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Properties

Properties. Jan Sands 2007 kesam@cox.net. Commutative Property. Order doesn’t matter. An operation is commutative if you can change the order of the numbers involved without changing the result. Addition 3 + 4 = 4 + 3 7 = 7 a + b = b + a. Commutative Property.

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Properties

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  1. Properties Jan Sands 2007 kesam@cox.net

  2. Commutative Property • Order doesn’t matter. • An operation is commutative if you can change the order of the numbers involved without changing the result. • Addition • 3 + 4 = 4 + 3 • 7 = 7 • a + b = b + a

  3. Commutative Property • Order doesn’t matter. • An operation is commutative if you can change the order of the numbers involved without changing the result. • Multiplication • 5 ∙ 7 = 7 · 5 • 35 = 35 • a ∙ b = b ∙ a

  4. Commutative Property • Choose one and illustrate the commutative property of addition or multiplication. • Draw a picture. • Act it out. • Tell a story. • Make an advertisement. • Create a car tag. • Write your own definition.

  5. Practice – Addition Ex. 2 + 3 = 3 + 2 5 + 8 = 7 + 4 = 2 + 9 = 8 + 1 = 9 + 5 = 5 + 3 = 4 + 8 = 5 + 2 = 6 + 8 = 7 + 3 = Practice – Multiplication Ex. 2 ∙ 3 = 3 ∙ 2 4 ∙ 5 = 6 ∙ 3 = 2 ∙ 7 = 8 ∙ 4 = 9 ∙ 2 = 3 ∙ 8 = 5 ∙ 1 = 9 ∙ 3 = 4 ∙ 5 = 7 ∙ 6 = Commutative Property

  6. Associative Property • Grouping Property • An operation is associative if you can group numbers in any way without changing the answer. • Addition • 3 + (4 + 5) = (3 + 4) + 5 • 3 + 9 = 7 + 5 • 12 = 12 • a + (b + c) = (a + b) + c

  7. Associative Property • Grouping Property • An operation is associative if you can group numbers in any way without changing the answer. • Multiplication • 2 (5 ∙ 6) = (2 ∙ 5) 6 • 2 (30) = (10) 6 • 60 = 60 • a (b ∙ c) = (a ∙ b) c

  8. Associative Property • Choose one and illustrate the associative property of addition or multiplication. • Draw a picture. • Act it out. • Tell a story. • Make an advertisement. • Create a car tag. • Write your own definition.

  9. Practice – Addition Ex. 2 + (3 + 4) = (2 + 3) + 4 5 + (8 + 4) = 7 + (4 + 6) = 2 + (9 + 3) = 8 + (1 + 7) = 9 + (5 + 2) = (5 + 3) + 4 = (4 + 8) + 2 = (5 + 2) + 6 = (6 + 8) + 3 = (7 + 3) + 4 = Practice – Multiplication Ex. 3 (2 ∙ 9) = (3 ∙ 2) + (3 ∙ 9) 3 (4 ∙ 5) = 2 (6 ∙ 3) = 4 (2 ∙ 7) = 2 (8 ∙ 4) = 5 (9 ∙ 2) = (2 ∙ 8) 3 = (4 ∙ 2) 5 = (5 ∙ 3) 9 = (2 ∙ 5) 4 = (3 ∙ 6) 7 = Associative Property

  10. Identity Property - Addition • The Identity Property of Addition is Zero. • Any number added to zero will retain its identity. • Addition • 7 + 0 = 7 • 0 + 8 = 8 • a + 0 = a • 0 + a = a

  11. Identity Property - Multiplication • The Identity Property of Multiplication is One. • Any number multiplied by one will retain its identity. • Multiplication • 7 ∙ 1 = 7 • 1 ∙ 8 = 8 • a ∙ 1 = a • 1 ∙ a = a

  12. Identity Property • Choose two activities. • Use one to illustrate the identity property of addition and the other to show the identity property of multiplication. • Draw a picture. • Act it out. • Tell a story. • Make an advertisement. • Create a car tag. • Write your own definition.

