COMMUTATIVE PROPERTY OF MULTIPLICATION

Commutative Property Of Multiplication

Definition Of Commutative Property Of Multiplication

The Commutative Property of Multiplication states that changing the order of factors does not change the product, i.e. if a and b are two real numbers, then a × b = b × a.

More About Commutative Property of Multiplication

Matrix multiplication is not commutative.

Video Examples:Commutative Property of Multiplication

Example of Commutative Property of Multiplication

As per the commutative property of multiplication, the expression 3 × 9 = 27 can be written as
9 × 3 = 27. So, 3 × 9 = 9 × 3.
As per the commutative property of multiplication, the expression (- 7)6 = - 42 can be written as
6 (- 7) = - 42. So, (- 7)6 = 6(- 7).

Solved Example on Commutative Property of Multiplication

Ques: Which of these is equivalent to 18 × 13?

Choices:

A. 13 × 18
B. 13 ÷ 18
C. 13 - 18
D. 13 + 18
Correct Answer: A

Solution:

Step 1: As per the commutative property of multiplication, changing the order of factors does not change the product.
Step 2: Value of the expression 18 × 13 = 234.
Step 3: Value of the expression 13 × 18 = 234.
Step 4: So, 18 × 13 is same as 13 × 18.

Quick Summary

Changing the order of numbers being multiplied doesn't change the answer.
This property makes calculations easier.

\[ a \times b = b \times a \]

⚠️ Common Mistakes

Assuming the commutative property applies to division or subtraction.
Forgetting that the property only applies to multiplication (and addition).

🌍 Real-World Uses

Calculating the area of a rectangular garden: Length times width is the same as width times length.
Determining the total cost of buying multiple items: The number of items multiplied by the price per item yields the same total cost as the price per item multiplied by the number of items.
Calculating total travel distance when segments are involved: If you drive 5 hours at 60 mph, the distance is the same as driving 60 mph for 5 hours.

📋 Standards Alignment

CCSS.MATH.CONTENT.3.OA.B.5

🍎 Teacher Insights

Use visual aids and real-world examples to demonstrate the property. Have students practice rearranging multiplication problems to find the easiest way to solve them.

🎓 Prerequisites

Basic multiplication facts
Understanding of factors and products

Check Your Knowledge

Q1: Which equation demonstrates the commutative property of multiplication?

A. 5 x 1 = 5 B. 3 x 2 = 2 x 3 C. 4 x (2 + 3) = 4 x 2 + 4 x 3 D. (2 x 3) x 4 = 2 x (3 x 4)

Q2: Which of these is equivalent to 18 × 13?

A. 13 × 18 B. 13 ÷ 18 C. 13 - 18 D. 13 + 18

Frequently Asked Questions

Q: Does the commutative property work for division?
A: No, the commutative property does not work for division. For example, 6 / 2 is not the same as 2 / 6.

Q: Why is this property useful?
A: It allows you to rearrange multiplication problems to make them easier to solve, especially mentally.