Q. Which equation shows the distributive property of multiplication?Choices:(A) (r⋅s)⋅t=r⋅(s⋅t)(B) (r+s)⋅t=r⋅t+s⋅t(C) r⋅s=s⋅r(D) 0=r⋅0
Understand Distributive Property: Understand the distributive property of multiplication. The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. The general form of the distributive property is a×(b+c)=a×b+a×c.
Examine Choice (A): Examine choice (A) to see if it represents the distributive property. (A) states (r⋅s)⋅t=r⋅(s⋅t). This is an example of the associative property, not the distributive property, because it deals with the grouping of multiplication, not the distribution over addition.
Examine Choice (B): Examine choice (B) to see if it represents the distributive property. (B) states (r+s)⋅t=r⋅t+s⋅t. This matches the form of the distributive property, where t is distributed over the sum of r and s.
Examine Choice (C): Examine choice (C) to see if it represents the distributive property. (C) states r⋅s=s⋅r. This is an example of the commutative property, which states that the order of multiplication does not affect the product.
Examine Choice (D): Examine choice (D) to see if it represents the distributive property. (D) states 0=r⋅0. This is an example of the multiplication property of zero, which states that any number multiplied by zero is zero.