Commutative Property of Multiplication
The Commutative Property of Multiplication states that the order of factors does not change the product: m × n = n × m. In Grade 4 math from Saxon Math Intermediate 4 Chapter 3, students see that 9 × 3 = 27 and 3 × 9 = 27—swapping the factors gives the same answer. This property effectively halves the number of facts to memorize, since knowing 4 × 7 automatically gives 7 × 4, and it underpins flexible mental math and algebraic reasoning.
Key Concepts
Property $m \times n = n \times m$.
Examples $9 \times 3 = 27$ is the same as $3 \times 9 = 27$. $6 \times 4 = 24$ is the same as $4 \times 6 = 24$. $12 \times 11 = 132$ is the same as $11 \times 12 = 132$.
Explanation It's the 'order doesn't matter' rule! Swapping the numbers you multiply doesn't change the answer. Think of it like $3 \times 9$ and $9 \times 3$—both get you to 27. Easy!
Common Questions
What is the Commutative Property of Multiplication?
The Commutative Property says that changing the order of factors does not change the product: a × b = b × a. For example, 6 × 4 = 4 × 6 = 24.
How does the Commutative Property help memorize multiplication facts?
Every fact comes in a pair: knowing 7 × 8 = 56 immediately gives 8 × 7 = 56. This cuts the 100-fact table down to about 55 unique facts.
Does the Commutative Property work for division?
No. Division is not commutative: 12 ÷ 4 = 3, but 4 ÷ 12 = 1/3. Order matters in division.
When do Grade 4 students learn the Commutative Property of Multiplication?
This property is introduced in Chapter 3 of Saxon Math Intermediate 4, reinforcing multiplication concepts with a formal rule.
How does the Commutative Property relate to arrays?
A 3×5 array (3 rows, 5 columns) and a 5×3 array (5 rows, 3 columns) both contain 15 objects. Rotating the array 90° demonstrates commutativity visually.
How does the Commutative Property apply in algebra?
In algebraic expressions, xy = yx allows rearranging factors for easier computation—for example, rewriting 5 × 13 as 13 × 5 may be easier to calculate mentally.