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# Add and subtract pos and neg numbers 4 parts

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• 1. INTERESTINGINTERESTING INTEGERS!INTEGERS! 5 -7 -3 -8 4
• 2. What You Will Learn:What You Will Learn:  Vocabulary related to integers  Rules for adding and subtracting integers  A method for proving that a rule is true Are you ready??Are you ready??
• 3. Part I: Introduction to IntegersPart I: Introduction to Integers •VocabularyVocabulary • positive numberpositive number • negative numbernegative number •Horizontal & vertical number linesHorizontal & vertical number lines •Comparing IntegersComparing Integers •Ordering IntegersOrdering Integers •Vocabulary - continuedVocabulary - continued • opposite numberopposite number • integerinteger •Real World Applications & ExamplesReal World Applications & Examples • temperaturetemperature • sea levelsea level • moneymoney
• 4.  Positive number – a number greater than (>) zero 0 1 2 3 4 5 6 Vocabulary:
• 5. Hint:Hint:  If you don’t see a negative or positive sign in front of a number, the number is positive. 9 is the same as +9
• 6.  Negative number – a number less than (<) zero 0 1 2 3 4 5 6-1-1-2-2-3-3-4-4-5-5-6-6 Vocabulary:
• 7. Integer Number LineInteger Number Line Horizontal Numbers above or right of 0 are positive Numbers below or left of 0 are negative ZERO
• 8. Integer Number LineInteger Number Line Vertical Numbers above 0 are positive ZER O Numbers below 0 are negative
• 9. Use the number line to compare the following integers with >, <, or =. -4 -2 1 -3 -5 0 Hint: On a number line, the number to the left is always less than the number to the right. Comparing IntegersComparing Integers < < >
• 10. Use the number line to compare the following integers with >, <, or =. Comparing IntegersComparing Integers Hint: On a number line, the number on the top is always greater than the number on the bottom. -3 -5 -5 0 0 -1> > >
• 11. Ordering IntegersOrdering Integers Use the number line to put the following integers in order from least to greatest. -4, 3, 0, and -5 -5, -4, 0, 3
• 12.  Opposite Numbers – numbers that are the same distance from zero in the opposite direction 0 1 2 3 4 5 6-1-2-3-4-5-6 Vocabulary:
• 13. What is the opposite of each integer? +7 -7 +5 -1 +8 +1 5 -8
• 14. Vocabulary: Integers – all the whole numbers and all of their opposites on the number line including zero 0 1 2 3 4 5 6-1-2-3-4-5-6 integers
• 15. Now, you’re probably saying, “That’s interesting and everything, BUT where are negative numbers in the real world?? ??
• 16. Negative Numbers Are Used to Measure Temperature
• 17. Negative Numbers Are Used to Measure Under Sea Level 0 10 20 30 -10 -20 -30 -40 -50
• 18. Positive and negative numbers are used when keeping track of money. + Positive + \$\$ you earn - Negative - \$\$ you spend
• 19. Positive Numbers are Used to Show Earnings or Assets When you get paid (or win the lottery), you add that \$\$ to your account.
• 20. Negative Numbers are Used to Show What You Owe or Debt If your mom loaned you \$10 for pizza, Mom, I. O. U. \$10 The \$10 you owe her is described by the integer -10.
• 21. Write an integer to describe the real world situation:  Gain 3 pounds:  Withdraw \$15:  5 feet below sea level:  Move ahead 4 spaces: 3 or +3 -15 -5 4 or +4
• 22. End - Part I: Introduction to IntegersEnd - Part I: Introduction to Integers •VocabularyVocabulary • positive numberpositive number • negative numbernegative number •Horizontal & vertical number linesHorizontal & vertical number lines •Comparing IntegersComparing Integers •Ordering IntegersOrdering Integers •Vocabulary - continuedVocabulary - continued • opposite numberopposite number • integerinteger •Real World Applications & ExamplesReal World Applications & Examples • temperaturetemperature • sea levelsea level • moneymoney
• 24. ** Key Concepts **** Key Concepts ** The sum of two positive numbers is always positive  (+) + (+) = (+) ex. 5 + 1 = 6 The sum of two negative numbers is always negative  (-) + (-) = (-) ex. -5 + -1 = -6
• 25. ** Key Concepts ** (+) + (+) = (+) (-) + (-) = (-) (+) + (-) = sometimes (+) = sometimes (-) = sometimes 0 AND
• 26. Integer Addition RulesInteger Addition Rules  Rule #1 – If the signs are the same, add the numbers and then put the sign of the addends in front of your answer. b) -9 + -5 = -14 a) -9 + -5 =
• 27. SolveSolve the Problemsthe Problems  -3 + -5 =  4 + 6 =  +3 + (+4) =  -6 + -7 =  5 + 9 =  -9 + -9 = -8 -18 14 -13 7 10
• 28.  Rule #2 – If the signs of the addends are DIFFERENT, start at the location of the first integer on the number line and:  a) move RIGHT to add a positive integer Integer Addition RulesInteger Addition Rules -5 + 3 = -2 1 2 3
