QuestionWhich option shows the associative property of multiplication? A. $ab=ba$ B. $a(bc)=(ab)c$ C. $a \cdot 1=a$ D. $a(b+c)=ab+ac$

Studdy Solution

STEP 1

Assumptions1. We are looking for the sentence that illustrates the associative property for multiplication.

STEP 2

Let's recall the associative property for multiplication. It states that when three or more numbers are multiplied, the product is the same regardless of the grouping of the factors.
The mathematical representation of the associative property for multiplication is $a(bc) = (ab)c$

STEP 3

Now, let's compare this property with the given options.
Option A $ab=ba$ is the commutative property of multiplication, not the associative property.
Option B $a(bc) = (ab)c$ is exactly the associative property of multiplication.
Option C $a \cdot1 = a$ is the multiplicative identity property, not the associative property.
Option D $a(b+c) = ab + ac$ is the distributive property, not the associative property.

STEP 4

From the above analysis, we can see that Option B $a(bc) = (ab)c$ is the sentence that illustrates the associative property for multiplication.
So, the solution to the problem is Option B $a(bc) = (ab)c$ .

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