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Commutative Property for Addition. Created by Sal Khan and Monterey Institute for Technology and Education.
Video transcript
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.