• 29. ex. (-6) + 5 = -1Start here at -6 0 1 2 3 4 5 6-1-2-3-4-5-6 then count forward or right 5 spaces + Adding Integers Using a Number LineAdding Integers Using a Number Line * adding a* adding a positive integer *integer *
• 30. Solve the ProblemsSolve the Problems • 8 + 6 = • (-9) + 5 = • (–11) + 11 = • (–8) + 16 = 14 0 8 -4
• 31.  Rule #2 – If the signs of the addends are DIFFERENT, start at the location of the first integer on the number line and:  b) move LEFT to add a negative integer Integer Addition RulesInteger Addition Rules 4 + -3 = 1 123
• 32. 0 1 2 3 4 5 6-1-2-3-4-5-6 - ex. +3 + (-5) = -2 Start here at +3 Then count back or left 5 spaces Adding Integers Using a Number LineAdding Integers Using a Number Line * adding a* adding a negative integer *integer *
• 33. Solve the ProblemsSolve the Problems • 2 + (-12) = • –8 + (-5) = • 14 + (-7) = • 15 + (-15) = -10 7 -13 0
• 34. Part III
• 35. Part III: Subtracting IntegersPart III: Subtracting Integers ** Key Concept **** Key Concept ** To subtract an integer, add its opposite ex. 5 – 2 = 5 + (-2) = 3 KEEP CHANGE CHANGE
• 36. ex. -1 – (-2) is the same as -1 + (+2) and -1 + 2 = 1 Subtracting a negative number is the same as adding a positive. Change the signs and add. Integer Subtraction Rule KEEP CHANGE CHANGE
• 37. -3 – 4 is the same as -3 + (-4) and -3 + (-4) = -7 More Examples 2 – (-7) is the same as 2 + (+7) and 2 + 7 = 9 KEEP the sign of the 1st integer the same CHANGE the operation ( + to – or – to +) CHANGE the sign of the 2nd integer
• 38. More Examples 12 – (-8) is the same as 12 + (+8) and 12 + 8 = 20 -3 – (-11) is the same as -3 + (+11) and -3 + 11 = 8 KEEP the sign of the 1st integer the same CHANGE the operation ( + to – or – to +) CHANGE the sign of the 2nd integer
• 39. Problems to Solve 8 – (-12) is the same as 8 + (+12) and 8 + 12 = 20 22 – (-30) is the same as 22 + (+30) and 22 + 30 = 52 KEEP the sign of the 1st integer the same CHANGE the operation ( + to – or – to +) CHANGE the sign of the 2nd integer
• 40. Problems to Solve -17– (-3) is the same as -17 + (+3) and -17 + 3 = -14 -8 – 3 is the same as -8 + (-3) and -8 + -3 = -11 KEEP the sign of the 1st integer the same CHANGE the operation ( + to – or – to +) CHANGE the sign of the 2nd integer
• 41. Part IV
• 42. How do we know that “Subtracting a negative number is the same as adding a positive” is true? We can use the same method we use to check our answers when we do regular subtraction.
• 43. When you subtract a – b it equals c a – b = c ex. 5 – 2 = 3 To check if your answer is correct, add b and c a = b + c ex. 5 = 2 + 3
• 44. If a – b = c, and…. 2 – (-5) is the same as 2 + (+5), which equals 7, Then let’s check with the negative numbers to see if it’s true…
• 45. Here are some examples: a – b = c a = b + c 9 – 5 = 4 9 = 5 + 4 a – b = c a = b + c 20 – 3 = 17 20 = 3 + 17
• 46. If the method for checking subtraction works, it should also work for subtracting negative numbers.
• 47. a – b = c a = b + c 2 – (-5) = 7 2 = -5 + 7 It works! a – b = c a = b + c -11 – (-3) = -8 -11 = -3 + -8 YES!
• 48. Check Your Answers 1. Solve: 3 – 10 = 7 Check: 3 = 10 + (-7) 2. Solve: 17 – ( 12) = 29 Continued on next slide Check: 17 = -12 + 29
• 49. Check Your Answers 1. Solve: 20 – ( 5) = 25 Check: 20 = -5 + 25 1. Solve: -7 – ( 2) = -5 Check: -7 = -2 + -5
• 50. Review Integers Part V
• 51. You have learned many things about adding and subtracting positive and negative numbers. Let’s review!
• 52. Definition:  Absolute Value – the size of a number with or without the negative sign. The absolute value of 9 or of –9 is 9.
• 53. Integer Addition Rules  Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14 -9 + -5 = -14
• 54. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. -9 + +5 = 9 - 5 = 4 Larger abs. value Answer = - 4
• 55. 0 1 2 3 4 5 6-1-2-3-4-5-6 • When the number is positive, count to the right • When the number is negative, count to the left +- Adding Integers Using a Number LineAdding Integers Using a Number Line
• 56. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9!
• 57. How do we know that “Subtracting a negative number is the same as adding a positive” is true? We can use the same method we use to check our answers when we subtract.
• 58. a – b = c a = b + c 2 – (-5) = 7 2 = -5 + 7 It works! a – b = c a = b + c -11 – (-3) = -8 -11 = -3 + -8 YES!
• 59. Discuss with a partner ways that you know that that is problem is solved correctly. 6 – (-9) = 15
• 60. Aren’t integers interesting?
• 61. Independent Practice
• 62. Solve The ProblemsSolve The Problems  3 + -5 =  -4 + 7 =  (+3) + (-4) =  -6 + 7 =  5 + -9 =  -9 + 9 = -25 – 3 = 2 0 -4 1 -1 3 9 – 9 = 0 9 – 5 = 4 7 – 6 = 1 4 – 3 = 1 7 – 4 = 3