Communicative property

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

• 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