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Which equation shows the zero property of multiplication?\newlineChoices:\newline(A) 1m=m1 \cdot m = m\newline(B) mn=nmm \cdot n = n \cdot m\newline(C) (mn)p=m(np)(m \cdot n) \cdot p = m \cdot (n \cdot p)\newline(D) 0=0m0 = 0 \cdot m

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Q. Which equation shows the zero property of multiplication?\newlineChoices:\newline(A) 1m=m1 \cdot m = m\newline(B) mn=nmm \cdot n = n \cdot m\newline(C) (mn)p=m(np)(m \cdot n) \cdot p = m \cdot (n \cdot p)\newline(D) 0=0m0 = 0 \cdot m
  1. Understand zero property of multiplication: Understand the zero property of multiplication.\newlineThe zero property of multiplication states that any number multiplied by zero equals zero. This can be written as a×0=0a \times 0 = 0 or 0×a=00 \times a = 0, where 'aa' is any real number.
  2. Examine choices for representation: Examine each choice to see which one represents the zero property of multiplication. \newline(A) 1m=m1 \cdot m = m - This is the identity property of multiplication, which states that any number multiplied by 11 is the number itself.
  3. Identify identity property: Continue examining the choices.\newline(B) mn=nmm \cdot n = n \cdot m - This is the commutative property of multiplication, which states that the order in which two numbers are multiplied does not change the product.
  4. Recognize commutative property: Continue examining the choices.\newline(C) (mn)p=m(np)(m \cdot n) \cdot p = m \cdot (n \cdot p) - This is the associative property of multiplication, which states that the way in which numbers are grouped when being multiplied does not change the product.
  5. Understand associative property: Continue examining the choices.\newline(D) 0=0m0 = 0 \cdot m - This choice shows that zero multiplied by any number 'mm' equals zero, which is a direct representation of the zero property of multiplication.

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