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Boardwork - Solve

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Boardwork - Solve

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  1. Boardwork - Solve • 4 + -3 6. -3 x -8 • 9 + -18 7. -9 x 6 • -14 + -3 8. -3 x 14 • -19 – (-9) 9. -25 ÷ 5 • 10 – (-2) 10. -36 ÷ 3

  2. Announcements! Tutoring EVERY morning starting at 7:50!! Binder check on Monday. Vocab def/quiz on Thursday Unit 1 test on Friday Don’t pick the tape! Homework excuse form!

  3. Homework: Worksheet 1-1 • 1-17

  4. Continued: Sample answers 18. 23 times a number 19. Seven to the third power 20. 5 times a number squared plus 2 21. Four times a number cubed minus 10 22. A number cubed times another number to the fourth power 23. B squared minus three times c cubed 24. K to the fifth power, divided by 6 25. The product of 4 times n squared all divided by 7

  5. Homework continued 26. 2.50e + .50f (e = excellent, f = fair) 27. 2πrh

  6. LET’S REVIEW!!!!!! Combining like terms

  7. A term is a 1) number, 2) variable, or 3) Combination of numbers and variables Example 5 m 2x2

  8. 3) The coefficient is the Number in front of the variables. Examples 1) 4a 4 2) y2 1

  9. Like Termsare terms with the same variable AND exponent. You can COMBINE like terms!

  10. Are these like terms? 1) 13k, 22k Yes, the variables are the same. 2) 5ab, 4ba Yes, the order of the variables doesn’t matter. 3) x3y, xy3 No, the exponents are on different variables.

  11. Answer Now Which of the following is the simplified form of -4x + 7x ? • -4 • 3x • -3x • 4

  12. are like terms and 5a and a are like terms The above expression simplifies to:

  13. Simplify1) 5a + 7a 12a 2) 4x2y + x2y 5x2y 3) 3m2n + 10mn2 + 7m2n - 4mn2 10m2n + 6mn2

  14. 5) 4) 4d + 6a2 - d + 12a2 18a2 + 3d y

  15. Answer Now Which of the following is the simplified form of 5x - 4 - 7x + 14 ? • -12x + 10 • -2x + 10 • 2x - 18 • 12x – 18

  16. Answer Now If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle? • 4x - 2 • 4x + 2 • 5x - 2 • 5x - 7

  17. Answer Now Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ? • -36 • 3a - 36 • 8a - 36 • 8a + 36

  18. ObjectiveThe student will be able to: recognize and use the properties of identity and equality. Designed by Skip Tyler, Varina High School and Nicole Kessinger, Deep Run High School

  19. Identity Properties 1) Additive Identity What do you add to get the same? a + 0 = a 2) Multiplicative Identity What do you mult. to get the same? a • 1 = a

  20. Inverse Properties 1) Additive Inverse (Opposite) a + (-a) = 0 2) Multiplicative Inverse (Reciprocal)

  21. Multiplicative Property of Zero a • 0 = 0 (If you multiply by 0, the answer is 0.)

  22. Properties of Equality 1) Reflexive: a = a 5 = 5 2) Symmetric: If a = b then b = a. If 4 = 2 + 2 then 2 + 2 = 4. 3) Transitive:If a = b and b = c, then a = c. If 4 = 2 + 2 and 2 + 2 = 3 + 1 then 4 = 3 + 1. 4) Substitution: If a = b, then a can be replaced by b. (5 + 2)x = 7x

  23. Name the Property 1. 0  12 = 0 Multiplicative Prop. Of Zero 2. (10 + 2)  3 = 12  3 Substitution 3. 2 + 3 = 5 then 5 = 2 + 3 Symmetric

  24. 4. If 5  2 = 10 & 10 = 5 + 5 then 5  2 = 5 + 5 Transitive 5. 6 + (-6) = 0 Additive Inverse

  25. 9. 6. 1  m = m Multiplicative Identity 7. k + 7 = k + 7 Reflexive 8. x + 0 = x Additive Identity Multiplicative Inverse

  26. Answer Now Name the property.0 + 4 = 4 • Additive Identity • Additive Inverse • Additive Property of Zero • Substitution

  27. Answer Now Name the property.8 – (6 + 2) = 8 - 8 • Additive Identity • Additive Inverse • Associative • Substitution

  28. Answer Now Name the property.2 + (x – 3)1 = 2 + (x – 3) • Reflexive • Multiplicative Inverse • Multiplicative Identity • Symmetric

  29. ObjectiveThe student will be able to: use the distributive property to simplify expressions. Designed by Skip Tyler, Varina High School and Nicole Kessinger, Deep Run High School

  30. The Distributive Property a(b + c) = ab + ac and (b + c) a = ba + ca a(b - c) = ab - ac and (b - c) a = ba - ca Example #1 5(x + 7) 5 • x + 5 • 7 5x + 35

  31. Answer Now Which statement demonstrates the distributive property incorrectly? • 3(x + y + z) = 3x + 3y + 3z • (a + b) c = ac + bc • 5(2 + 3x) = 10 + 3x • 6(3k - 4) = 18k - 24

  32. ObjectiveThe student will be able to: recognize and use the commutative and associative properties and the properties of equality. Designed by Skip Tyler, Varina High School

  33. Commutative Property Commutative means that the order does not make any difference. a + b = b + a a • b = b • a Examples 4 + 5 = 5 + 4 2 • 3 = 3 • 2

  34. Commutative Property The commutative property DOES NOT WORK for SUBTRACTION or DIVISION!!!!!!!

  35. Associative Property Associative means that the grouping does not make any difference. (a + b) + c = a + (b + c) (ab) c = a (bc) Examples (1 + 2) + 3 = 1 + (2 + 3) (2 • 3) • 4 = 2 • (3 • 4)

  36. Associative Property The associative property DOES NOT WORK for SUBTRACTION OR DIVISION!!!!!

  37. Name the property1) 5a + (6 + 2a) = 5a + (2a + 6) commutative (switching order) 2) 5a + (2a + 6) = (5a + 2a) + 6 associative (switching groups) 3) 2(3 + a) = 6 + 2a distributive

  38. Which property would justify rewriting the following expression without parentheses? 3(2x + 5y) • Associative property of multiplication • Distributive property • Addition property of zero • Commutative property of multiplication

  39. Which property would justify the following statement? 8x + 4 = 4 + 8x • Associative property of addition • Distributive property • Addition property of zero • Commutative property of addition

  40. Which property would justify the following statement?8 + (2 + 6) = (8 + 2) + 6 • Associative property of addition • Distributive property • Addition property of zero • Commutative property of addition

  41. Homework: Due Tomorrow Worksheet 1-2 FRONT AND BACK!!!!!

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