Math 1 · Lesson 2 · part 4 of 5
The scoreboard: which operations pass?
Test each property with numbers.
The scoreboard: which operations pass?
Test each property with numbers. Trading places: 17 + 48 and 48 + 17 both make 65, but 10 - 4 = 6 while 4 - 10 = -6. Changing partners: (18 + 7) + 3 and 18 + (7 + 3) both make 28, but (24 / 6) / 2 = 2 while 24 / (6 / 2) = 8.
| Does it... | Add | Subtract | Multiply | Divide |
|---|---|---|---|---|
| commute? (trade places) | yes | no | yes | no |
| associate? (change partners) | yes | no | yes | no |
Multiplication also distributes over addition: 7 x (10 + 3) = 7 x 10 + 7 x 3 = 91. Watch the direction: 7 + (10 x 3) is not (7 + 10) x (7 + 3).