  13. Practice – Addition Ex. 9 + 0 = 9 5 + 0 = 0 + 7 = 92 + 0 = 47 + 0 = 0 + 8 = 0 + 231 = 6,478 + 0 = 732 + 0 = 56 + 0 = 0 + 2,436,359 = Practice – Multiplication Ex. 1 ∙ 5 = 5 1 ∙ 8 = 5 ∙ 1 = 15 ∙ 1 = 1 ∙ 19 = 24 ∙ 1 = 654 ∙ 1 = 1 ∙ 562 = 1 ∙ 67 = 2,498 ∙ 1 = 1 ∙ 3,985,426 = Identity Property

  14. Distributive Property • The Distributive Property is the distribution of multiplication over another operation (addition or subtraction). • You can either add or subtract the numbers and then multiply or you can multiply the numbers individually and add the products. • a (b + c) = ab + ac

  15. Distributive Property • The Distributive Property over addition. • 3 ( 4 + 5) = (3 ∙ 4) + (3 ∙ 5) • 3 (9) = 12 + 15 • 27 = 27 • The Distributive Property over subtraction. • 2 (7 - 3) = (2 ∙7) – (2 ∙ 30) • 2 (4) = 14 - 6 • 8 = 8

  16. Distributive Property • Choose two activities. • Use one to illustrate the distributive property of multiplication over addition and the other to show the distributive property of multiplication over subtraction. • Draw a picture. • Act it out. • Tell a story. • Make an advertisement. • Create a car tag. • Write your own definition.

  17. Distributive Property • Practice – Distributive Property of Multiplication over Addition • Ex. 4 (3 + 2) = (4 ∙ 3) + (4 ∙ 2) = 20 • 2 (5 + 3) = • 3 (2 + 4)= • 7 (3 + 4) = • 6 (5 + 2) = • 4 ( 3 + 6) =

  18. Distributive Property • Practice – Distributive Property of Multiplication over Subtraction • Ex: 3 (7 – 5) = (3 ∙ 7) – (3 ∙ 5) = 6 • 2 (8 - 3) = • 3 (9 - 4)= • 7 (6 - 4) = • 6 (8 - 2) = • 4 ( 9 - 6) =

  19. Inverse Property The inverse of something is that thing turned inside out or upside down. The inverse of an operation undoes the operation: • subtraction undoes addition • division undoes multiplication

  20. Inverse Property • A number's additive inverse is another number that you can add to the original number to get the additive identity. • For every a, there is an additive inverse -a such that a + (-a) = 0. • For example, the additive inverse of 67 is -67, because 67 + -67 = 0, the additive identity.

  21. Inverse Property • Similarly, if the product of two numbers is the multiplicative identity, the numbers are multiplicative inverses. • For every a, there is a multiplicative inverse 1/a such that a (1/a) = 1. • Since 6 * 1/6 = 1, the multiplicative inverse of 6 is 1/6.

  22. Inverse Property Zero does not have a multiplicative inverse, since no matter what you multiply it by, the answer is always 0, not 1.

  23. Assessment • Name the property. • 5 + 3 = 3 + 5 • 2 (3 – 1) = (2 ∙ 3) – (2 ∙ 1) • 1 ∙ 46 = 46 • 5 + (4 + 6) = (5 + 4) + 6 • 8 ∙ 1 = 8 • 4 + 6 = 6 + 4 • 0 + 52 = 52 • 6 (4 + 3) = (6 ∙ 4) + (6 ∙ 3) • 15 + 0 = 15 • (2 + 6) + 4 = 2 + (6 + 4)

  24. Assessment • Write a definition for each property in your own words. • Give an example of each property using numbers and another example using letters. • Commutative Property of Addition • Commutative Property of Multiplication • Associative Property of Addition • Associative Property of Multiplication

  25. Assessment • Write a definition for each property in your own words. • Give an example of each property using numbers and another example using letters. • Identity Property of Addition • Identity Property of Multiplication • Distributive Property of Multiplication over Addition • Distributive Property of Multiplication over Subtraction

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