Multiplication Table
Multiplication Table in Grade 4 Saxon Math Intermediate 4 Chapter 3 uses the table to introduce the Commutative Property of Multiplication: changing the order of factors does not change the product, expressed as m x n = n x m. For example, 4 x 8 = 32 and 8 x 4 = 32. Students explore this by arranging a garden with 5 rows of 9 carrots (5 x 9 = 45) and confirming that 9 rows of 5 carrots yields the same total. The property applies to multiplication and addition but not to subtraction or division, making it important for students to distinguish when order matters.
Key Concepts
New Concept Changing the order of factors does not change the product. This is the Commutative Property of Multiplication . $$m \times n = n \times m$$.
Why it matters This isn't just a rule for multiplication tables; it's a fundamental law of algebra that allows you to simplify complex expressions. Mastering these properties is the difference between simply doing math and truly understanding how it works.
What’s next Next, you'll use the multiplication table to explore this property and others, building a solid foundation for your calculations.
Common Questions
What is the Commutative Property of Multiplication?
The order of factors does not change the product. 3 x 7 = 21 and 7 x 3 = 21. Written as m x n = n x m.
How does the multiplication table show the commutative property?
Corresponding cells across the diagonal are equal: row 4, column 8 and row 8, column 4 both show 32.
Does the commutative property apply to division?
No. Division is not commutative: 10 divided by 2 equals 5, but 2 divided by 10 does not equal 5.
Why is the commutative property useful?
It gives flexibility when calculating. If 9 x 5 is easier for you than 5 x 9, you can rearrange the factors without changing the answer.
Does swapping factors in 5 x 9 give the same product as 9 x 5?
Yes. Both equal 45. This is a direct application of the Commutative Property of Multiplication.