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Which equation shows the commutative property of multiplication?\newlineChoices:\newline(A) q=mnpq = m \cdot n \cdot p\newline(B) mn+mp=m(n+p)m \cdot n + m \cdot p = m \cdot (n + p)\newline(C) mn=nmm \cdot n = n \cdot m\newline(D) 0m=00 \cdot m = 0

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Q. Which equation shows the commutative property of multiplication?\newlineChoices:\newline(A) q=mnpq = m \cdot n \cdot p\newline(B) mn+mp=m(n+p)m \cdot n + m \cdot p = m \cdot (n + p)\newline(C) mn=nmm \cdot n = n \cdot m\newline(D) 0m=00 \cdot m = 0
  1. Understand Commutative Property: Understand the commutative property of multiplication. The commutative property states that changing the order of the factors does not change the product. In mathematical terms, this means a×b=b×aa \times b = b \times a.
  2. Examine Choice (A): Examine choice (A) q=mnpq = m \cdot n \cdot p to see if it demonstrates the commutative property. This equation simply states that qq is the product of mm, nn, and pp, but does not show any change in the order of multiplication. Therefore, it does not demonstrate the commutative property.
  3. Examine Choice (B): Examine choice (B) mn+mp=m(n+p)m \cdot n + m \cdot p = m \cdot (n + p) to see if it demonstrates the commutative property. This equation is an example of the distributive property, where a common factor is distributed across terms inside a parenthesis. It does not show the commutative property.
  4. Examine Choice (C): Examine choice (C) mn=nmm \cdot n = n \cdot m to see if it demonstrates the commutative property. This equation shows two factors, mm and nn, being multiplied in both possible orders and set equal to each other. This is a direct representation of the commutative property of multiplication.
  5. Examine Choice (D): Examine choice (D) 0m=00 \cdot m = 0 to see if it demonstrates the commutative property. This equation shows the multiplication of a number by zero, which always results in zero. It does not show the commutative property, but rather the property that any number multiplied by zero equals zero.

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