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Which equation shows the associative property of multiplication?\newlineChoices:\newline(A) g(hj)=(gh)jg \cdot (h \cdot j) = (g \cdot h) \cdot j\newline(B) g=g1g = g \cdot 1\newline(C) g1=gg \cdot 1 = g\newline(D) 0=g00 = g \cdot 0

Full solution

Q. Which equation shows the associative property of multiplication?\newlineChoices:\newline(A) g(hj)=(gh)jg \cdot (h \cdot j) = (g \cdot h) \cdot j\newline(B) g=g1g = g \cdot 1\newline(C) g1=gg \cdot 1 = g\newline(D) 0=g00 = g \cdot 0
  1. Property of Multiplication: The associative property of multiplication states that when three or more numbers are multiplied, the way in which they are grouped does not affect the product. In other words, (ab)c=a(bc) (a \cdot b) \cdot c = a \cdot (b \cdot c) . We need to find the equation that represents this property from the given choices.
  2. Examine Choice (A): Let's examine choice (A): g(hj)=(gh)jg \cdot (h \cdot j) = (g \cdot h) \cdot j. This equation shows that the product of gg and the product of hh and jj is the same as the product of gg and hh and then multiplying the result by jj. This is the associative property of multiplication.
  3. Choice (B): Choice (B): g=g1g = g \cdot 1 does not represent the associative property. It represents the identity property of multiplication, which states that any number multiplied by 11 equals the number itself.
  4. Choice (C): Choice (C): g1=gg \cdot 1 = g also represents the identity property of multiplication, not the associative property.
  5. Choice (D): Choice (D): 0=g00 = g \cdot 0 represents the zero property of multiplication, which states that any number multiplied by 00 equals 00.
  6. Conclusion: Based on the examination of all choices, we can conclude that choice (A) correctly represents the associative property of multiplication.