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Which property of multiplication is shown?\newline(tu)v=t(uv)(t \cdot u) \cdot v = t \cdot (u \cdot v)\newlineChoices:\newline(A) identity\newline(B) distributive\newline(C) associative\newline(D) zero\newline

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Q. Which property of multiplication is shown?\newline(tu)v=t(uv)(t \cdot u) \cdot v = t \cdot (u \cdot v)\newlineChoices:\newline(A) identity\newline(B) distributive\newline(C) associative\newline(D) zero\newline
  1. Identify Property of Multiplication: Identify the property of multiplication shown by the equation t \cdot u) \cdot v = t \cdot (u \cdot v)\. The equation suggests that no matter how we group the numbers when we multiply them, the result is the same. This is a fundamental property of multiplication.
  2. Match with Choices: Match the property identified in Step \(1 with the given choices.\newlineThe property that describes the ability to group numbers in different ways when multiplying without changing the result is known as the associative property.
  3. Eliminate Other Choices: Eliminate the other choices based on the definition of the associative property.\newline(A) Identity property involves the multiplication by 11, which is not shown here.\newline(B) Distributive property involves the distribution of multiplication over addition or subtraction, which is not shown here.\newline(D) Zero property involves the multiplication by 00, which is not shown here.\newlineTherefore, the correct choice is (C) associative.

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