Q. Which equation shows the commutative property of multiplication?Choices:(A) k⋅1=k(B) k⋅m=m⋅k(C) (k⋅m)⋅n=k⋅(m⋅n)(D) 1⋅k=k
Define Commutative Property: Identify the definition of the commutative property of multiplication. The commutative property states that changing the order of the factors does not change the product. In other words, for any numbers a and b, the property is defined as a×b=b×a.
Evaluate Choice (A): Examine choice (A) k⋅1=k to see if it demonstrates the commutative property. This equation actually represents the identity property of multiplication, which states that any number multiplied by 1 equals the original number. Therefore, choice (A) does not show the commutative property.
Evaluate Choice (B): Examine choice (B) k⋅m=m⋅k to see if it demonstrates the commutative property. This equation shows that the order of multiplication between k and m can be reversed without changing the product, which is exactly what the commutative property states. Therefore, choice (B) does show the commutative property.
Evaluate Choice (C): Examine choice (C) k \cdot m) \cdot n = k \cdot (m \cdot n)\ to see if it demonstrates the commutative property. This equation actually represents the associative property of multiplication, which states that the way in which factors are grouped does not change the product. Therefore, choice (C) does not show the commutative property.
Evaluate Choice (D): Examine choice (D) \(1 \cdot k = k to see if it demonstrates the commutative property. Similar to choice (A), this equation represents the identity property of multiplication. Therefore, choice (D) does not show the commutative property.