Can someone help define these property's Distributive property, Commutative property of multiplication, Associative property of multiplication, and Identity property for multiplication. I'm trying to figure out which property is a statement like (17 · 7) · 12 = 17 · (7 · 12) or -6(17 + 14) = -6(17) + (-6)(14)

Question

anonymous · Answer

The first statement shows that you can "associate" the terms differently and still maintain the equality... you can either multiply 17 by 7 first, then multiply by 12,  or you can start with 7 x 12 and then multiply by 17.

You are "associating" the terms differently, but you are NOT changing their order... you are just changing the location of the parenthesis.  So this is the Associative Property of Multiplication.

anonymous · Answer

ok i see

anonymous · Answer

The 2nd equation involves distributing the "-6" term across the two terms inside the parenthesis... so it's Distributive.

Distributive means that when you multiply one term times a parenthesis with several terms added or subtracted inside, then you multiply that first term by EACH of the terms inside the parenthesis.

So like 5(4 + 6) = (5)(4) + (5)(6)

or if you have subtraction inside... 5(6 - 4) = (5)(6) - (5)(4)

or if you have a negative number on the outside...
-5(4 + 6) = (-5)(4) + (-5)(6)

anonymous · Answer

oh ok i understand now thank you

anonymous · Answer

glad to help :)