Activities
Commutative, Associative & Distributive
Three big laws of arithmetic — try to break them with examples.
Three laws govern arithmetic. Boring names, beautiful consequences — they're why algebra works.
The three laws
- Commutative: order doesn't matter. 3 + 5 = 5 + 3. 2 × 7 = 7 × 2.
- Associative: grouping doesn't matter. (2 + 3) + 4 = 2 + (3 + 4).
- Distributive: 3 × (4 + 5) = 3×4 + 3×5. The 3 spreads across.
Try it
Quick: 7 × 23
Distribute: 7 × 23 = 7 × 20 + 7 × 3 = 140 + 21 = 161. Mental math, no calculator.
Subtraction and division are NOT commutative. 5 − 3 ≠ 3 − 5. Order matters there.