÷ 5 = 0
  • Reason: Zero items divided into any number of groups results in groups of zero items.

Conclusion

• Division by zero is undefined.
• Zero divided by any number results in zero.
• The division rules follow logically from multiplication rules.
• The lecture provides a basic understanding of integer division.