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Final Exam Review: Part II (Chapters 9+)

Final Exam Review: Part II (Chapters 9+). 5 th Grade Advanced Math. First topic!. Chapter 9 Integers. Definition. Positive integer – a number greater than zero. 0. 1. 2. 3. 4. 5. 6. Definition. Negative number – a number less than zero. -6. -5. -4. -3. -2. -1. 0. 1. 2.

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Final Exam Review: Part II (Chapters 9+)

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  1. Final Exam Review: Part II (Chapters 9+) 5th Grade Advanced Math

  2. First topic!

  3. Chapter 9Integers

  4. Definition • Positive integer – a number greater than zero. 0 1 2 3 4 5 6

  5. Definition • Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

  6. Place the following integers in order from least to greatest: 297 -56 39 -125 78 0

  7. Place the following integers in order from least to greatest: 297 -56 39 -125 78 0 -125 -56 0 39 78 297

  8. Definition • Absolute Value – The distance a number is from zero on the number line The absolute value of 9 or of –9 is 9.

  9. Hint • If you don’t see a negative or positive sign in front of a number, it is ALWAYS positive. 9 +

  10. Integer Addition Rules • Rule #1 – When adding two integers with the same sign, ADD the numbers and keep the sign. 9 + 5 = 14 -9 + -5 = -14

  11. Solve the Following Problems: • -3 + -5 = • 4 + 7 = • (+3) + (+4) = • -6 + -7 = • 5 + 9 = • -9 + -9 =

  12. Check Your Answers: -8 • -3 + -5 = • 4 + 7 = • (+3) + (+4) = • -6 + -7 = • 5 + 9 = • -9 + -9 = +11 +7 -13 14 -18

  13. Solve the following: 1. 8 + 13 = 2. –22 + -11 = 3. 55 + 17 = 4. –14 + -35 =

  14. Check Your Answers 1. 8 + 13 = +21 2. –22 + -11 = -33 3. 55 + 17 = +72 4. –14 + -35 = -49

  15. Integer Addition Rules • Rule #2 – When adding two integers with different signs, find the difference (SUBTRACT) and take the sign of the larger number. -9 + +5 = Larger absolute value: Answer = - 4 9 - 5 = 4

  16. Solve These Problems -2 5 – 3 = 2 • 3 + -5 = • -4 + 7 = • (+3) + (-4) = • -6 + 7 = • 5 + -9 = • -9 + 9 = 7 – 4 = 3 +3 4 – 3 = 1 -1 7 – 6 = 1 +1 9 – 5 = 4 -4 0 9 – 9 = 0

  17. Solve the following: 1. –12 + 22 = • –20 + 5 = • 14 + (-7) = 4. –70 + 15 =

  18. Check Your Answers 1. –12 + 22 = +10 2. –20 + 5 = -15 3. 14 + (-7) = +7 4. –70 + 15 =-55

  19. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive one. Change the sign and add. “Keep, change, change.” 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9

  20. Here are some more examples. 12 – (-8) 12 + (+8) 12 + 8 = 20 -3 – (-11) -3 + (+11) -3 + 11 = 8

  21. Solve the following: 1. 8 – (-12) = 2. 22 – (-30) = 3. – 17 – (-3) = 4. –52 – 5 =

  22. Check Your Answers 1. 8 – (-12) = 8 + 12 = +20 2. 22 – (-30) = 22 + 30 = +52 3. – 17 – (-3) = -17 + 3 = -14 4. –52 – 5 = -52 + (-5) = -57

  23. Integer Multiplication Rules • Rule #1 When multiplying two integers with the same sign, the product is always positive. • Rule #2 When multiplying two integers with different signs, the product is always negative. • Rule #3 If the number of negative signs is even, the product is always positive. • Rule #4 If the number of negative signs is odd, the product is always negative.

  24. Solve the following: 1. +8 x (-12) = 2. -20 x +30 = 3. – 17 x (-3) = 4. +50 x +5 =

  25. Check Your Answers: 1. +8 x (-12) = -96 2. -20 x +30 = -600 3. – 17 x (-3) = +51 4. +50 x +5 = +250

  26. Integer Division Rules • Rule #1 When dividing two integers with the same sign, the quotient is always positive. • Rule #2 When dividing two integers with different signs, the quotient is always negative.

  27. Solve the following: 1. (-36)÷ 4 = 2. 200 ÷ -5 = 3. – 18 ÷ (-9) = 4. +50 ÷ +5 =

  28. Check Your Work: 1. (-36)÷ 4 = -9 2. 200 ÷ -5 = -40 3. – 18 ÷ (-9) = +2 4. +50 ÷ +5 = +10

  29. Evaluate the following: 1. -45 + 10 3² - 2 2. 7 + -4(9 – 4) = 3. -50 ÷ 5² + (3 - 7) =

  30. Check Your Work: 1. -45 + 10-35=-5 3² - 2 7 2. 7 + -4(9 – 4) = -13 3. -50 ÷ 5² + (3 - 7) = -6

  31. Evaluate the following if n = -2 : 1. -5 (2n – 2)² 2. -48 n - 6

  32. Check Your Work: 1. -5 (2n – 2)² -180 2. -486 n - 6

  33. Next chapter…

  34. Chapter 11Expressions & Equations

  35. Write an algebraic expression for the following. Tell what the variable represents.Ben has 12 pencils. He lost 3 and bought some more.

  36. Write an algebraic expression for the following. Tell what the variable represents.Ben has 12 pencils. He lost 3 and bought some more.12 – 3 + p (p = pencils that Ben bought)

  37. Write each algebraic expression in words s - 47

  38. Write each algebraic expression in words s - 4747 less than some number

  39. Write each algebraic equation in words ½ n = 16

  40. Write each algebraic equation in words ½ n = 16one half of some number is 16

  41. Evaluate the following algebraic expressions for the given value of the variable:(n = 11) (n + 25)9

  42. Evaluate the following algebraic expressions for the given value of the variable:(n = 11) (n + 25) 9 4

  43. Simplify the following expressions (combine like terms). Then evaluate the expression for the given value of the variable: (if a = 3)3a + 10 - a

  44. Simplify the following expressions (combine like terms). Then evaluate the expression for the given value of the variable: (if a = 3)3a + 10 - a2a + 102(3) + 10 16

  45. Write an algebraic equation for the following and evaluate. Tell what the variable represents.Sam had fish in his fish tank. 6 of them died. There were 12 left swimming in the tank. How many fish did Sam have originally?

  46. Sam had fish in his fish tank. 6 of them died. There were 12 left swimming in the tank. How many fish did Sam have originally?f – 6 = 12f = 18f is the number of fish Sam had originally in his tank.

  47. Evaluate the following algebraic equations. Show your work.30 = 5y ¼n = 78 = x ÷ 9 3 = 18 + s t - 12 = 23 y ÷ 6 = 7

  48. Evaluate the following algebraic equations. Show your work.30 = 5y 6 ¼n = 7 288 = x ÷ 9 72 3 = 18 + s -15t - 12 = 23 35 y ÷ 6 = 7 42

  49. For word problem practice, review textbook pages 331, 340 and 341.

  50. Next topic…

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