# Commutative property for addition | Arithmetic properties | Pre-Algebra | Khan Academy

Rewrite the expression

below applying the commutative and associative

properties of addition. And then show that

both expressions yield the same result. So one, we could just evaluate

the expression the way it’s written. And then we can

kind of mess around with it using the commutative

and associative properties of addition. So let’s first add 17.5 plus 3. So that’s going to give us 20.5. So this is going to be 20.5. And then to that, we’re

going to add negative 7.5. Now, adding negative 7.5

is the exact same thing as subtracting 7.5. So this is going to be equal

to– the 0.5’s cancel out. And then 20 minus 7 is 13. So that’s our first way

of getting the answer. And we kind of adhered

to the parentheses. Now let’s use the

commutative property. The commutative

property tells us that the order doesn’t matter. We can commute these

numbers around. They can move, commute. It’s like you’re going to work. They can move around. So let’s just move

the numbers around. Let’s make it–

actually, we could do all sorts of crazy things. We could just change

the order here. We could make this negative

7.5 plus 17.5 plus 3. We could keep the

parentheses, just like that. So we would have

essentially just changed the order of this

expression right over here. But let’s use both

the commutative and the associative properties. So now we’ve commuted

everything around. And now we can

re-associate everything. So instead of putting the

parentheses like that, we could put the

parentheses like that. So that’s what the

associative property tells us. So let me write this down. So associative

property of addition tells us that a plus b plus

c– we do a plus b first– is the same thing as a plus b

plus c, where you do b plus c first. The commutative

property tells us that a plus b is

equal to b plus a, that you can move

these guys around. So let’s evaluate this one. We actually got here

using both the commutative and the associative property. So we get negative

7.5 plus 17.5. This is the exact same

thing as 17.5 minus 7.5. It might be easier for

you to realize, OK, I’m adding two numbers

of different signs, so what I could do is take the

difference between the two. And since the larger

number is positive, I have a larger number. Or you could just view

this as 17.5 minus 7.5. So 17.5 minus 7.5–

the 0.5’s cancel out. 17 minus 7 is 10. So this part right

here becomes 10. And then we still

have the plus 3 there. And that, once again, is

going to be equal to 13. And we could keep

commuting this around and keep re-associating it. No matter how we do it,

we are going to get 13.

thanks

Thank you for explaining. I know that you didn't make this property, but that's dumb! Commutative just means you change the order? I'm helping my son with his homework because his Dad is out of town. I SUCK at math, I mean really really really suck! Thank you for explaining I wouldn't have gotten it without you!

OMG THANK YOU!!!!!!!!!!!!!!!! 🙂

This totally helped me with my home work!!!!!!! Thanks

Khan, How do i solve this?: 2(x+y) = 8 + 2y

How the hell does this guy write so well with a mouse. I don't comprehend. Maybe he should make a video on how to do that. XD This guy is a god

Still dont understand 🙁

im in 7th grade and i suck at math problems like this

OMG I WATCHED THIS 6 TIMES I KNOWWWWWWWW HOWWWWWWWW TO DOOOOOOOO ITTTTTTTTTTT THANK YOUUUUUUUUUUUUUUUUUUUUUUUUUUThx I proved my mom wrong with this and now she is saying this is a lie

When you realise a mouse can write better than you.The person's name isn't Khan, that is just the name of the website