Overview
This lecture introduces the fundamental arithmetic operations of addition and subtraction, discusses their properties, and explains their concrete meaning using simple examples.
Origins and Purpose of Arithmetic
- Arithmetic began as a practical tool for counting and handling real-world quantities.
- Early humans used math to count people, track goods, and describe their environment.
- Our base-10 (decimal) system likely arose from counting on ten fingers.
Addition
- Addition combines two numbers to form a sum.
- Example: 2 + 3 = 5, meaning two apples and three apples make five apples.
- The equation format is: [number] + [number] = [sum].
- Addition is commutative: changing the order does not change the result (e.g., 2 + 3 = 3 + 2).
- Addition is associative: grouping does not affect the sum (e.g., (2 + 3) + 4 = 2 + (3 + 4)).
Subtraction
- Subtraction finds the difference between two numbers, acting as the inverse of addition.
- Example: 5 - 1 = 4, meaning you have five apples, eat one, and four remain.
- The equation format is: [number] - [number] = [difference].
- Subtraction is not commutative: 3 - 2 ≠ 2 - 3.
- Subtraction is not associative: (5 - 3) - 2 ≠ 5 - (3 - 2).
- On a number line, subtraction represents the distance between two numbers.
Key Terms & Definitions
- Addition — combining two numbers to make a larger number (the sum).
- Subtraction — removing one number from another to find the difference.
- Sum — the result of an addition operation.
- Difference — the result of a subtraction operation.
- Commutative Property — order does not matter (true for addition, not for subtraction).
- Associative Property — grouping does not matter (true for addition, not for subtraction).
- Equation — a mathematical statement showing two expressions are equal.
Action Items / Next Steps
- Review the properties of addition and subtraction.
- Prepare for a comprehension check on these concepts.