 # © 2007 M. Tallman. Commutative Property © 2007 M. Tallman The order of the factors does not change the product. 15 53 × = factors product 5 × 3 = 3 ×

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Commutative Property

© 2007 M. Tallman The order of the factors does not change the product. 15 53 × = factors product 5 × 3 = 3 × 5

© 2007 M. Tallman 15 =3×515 =5×3

 3 × 5 = j × 3  12 × p = 7 × 12  f f × 6 = 6 × 9  9 × 4 = 4 × s j = 5 p = 7 f = 9 s = 9 Use the Commutative Property to find the value of the variable.

© 2007 M. Tallman Commutative Property Associative Property

© 2007 M. Tallman The way the factors are grouped does not change the product. In math, parentheses are used to group numbers. They tell us which part of the problem to solve first. = 24 2 4 × × 3 ( ) (3 × 2) × 4 = 3 × (2 × 4)

© 2007 M. Tallman = 24(3×2)×4= 24(3×2)×4

 (8 × 5) × 12 = w × (5 × 12) 8 × e) × 2 = 8 × (9 × 2)  y y × (5 × 8) = (4 × 5) × 8  5 × (4 × 1) = (5 × 4) × h w = 8 e = 9 y = 4 h = 1 Use the Associative Property to find the value of the variable.

© 2007 M. Tallman Commutative Property Associative Property Identity Property

© 2007 M. Tallman The product of any number and 1 equals the number. 1 × 13 = 13

1 13 ×= 13

Use the Identity Property to find the value of the variable.  39 × 1 = u  2,198 × b = 2,198  z z × 68 = 68 9901 = 1 × s u = 39 b = 1 z = 1 s = 901

© 2007 M. Tallman Commutative Property Associative Property Identity Property Zero Property

© 2007 M. Tallman The product of any number and 0 equals zero. 4 × 0 = 0

4 0 ×= 0

Use the Zero Property to find the value of the variable.  82 × 0 = u  218 × b = 0  z z × 629 = 0 99,788 = 0 × s u = 0 b = 0 z = 0 s = 0

8 × 3 = 3 × 8

© 2007 M. Tallman 4 × (7 × 8) = (4 × 7) × 8

© 2007 M. Tallman 9 × 1 = 9

© 2007 M. Tallman 22 × 0 = 0

© 2007 M. Tallman (5 × 4) × 3 = 5 × (4 × 3)

4 × 0 = 0

© 2007 M. Tallman 34 × 1 = 34

© 2007 M. Tallman 53 × 5 = 5 × 53

© 2007 M. Tallman 11 × 9 = 9 × 11

© 2007 M. Tallman 6 × (9 × 8) = (6 × 9) × 8

© 2007 M. Tallman 0 × 345 = 0

© 2007 M. Tallman 1 × 8 = 8

© 2007 M. Tallman Multiply. Then write a different multiplication sentence using the Commutative Property. 1. 3 × 3 2. 5 × 3 3. 5 × 9 4. 6 × 8 5. 7 × 9 6. 4 × 6 7. 3 × 8 8. 7 × 4 9. 2 × 11 10. 12 × 3 = 9 = 15 = 45 = 48 = 63 = 24 = 24 = 28 = 22 = 36 3 × 3 = 9 3 × 5 = 15 9 × 5 = 45 8 × 6 = 48 9 × 7 = 63 6 × 4 = 24 8 × 3 = 24 4 × 7 = 28 11 × 2 = 22 3 × 12 = 36

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