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3. What is the expression of an Associative Property?

User James Amo
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The Associative Property

It applies to the operations of sum and multiplication.

Given three numbers a,b, and c, we can sum them as follows:

(a + b) + c

Here, we first added a+b and the result was then added with c

We can also sum them as:

a + (b + c).

Now we first added b+c and the result was then added with a

Both results are equivalent because of the distributive property with respect to the addition.

Applying to the multiplication we have:

(a * b) * c = a * (b * c)

For example, for the numbers a=5, b=2, c=4.

(5 + 2) + 4 = 7 + 4 = 11

5 + (2 + 4) = 5 + 6 = 11

Both sums are equivalent

(5 * 2 ) * 4 = 10 * 4 = 40

5 * (2 * 4) = 5 * 8 = 40

Both multiplications are equivalent