Commutative Property of Multiplication
a × b = b × a. Changing the order of the numbers doesn't change the answer: 3 × 4 = 12 and 4 × 3 = 12.
See it on the multiplication chart
The multiplication chart is a mirror image across its diagonal. The square in row 3, column 4 holds 12, and so does the square in row 4, column 3. Tap one, then the other, to see both paths.
That is why a 12 × 12 chart has 144 squares but only 78 different pairs of numbers: 12 squares on the diagonal plus 66 pairs that each appear twice (12 + 2 × 66 = 144).
Examples
- 2 × 9 = 18 and 9 × 2 = 18
- 6 × 7 = 42 and 7 × 6 = 42
- 5 × 12 = 60 and 12 × 5 = 60
- It works for any numbers, including fractions and decimals: 0.5 × 8 = 4 and 8 × 0.5 = 4.
Questions and answers
What is the commutative property of multiplication?
It says that the order of the numbers doesn't change the product: a × b = b × a. For example, 3 × 5 = 15 and 5 × 3 = 15.
Is division commutative?
No. 12 ÷ 3 = 4, but 3 ÷ 12 = 0.25. Subtraction is not commutative either. Addition and multiplication are.
How does the commutative property help with times tables?
It halves the work. On a 12 × 12 chart there are 144 squares, but only 78 different pairs, because each fact below the diagonal is a copy of one above it.
What is the difference between the commutative and associative properties?
Commutative is about order: 2 × 7 = 7 × 2. Associative is about grouping when there are three or more numbers: (2 × 3) × 4 = 2 × (3 × 4) = 24.
How many multiplication facts are there? · Times tables tricks