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Which equation shows the associative property of multiplication?\newlineChoices:\newline(A) 0=c⋅00 = c \cdot 0\newline(B) (c+d)⋅f=c⋅f+d⋅f(c + d) \cdot f = c \cdot f + d \cdot f\newline(C) f+g=c⋅df + g = c \cdot d\newline(D) (c⋅d)⋅f=c⋅(d⋅f)(c \cdot d) \cdot f = c \cdot (d \cdot f)

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Q. Which equation shows the associative property of multiplication?\newlineChoices:\newline(A) 0=c⋅00 = c \cdot 0\newline(B) (c+d)⋅f=c⋅f+d⋅f(c + d) \cdot f = c \cdot f + d \cdot f\newline(C) f+g=c⋅df + g = c \cdot d\newline(D) (c⋅d)⋅f=c⋅(d⋅f)(c \cdot d) \cdot f = c \cdot (d \cdot f)
  1. Understand Associative Property: Understand the associative property of multiplication. The associative property states that when three or more numbers are multiplied together, the way in which they are grouped does not affect the product. In other words, changing the grouping of the numbers does not change the result.
  2. Examine Choice (A): Examine each choice to see which one represents the associative property.\newline(A) 0=c⋅00 = c \cdot 0 does not show any property related to the grouping of multiplication.
  3. Examine Choice (B): Examine choice (B).\newline(B) (c+d)⋅f=c⋅f+d⋅f(c + d) \cdot f = c \cdot f + d \cdot f shows the distributive property, not the associative property.
  4. Examine Choice (C): Examine choice (C).\newline(C) f+g=c⋅df + g = c \cdot d does not involve the multiplication of three or more numbers, so it cannot show the associative property.
  5. Examine Choice (D): Examine choice (D).\newline(D) (c⋅d)⋅f=c⋅(d⋅f)(c \cdot d) \cdot f = c \cdot (d \cdot f) shows the multiplication of three numbers with different groupings but the same result, which is the definition of the associative property.

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