Math CentralQuandaries & Queries


Question from Terry, a parent:

5*(7*2)=(7*5)*2 Is this associative property or commutative ??? Both?

Hi Terry,

The commutative property states that for any numbers a and b, a*b = b*a.

The associative property states that for any numbers a, b and c, a*(b*c) = (a*b)*c.

To show that 5*(7*2) = (7*5)*2 you need to use two steps. First shift the parentheses using the associative property.

5*(7*2) = (5*7)*2

Now use the commutative property inside the parentheses on the right to get

5*(7*2) = (5*7)*2 = (7*5)*2

I hope this helps,

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