In this lesson, we will learn:
- What is the commutative property of addition?
- What is the commutative property of multiplication?
- How to write the general formulas/equations for the commutative properties
- Changing the order of a list of addends/factors does not change the answer
- How to solve word problems for the commutative property
Notes:
- The commutative property means that changing the order of numbers in an equation does NOT change the answer ONLY when you are performing addition or multiplication
- The numbers can be any real number (whole numbers, fractions, decimals, integers, etc.)
- To “commute” can mean to travel between home and school—when you switch places, the travel time does not change (going to school and going back home).
- If you switch the places of the numbers in an addition or multiplication equation, it will not change the answer in the end.
- For addition: the order of addends does not change the answer
- Ex. 3 + 5 = 5 + 3 (equals 8 either way)
- Ex. 0.3 + 0.5 = 0.5 + 0.3 (equals 0.8 either way)
- Ex. $\frac{3}{10}$ + $\frac{5}{10}$ = $\frac{5}{10}$ + $\frac{3}{10}$ (equals $\frac{8}{10}$ either way)
- For multiplication: the order of factors does not change the answer
- Ex. 3 × 4 = 4 × 3 (equals 12 either way)
- Ex. 0.3 × 0.4 = 0.4 × 0.3 (equals 0.12 either way)
- Ex. $\frac{3}{10}$ + $\frac{4}{10}$ = $\frac{4}{10}$ + $\frac{3}{10}$ (equals $\frac{12}{100}$ either way)
- The general formulas (where a and b are variables that represent real numbers) for the commutative property are:
- The commutative property does NOT work for subtraction nor division. In subtraction and division, the order of numbers DO matter and will change the answer
- Ex. 5 – 2 = 3, but if you switch the order, the answer will change: 2 – 5 = -3
- Ex. 10 ÷ 2 = 5, but if you switch the order, the answer will change: 2 ÷ 10 = 0.2