Swap and regroup the terms
Two shoppers add the same three amounts in different orders. Will their totals match?
Loading lab…
Step 1 of 5
- The line 14 − 9 + 6 has three terms: 14, −9 and 6.
- Added in this order, the total is 11.
- Swap two terms: 6 + 14 − 9. Still 11.
- Group the last two: 14 + (−9 + 6). Still 11.
- Three ways, one total: 11.
The rule
Yes. Their totals match, as long as each term keeps its sign.
A rule that holds for all numbers is called a property.
Swap two terms. The total stays the same. This is the commutative property of addition.
To group terms is to choose which two to add first.
Group the terms a different way. The total stays the same. This is the associative property of addition.
A term moves with its sign. So 14 − 9 + 6 can be 6 + 14 − 9.
| The way | First sum | Total |
|---|---|---|
| 14 − 9 + 6 | 14 − 9 = 5 | 11 |
| 6 + 14 − 9 | 6 + 14 = 20 | 11 |
| 14 + (−9 + 6) | −9 + 6 = −3 | 11 |
Watch out!
Do not put a bracket after a − just to regroup. 20 − 8 − 5 is 7. But 20 − (8 − 5) is 17.