Swap the terms
Swapping two terms does not change the sum.
Madhu’s drone
Madhu flies a drone from a terrace. It goes 6 m up, then 4 m down. Its height above the terrace is 6 + (−4).
What if it goes 4 m down first, and then 6 m up? Where does the drone end?
What this lesson covers
The idea
In an expression having two terms, swapping them does not change the value: Term 1 + Term 2 = Term 2 + Term 1; this is called the commutative property of addition.
Madhu’s drone
Madhu flies a drone from a terrace. It goes 6 m up, then 4 m down. Its height above the terrace is 6 + (−4).
What if it goes 4 m down first, and then 6 m up? Where does the drone end?
- Higher than before
- At the same height as before
- Lower than before
Fly it both ways
Tap Swap to change the order of the two moves. Watch where the route ends.
The end point stays
6 + (−4) = 2 and (−4) + 6 = 2. The route changes, but the drone ends at the same height. The same happens with every pair of terms.
In an expression with two terms, swapping them does not change the value: Term 1 + Term 2 = Term 2 + Term 1. This is the commutative property of addition.
Not everything in life can be swapped. *Hat then shoes* looks the same as *shoes then hat*. But *socks then shoes* is very different from *shoes then socks*! For the terms of a sum, the order never matters.
Notes
In an expression with two terms, swapping them does not change the value: Term 1 + Term 2 = Term 2 + Term 1. This is the commutative property of addition.
Check yourself
(−9) + 4 = −5. What is 4 + (−9)?
Answer: -5
4 + (−9) = (−9) + 4 = −5. Swapping the terms does not change the value.
Which expression has the same value as 15 + (−6)?
Which job can you do in either order with the same result?
- 6 + (−15). That is −9. Swapping means the same numbers with the same signs, in the other order.
- (−15) + 6. That is −9. The signs changed, so this is not a swap.
- (−6) + 15 — correct. Yes! It is 15 + (−6) with the two terms swapped. Both are 9.
- Put on your socks, put on your shoes. The order matters here. Shoes first, then socks, feels very different!
- Open the door, walk through the door. The order matters here. You cannot walk through a closed door.
- Put on your hat, put on your shoes — correct. Yes! Like swapping two terms, the order does not matter.