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Variables & Properties

Variables & Properties. Identities, Inverses, Commutative, Associative, Distributive. I will be able to… ~ use the properties that we discuss to simplify and solve numerical and algebraic expressions . I will need to learn/recall… ~ properties & order of operations

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Variables & Properties

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  1. Variables & Properties Identities, Inverses, Commutative, Associative, Distributive

  2. I will be able to… ~ use the properties that we discuss to simplify and solve numerical and algebraic expressions. I will need to learn/recall… ~ properties & order of operations I will demonstrate my knowledge by… ~ showing correct work and answers on my classwork, clicker questions, and homework. Shared Learning Target

  3. What is a math property? • A shortcut • They teach about the character of numbers • They may be used to rearrange an expression or an equation to make the problem a little easier to work with • There are limits to the properties… • Some of them can only be used in certain cases.

  4. Additive identity • What number can you add to anything and still get the same number as the answer? Zero (0) • So the ADDITIVE IDENTITY PROPERTY tells us… n + 0 = n

  5. multiplicative identity • What number can you multiply by anything and still get the same number as the answer? ONE (1) • So the multiplicative IDENTITY PROPERTY tells us… n • 1 = n

  6. Additive inverse • What number can you add to a number and get zero for the answer? The number’s opposite! • So the ADDITIVE Inverse PROPERTY tells us… n + -n = 0 • The additive inverse “undoes” what you have.

  7. multiplicative inverse • What number can you multiply by and get 1 as the product? The number’s reciprocal! • So the mulitilicative Inverse PROPERTY tells us… n • = 1 • The multiplicative inverse takes our problem and gets us to one.

  8. Which property is this an example?15 + (-15) = ? • Additive Identity • Multiplicative Identity • Additive Inverse • Multiplicative Inverse 12 of 26

  9. Which property is this an example?257 + 0= ? • Additive Identity • Multiplicative Identity • Additive Inverse • Multiplicative Inverse 16 of 26

  10. Which property is this an example? • Additive Identity • Multiplicative Identity • Additive Inverse • Multiplicative Inverse 21 of 26

  11. Which property is this an example? • Additive Identity • Multiplicative Identity • Additive Inverse • Multiplicative Inverse 19 of 26

  12. Commutative property Only for … ADDITION & MULTIPLICATION n + s = s + nns = sn • What does this tell us? • It’s okay to switch the order of the numbers when adding or multiplying… • no combining the operations!

  13. Is this the commutative property?56 + 48 + 95 + 12 = 12 + 48 + 56 + 95 • Yes • No 0 of 30

  14. Is this the commutative property?A • b • c = b • c • a • Yes • No 0 of 30

  15. Is this the commutative property?15 + 24 • 2 = 2 + 15 • 24 • Yes • No 0 of 30

  16. associative property Only for … ADDITION & MULTIPLICATION a + (b + c) = (a + b) +ca(bc) = (ab)c • What does this tell us? • It’s okay to change how the numbers are grouped in the parenthesis… • no combining the operations!

  17. Is this the associative property?500 + (12 + 480) = (500 + 12 + 480) • Yes • No 20 0 of 20 Countdown

  18. Is this the associative property?56 + (48 + 95) + 12 = (56 + 48) + (95 + 12) • Yes • No 20 0 of 20 Countdown

  19. Is this the associative property?(ab)c= a(bc) • Yes • No 20 0 of 20 Countdown

  20. Is this the associative property?15 + 24 • 2 = (15 + 24) • 2 • Yes • No 20 0 of 20 Countdown

  21. distributive property May use… ADDITION & Subtraction a(b + c) = ab + aca(b - c) = ab- ac • What does this tell us? • We can take the number outside the parenthesis and multiply it by each term (number or variable) inside the parenthesis.

  22. distributive property Example… ADDITION 4(25 + 10) = 4(25) + 4(10) 4(35) = 100 + 40 140 = 140

  23. distributive property Example… Subtraction 5(52 - 22) = 5(52) – 5(22) 5(30) = 260 + 110 150 = 150

  24. distributive property Example… Algebraic ADDITION & Subtraction 5(b + 2) = 5b + 5(2)8(x - 6) = 8x – 8(6) 5(b + 2) = 5b + 10 8(x - 6) = 8x – 48 • How are these expressions equal? • We don’t know what “b” or “x” are… • That’s okay…it’s supposed to be like that!

  25. Summary • Additive Identity • Multiplicative Identity • Additive Inverse • Multiplicative Inverse • Commutative Property • Associative Property • Distributive Property • n + 0 = n • n • 1 = n • n + -n = 0 • n • = 1 • n + s = s + n ns = sn • a+(b + c) = (a + b)+c a(bc) = (ab)c • a(b + c) = ab + ac a(b - c) = ab - ac

  26. I will be able to… ~ use the properties that we discuss to simplify and solve numerical and algebraic expressions. I will need to learn/recall… ~ properties & order of operations I will demonstrate my knowledge by… ~ showing correct work and answers on my classwork, clicker questions, and homework. Shared Learning Target

  27. Do you feel that you have met the target of: use the properties that we discuss to simplify and solve numerical and algebraic expressions • Yes, I can see where the properties can/should be used. • I understand what they say but need to see more examples. • I remember their names.

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