Lecture Notes: Integer Operations
Overview
This lecture covers the basic arithmetic operations involving integers, including addition, subtraction, multiplication, and division. These foundational skills are crucial for understanding more complex mathematical concepts.
Key Concepts
Addition of Integers
- Same Sign: When adding two integers with the same sign, add their absolute values. The sum will have the same sign as the integers.
- Example: (+3 + +2 = +5)
- Example: (-3 + -2 = -5)
- Different Signs: When adding two integers with different signs, subtract the smaller absolute value from the larger absolute value. The sum will have the sign of the integer with the larger absolute value.
- Example: (+5 + -2 = +3)
- Example: (-5 + +2 = -3)
Subtraction of Integers
- Subtracting an integer is the same as adding its opposite.
- Example: (5 - 3 = 5 + (-3) = 2)
- Example: (-5 - 3 = -5 + (-3) = -8)
Multiplication of Integers
- Same Sign: The product of two integers with the same sign is positive.
- Example: (+3 \times +2 = +6)
- Example: (-3 \times -2 = +6)
- Different Signs: The product of two integers with different signs is negative.
- Example: (+3 \times -2 = -6)
- Example: (-3 \times +2 = -6)
Division of Integers
- Same Sign: The quotient of two integers with the same sign is positive.
- Example: (+6 / +2 = +3)
- Example: (-6 / -2 = +3)
- Different Signs: The quotient of two integers with different signs is negative.
- Example: (+6 / -2 = -3)
- Example: (-6 / +2 = -3)
- Zero Division: Division by zero is undefined.
Practice Resources
Summary
Mastering the operations of addition, subtraction, multiplication, and division of integers is crucial for tackling more advanced mathematics. Practice and review using the provided resources to strengthen your understanding.