a) 20 x 30 = 30 x 20 b) 32 x 15 = 480 15 x 32 = 480 d) 2697 = 31 x 87 87 x 31 = 2697 e) 1694 = 22 x 77 77 x 22 = 1694

The student's question involves understanding the commutative property of multiplication, which is a fundamental principle in mathematics.
Commutative Property of Multiplication: This property states that for any two numbers, the result of their multiplication is the same regardless of the order in which they are multiplied. In simpler terms, if you have two numbers, a and b , then:
a × b = b × a
Let's apply this property to each part of the question:

20 × 30 = 30 × 20


Both sides equal 600. This shows the commutative property in action, confirming that changing the order of multiplication does not affect the result.


32 × 15 = 480 and 15 × 32 = 480


Both expressions are equal to 480. Again, this demonstrates the commutative property since the numbers can be multiplied in any order, resulting in the same product.


2697 = 31 × 87 and 87 × 31 = 2697


Both expressions result in 2697. The commutative property of multiplication verifies that changing the sequence of multiplication does not change the outcome.


1694 = 22 × 77 and 77 × 22 = 1694


Both products are 1694. The order of multiplication can be changed without influencing the product, illustrating the commutative property.

In summary, the question is about understanding the commutative property of multiplication, whereby the order of numbers in a multiplication operation can switch places without affecting the outcome. This property makes it easier to perform calculations and is fundamental in algebra and arithmetic.

Answered by RyanHarmon181 | 2025-07-21