Which of the following demonstrates the commutative property across multiplication for [tex]$2 \times 10 \times 7$[/tex]?
A) [tex]$2+10 \times 7$[/tex]
B) [tex]$2 \times(10 \times 7)$[/tex]
C) [tex]$10 \times 7 \times 2$[/tex]
D) [tex]$(2 \times 10) \times 7$[/tex]
Answer (1)
The commutative property of multiplication states that the order of factors does not affect the product.
Option A involves addition, so it's not commutative multiplication.
Options B and D demonstrate the associative property, not the commutative property.
Option C, 10 × 7 × 2 , rearranges the factors, demonstrating the commutative property. The answer is C
Explanation
Understanding the Commutative Property The problem is to identify which of the given options demonstrates the commutative property of multiplication for the expression 2 × 10 × 7 . The commutative property states that the order of factors does not affect the product (e.g., a × b = b × a ).
Analyzing Option A Option A, 2 + 10 × 7 , involves addition, so it does not demonstrate the commutative property of multiplication.
Analyzing Option B Option B, 2 × ( 10 × 7 ) , demonstrates the associative property of multiplication, not the commutative property. The associative property states that the grouping of factors does not affect the product (e.g., ( a × b ) × c = a × ( b × c ) ).
Analyzing Option C Option C, 10 × 7 × 2 , shows a rearrangement of the factors 2, 10, and 7, thus demonstrating the commutative property.
Analyzing Option D Option D, ( 2 × 10 ) × 7 , demonstrates the associative property of multiplication, not the commutative property.
Conclusion Therefore, the correct option is C.
Examples
The commutative property is useful in everyday situations. For example, if you are buying 3 items that cost $2, $5, and $10, the total cost will be the same no matter in which order you add them: $2 + $5 + $10 = $10 + $5 + $2. This makes mental calculations easier and more flexible.
