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Commutative and Associative Properties

Commutative and Associative Properties. Properties of Addition and Multiplication. These properties are the “rules of the road”. They let us know if a particular maneuver is legal or not.

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Commutative and Associative Properties

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  1. Commutative and Associative Properties

  2. Properties of Addition and Multiplication These properties are the “rules of the road”. They let us know if a particular maneuver is legal or not. There are not very many of them, but you need to memorize them so that you will know what you can, and can’t, do when you add, subtract, multiply and divide.

  3. Commutative Property of Addition When you “commute” you go Home Work then Work Home The commutative property of addition follows the same pattern: a + b = b + a

  4. Commutative Property of Addition a + b = b + a Using numbers 3 + 5 = 5 + 3 8 = 8 Same answer! Order does not matter when we add. Addition is commutative

  5. Commutative Property of Subtraction? Seems obvious, but what about subtraction? Does order matter when you subtract? Different answers! YES order does matter when you subtract! Subtraction is not commutative

  6. Commutative Property of Multiplication How about multiplication? Does order matter when you multiply? Same answer! NO order does NOT matter when you multiply! Multiplication is commutative

  7. Commutative Property of Division? What about division? Does order matter when you divide? Different answers! YES order does matter when you divide! Division is not commutative

  8. Associative Property of Addition Frequently the group of people who live in a neighborhood form a neighborhood “association”. In math, a grouping symbol is the parentheses ( ). The associative property of addition tells us that we can group our numbers any way we want to and still get the same answer. ( a + b ) + c = a + ( b + c )

  9. Associative Property of Addition ( a + b ) + c = a + ( b + c ) Using numbers: ( 2 + 3 ) + 7 = 2 + ( 3 + 7 ) 5 + 7 = 2 + 10 12 = 12 Same answer! Addition is associative

  10. Associative Property of Multiplication ( a . b ) . c = a . ( b . c ) Using numbers: Same answer! Addition is associative

  11. Associative Property • Just like the commutative property, • the associative property does work with • addition • multiplication • the associative propertydoes not work with • Subtraction • division.

  12. Associative vs. Commutative Some people have difficulty keeping these two properties straight. If the numbers move (change order) 2 + 3 = 3 + 2 it’s the commutative property. If the numbers stand still and the parentheses move ( 2 + 3 ) + 7 = 2 + ( 3 + 7 ) it’s the associative property.

  13. Trick question Which property is illustrated by the following: 7( 2 + 3 ) = 7( 3 + 2) As soon as some people see the parentheses, they say “associative” - but the parentheses didn’t move. What changed was the order of the 2 and the 3. It is the commutative property of addition.

  14. Commutative and Associative Properties • The commutative properties of addition and multiplication involve the order in which the numbers are written – the numbers move. • The associative properties of addition and multiplication involve grouping – the parentheses move. • These properties do not work with subtraction or division.

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