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Which equation shows the zero property of multiplication?\newlineChoices:\newline(A) df=g+hd \cdot f = g + h\newline(B) dfdg=d(fg)d \cdot f - d \cdot g = d \cdot (f - g)\newline(C) (df)g=d(fg)(d \cdot f) \cdot g = d \cdot (f \cdot g)\newline(D) 0d=00 \cdot d = 0

Full solution

Q. Which equation shows the zero property of multiplication?\newlineChoices:\newline(A) df=g+hd \cdot f = g + h\newline(B) dfdg=d(fg)d \cdot f - d \cdot g = d \cdot (f - g)\newline(C) (df)g=d(fg)(d \cdot f) \cdot g = d \cdot (f \cdot g)\newline(D) 0d=00 \cdot d = 0
  1. Identify Zero Property: Identify the zero property of multiplication. The zero property of multiplication states that any number multiplied by 00 equals 00.
  2. Analyze Choices: Analyze each choice to see which one represents the zero property of multiplication.\newline(A) df=g+hd \cdot f = g + h does not show any number being multiplied by 00.
  3. Option (A): (B) dfdg=d(fg)d \cdot f - d \cdot g = d \cdot (f - g) demonstrates the distributive property, not the zero property.
  4. Option (B): (C)(df)g=d(fg)(C) (d \cdot f) \cdot g = d \cdot (f \cdot g) shows the associative property of multiplication, not the zero property.
  5. Option (C): (D)0d=0(D) 0 \cdot d = 0 clearly shows that zero multiplied by any number dd equals zero, which is the zero property of multiplication.

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