friloux
contestada

what is the difference between the commutative distributive and associative properties when multiplying?

Respuesta :

R1ddle
The associative rule is a rule about when it's safe to move parentheses around. You can remember that because the parentheses determine which expressions you have to do first--which numbers can associate with each other. It looks like this:

For addition: (a + b) + c = a + (b + c)
For multiplication: (ab)c = a(bc)

The commutative property is about which operations you can do backward and forward. You can remember this by thinking of people commuting to work: they go to work every morning, then they repeat the same operation backward when they commute home. It looks like this:

For addition: a + b = b + a
For multiplication: ab = ba

Finally, the distributive property tells you what happens when you distribute one operation against another kind in parentheses. It looks like this:

a * (b + c) = ab + ac

In other words, the a is "distributed" over the b and c.

Of course, you can make these work together:

a * (b + (c + d))
= a * ((b + c) + d) (by the associative property)
= a * (d + (b + c)) (by the commutative property)
= ad + a (b + c) (by the distributive property)
= ad + ab + ac (by the distributive property again).

Hope this helps.

Commutative Property. The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2.
ACCESS MORE
EDU ACCESS