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Which equation shows the distributive property of multiplication?\newlineChoices:\newline(A) (rs)t=r(st)(r \cdot s) \cdot t = r \cdot (s \cdot t)\newline(B) (r+s)t=rt+st(r + s) \cdot t = r \cdot t + s \cdot t\newline(C) rs=srr \cdot s = s \cdot r\newline(D) 0=r00 = r \cdot 0

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Q. Which equation shows the distributive property of multiplication?\newlineChoices:\newline(A) (rs)t=r(st)(r \cdot s) \cdot t = r \cdot (s \cdot t)\newline(B) (r+s)t=rt+st(r + s) \cdot t = r \cdot t + s \cdot t\newline(C) rs=srr \cdot s = s \cdot r\newline(D) 0=r00 = r \cdot 0
  1. 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×ca \times (b + c) = a \times b + a \times c.
  2. Examine Choice (A): Examine choice (A) to see if it represents the distributive property. (A) states (rs)t=r(st)(r \cdot s) \cdot t = r \cdot (s \cdot 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.
  3. Examine Choice (B): Examine choice (B) to see if it represents the distributive property. (B) states (r+s)t=rt+st(r + s) \cdot t = r \cdot t + s \cdot t. This matches the form of the distributive property, where tt is distributed over the sum of rr and ss.
  4. Examine Choice (C): Examine choice (C) to see if it represents the distributive property. (C) states rs=srr \cdot s = s \cdot r. This is an example of the commutative property, which states that the order of multiplication does not affect the product.
  5. Examine Choice (D): Examine choice (D) to see if it represents the distributive property. (D) states 0=r00 = r \cdot 0. This is an example of the multiplication property of zero, which states that any number multiplied by zero is zero.

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