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Warm Up

Warm Up. What number should come next? 1, 4, 7, 10, ____ What is the 10 th term of the sequence? 2, 4, 6 …. Translate each phrase into an algebraic expression. a. a number divided by 7 b. the sum of w and 14 Evaluate the expression if a = 5, b= 8, c= 0 5a + bc. Number Properties.

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Warm Up

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  1. Warm Up • What number should come next? • 1, 4, 7, 10, ____ • What is the 10th term of the sequence? • 2, 4, 6 …. • Translate each phrase into an algebraic expression. • a. a number divided by 7 • b. the sum of w and 14 • Evaluate the expression if a = 5, b= 8, c= 0 • 5a + bc

  2. Number Properties • Today we will be studying various number properties. It is important that you understand how to use them. Think about each property that we discuss and why the rule is true.

  3. Commutative Property Example: 2 + 3 = 3 + 2 Rule: For any number a and b, a + b = b + a Nunc rule- “SWITCH” Only works for add and multiply

  4. Commutative Property Example: 5 x 6 = 6 x 5 Rule: For any number a and b, ab = ba

  5. Associative Property Example: (3 + 4) + 5 = 3 + (4 + 5) Rule: For any number a, b,and c, (a + b) + c = a + (b + c) Nunc rule- move the parenthesis

  6. Associative Property Example: (5 x 6) x 4 = 5 x (6 x 4) Rule: For any number a, b,and c, (ab)c = a(bc)

  7. Distributive Property Example: 5 (3 + 4) = 5(3) + 5(4) Rule: For any number a, b,and c, a(b+c) = ab + ac a(b-c) = ab-ac Nunc rule- party property

  8. 4(5) 4(6) 4 (5+6) = + Did we touch the operation?? 8(5+3) = 8(5) + 8(3)

  9. Additive Inverse Example: 2 + (-2) = 0 Rule: The sum of an integer and its additive inverse is zero.

  10. Multiplicative Inverse Example: 2 x ½ = 1 Rule: A number times its multiplicative inverse is equal to 1.

  11. Additive Identity Example: 10 + 0 = 10 Rule: The sum of an integer and zero is always the integer.

  12. Multiplicative Identity Example: 33 x 1 = 33 Rule: The product of an integer and one is always the integer.

  13. 5 + (-5) = 0 Additive Inverse

  14. 3 x 9 = 9 x 3 Commutative Property of Multiplication

  15. (5+14)+3=5+(14+3) Associative Property of Addition

  16. 7(5+4)=7(5)+7(4) Distributive Property

  17. 41 x 1 = 41 Multiplicative Identity

  18. 9/1 x 1/9 = 1 Multiplicative Inverse

  19. 13 + 0 = 13 Additive Identity

  20. 3 x 5 = 5 x 3 Commutative Property of Multiplication

  21. 10 + (-10) = 0 Additive Inverse

  22. 3 + 7 = 7 + 3 Commutative Property of Addition

  23. 5x(5x8)=(5x5)x8 Associative Property of Multiplication

  24. 2/4 x 4/2 = 1 Multiplicative Inverse

  25. 5 x 10 = 10 x 5 Commutative Property of Multiplication

  26. 999,999 x 1/999,999=1 Multiplicative Inverse

  27. 3 + 5 = 5 + 3 Commutative Property of Addition

  28. 55 x 1 = 55 Multiplicative Identity

  29. (8+7)+2=8+(7+2) Associative Property of Addition

  30. 6(9+8)=6(9)+6(8) Distributive Property

  31. 50,000+0= 50,000 Additive Identity

  32. 20x(31x3)=(20x31)x3 Associative Property of Multiplication

  33. QUIZ commutative • What property is this • 25+ 33= 33 +25 2.What property is move the parenthesis? 3.Perform the distributive property 7 (x + y) 4. If the temperature is 5 degrees at night and it drops to – 9, how many degrees did it drop? 5. A running back carries 4 times and they are… lose 3 yards, gain 5 yards, gain 4 yards, lose 5 yards and gain 12 yards. What is his total? associative 7x + 7y 14 13

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