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What is the difference between a commutitative property and a associative propertyIn math?

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March 05, 2008 4:51AM

The "Commutative Laws" just mean that you can swap numbers over and still get the same answer when you add, or when you multiply. a + b = b + a

a × b = b × a You can swap when you add: 3 + 6 = 6 + 3

You can swap when you multiply: 2 × 4 = 4 × 2

The "Associative Laws" mean that it doesn't matter how you group the numbers (ie which you calculate first) when you add, or when you multiply. (a + b) + c = a + (b + c)

(a × b) × c = a × (b × c) This: (2 + 4) + 5 = 6 + 5 = 11 Has the same answer as this: 2 + (4 + 5) = 2 + 9 = 11

This: (3 × 4) × 5 = 12 × 5 = 60 Has the same answer as this: 3 × (4 × 5) = 3 × 20 = 60 Sometimes it is easier to add or multiply in a different order: {| ! What is 19 + 36 + 4? | 19 + 36 + 4 = 19 + (36 + 4) = 19 + 40 = 59 |} Or even rearrange a little: {| ! What is 2 × 16 × 5? | 2 × 16 × 5 = (2 × 5) × 16 = 10 × 16 = 160 |}