Overview
This lesson explains the commutative property for addition and multiplication, highlighting how changing the order of numbers does not affect the result.
The Commutative Property: Definition and Meaning
- "Commute" means "to move"; commutative property refers to moving numbers in an operation without changing the result.
- The property applies to both addition and multiplication.
Commutative Property of Addition
- Changing the order of numbers in addition does not change the sum.
- Example: 5 + 2 + 1 = 2 + 5 + 1 = 8.
- Example: 3 + 2 + 6 = 6 + 2 + 3 = 11.
- If any or all numbers are moved around in addition, the answer is the same.
Commutative Property of Multiplication
- Changing the order of numbers in multiplication does not change the product.
- Example: 3 × 2 × 4 = 2 × 4 × 3 = 24.
- You can rearrange the numbers in multiplication, and the result remains unchanged.
Non-Commutative Operations: Subtraction and Division
- The commutative property does NOT work for subtraction.
- Example: 7 - 3 ≠ 3 - 7; 7 - 3 = 4, 3 - 7 = -4.
- The commutative property does NOT work for division.
- Example: 10 ÷ 2 = 5, 2 ÷ 10 = 0.2; 10 ÷ 2 ≠ 2 ÷ 10.
Key Terms & Definitions
- Commutative Property — Changing the order (moving) of numbers in an operation does not affect the result (applies to addition and multiplication).
- Addition — Mathematical operation of combining numbers to get a sum.
- Multiplication — Mathematical operation of repeated addition of the same number.
- Subtraction — Mathematical operation of taking one number away from another; not commutative.
- Division — Mathematical operation of splitting a number into equal parts; not commutative.
Action Items / Next Steps
- Review the commutative property for addition and multiplication.
- Prepare to learn about associative and distributive properties in future lessons.