INTEGERS
What is an Integer?
<ul><li>An integer is a positive or negative whole number, including 0. </li></ul><ul><li>… -3, -2, -1, 0, 1, 2, 3… </li><...
There are  “4” Integer Operations
Addition
Subtraction
Multiplication
Division
4 Integer Operations <ul><li>Addition  + </li></ul><ul><li>Subtraction - </li></ul><ul><li>Multiplication x </li></ul><ul>...
Rule #1 for  Adding Integers (+) <ul><li>The sum of two positive integers is always positive. </li></ul><ul><li>5 + 1 = 6 ...
Rule #2 for  Adding Integers (+) <ul><li>The sum of two negative integers is always negative. </li></ul><ul><li>-5 + (-1) ...
Rule #3 for  Adding Integers (+) <ul><li>The sum of a positive and a negative integer could be positive, negative, or zero...
Rule #3 for  Adding Integers Continued <ul><li>When you add a positive and negative integer, you are really subtracting. T...
Let’s Practice “Addition” <ul><li>1)   5 + 6 = </li></ul><ul><li>-3 + (-2) = </li></ul><ul><li>-6 + 5 =  </li></ul><ul><li...
<ul><li>Let’s Check   </li></ul><ul><li>1)   5 + 6 = 11 </li></ul><ul><li>-3 + (-2) = -5 </li></ul><ul><li>-6 + 5 =  -1 </...
Rules for  Subtracting Integers (-) <ul><li>To subtract an integer, add its opposite. </li></ul><ul><li>You will need to c...
How do you change a subtraction problem into an addition problem?
<ul><li>There are three steps : </li></ul><ul><li>1.  Keep the first integer the same.  (Same) </li></ul><ul><li>2.  Chang...
Same
Change
Change
<ul><li>Examples: </li></ul><ul><li>5 – (-2) = 5 + 2 = 7 </li></ul><ul><li>-5 – 2 = -5 + (-2) = -7 </li></ul>Think …   Sam...
Let’s Practice “Subtraction” <ul><li>1) 5 – 2 = </li></ul><ul><li>2) -3 – 4 = </li></ul><ul><li>3) -1 – (-2) = </li></ul><...
<ul><li>Let’s Check   </li></ul><ul><li>1) 5 – 2 = 5 + (-2)  =  3 </li></ul><ul><li>2) -3 – 4 = -3 + (-4) = -7 </li></ul><...
Rules for  Multiplying Integers (x) <ul><li>The product of two integers with the same signs is POSITIVE. </li></ul><ul><li...
Rules Summary for Multiplication <ul><li>Positive x Positive = Positive </li></ul><ul><li>Negative x Negative = Positive <...
Let’s Practice “ Multiplication ” <ul><li>1) 6 x (-3) =  </li></ul><ul><li>2) 3 x 3 = </li></ul><ul><li>3) -4 x 5 =  </li>...
<ul><li>Let’s Check   </li></ul><ul><li>1) 6 x (-3) =  -18 </li></ul><ul><li>2) 3 x 3 = 9 </li></ul><ul><li>3) -4 x 5 =  -...
Did you know that the  rules  for  multiplication  and  division  are the  same ?
Guess what…. They are!
<ul><li>The rules for division are exactly the same as those for multiplication. </li></ul><ul><li>If we were to take the ...
Rules for  Dividing Integers (÷) <ul><li>The quotient of two integers with the same signs is POSITIVE. </li></ul><ul><li>T...
Rules Summary for Division <ul><li>Positive  ÷  Positive = Positive </li></ul><ul><li>Negative  ÷  Negative = Positive </l...
Let’s Practice “Division” <ul><li>1) 18  ÷  (-2) =   </li></ul><ul><li>2) -48  ÷  (-6) = </li></ul><ul><li>3) -27  ÷  9 = ...
<ul><li>Let’s Check   </li></ul><ul><li>1) 18  ÷  (-2) =   -9 </li></ul><ul><li>2) -48  ÷  (-6) = 8 </li></ul><ul><li>3) -...
Let’s Review…
What is an integer?
ANSWER <ul><li>An integer is a positive or negative whole number, including 0. </li></ul>
Can you give an example of an integer?
ANSWER <ul><li>… -3, -2, -1, 0, 1, 2, 3… </li></ul>
What are the four operations?
ANSWER <ul><li>The four operations are: addition, subtraction, multiplication, and division. </li></ul>
How do you add integers?
ANSWER <ul><li>The sum of two positive integers is always positive. </li></ul><ul><li>The sum of two negative integers is ...
How do you subtract integers?
ANSWER <ul><li>To subtract an integer, add its opposite. </li></ul><ul><li>Same, Change, Change </li></ul>
How do you multiply integers?
ANSWER <ul><li>If the signs are the same, your answer is always positive. </li></ul><ul><li>If the signs are different, yo...
How do you divide integers?
ANSWER <ul><li>If the signs are the same, your answer is always positive. </li></ul><ul><li>If the signs are different, yo...
The End -7 15 -8 3 6 10 -9
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Integers

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Integer Rules

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Integers

  1. 1. INTEGERS
  2. 2. What is an Integer?
  3. 3. <ul><li>An integer is a positive or negative whole number, including 0. </li></ul><ul><li>… -3, -2, -1, 0, 1, 2, 3… </li></ul>
  4. 4. There are “4” Integer Operations
  5. 5. Addition
  6. 6. Subtraction
  7. 7. Multiplication
  8. 8. Division
  9. 9. 4 Integer Operations <ul><li>Addition + </li></ul><ul><li>Subtraction - </li></ul><ul><li>Multiplication x </li></ul><ul><li>Division ÷ </li></ul>
  10. 10. Rule #1 for Adding Integers (+) <ul><li>The sum of two positive integers is always positive. </li></ul><ul><li>5 + 1 = 6 </li></ul>
  11. 11. Rule #2 for Adding Integers (+) <ul><li>The sum of two negative integers is always negative. </li></ul><ul><li>-5 + (-1) = -6 </li></ul>
  12. 12. Rule #3 for Adding Integers (+) <ul><li>The sum of a positive and a negative integer could be positive, negative, or zero. </li></ul>
  13. 13. Rule #3 for Adding Integers Continued <ul><li>When you add a positive and negative integer, you are really subtracting. Then, you give the answer the sign of the greater absolute value. </li></ul><ul><li>5 + (-1) = -4 </li></ul><ul><li>-5 + 1 = 4 </li></ul><ul><li>-5 + (-5) = 0 </li></ul>
  14. 14. Let’s Practice “Addition” <ul><li>1) 5 + 6 = </li></ul><ul><li>-3 + (-2) = </li></ul><ul><li>-6 + 5 = </li></ul><ul><li>8 + (-7) = </li></ul><ul><li>-9 + 9 = </li></ul>
  15. 15. <ul><li>Let’s Check </li></ul><ul><li>1) 5 + 6 = 11 </li></ul><ul><li>-3 + (-2) = -5 </li></ul><ul><li>-6 + 5 = -1 </li></ul><ul><li>8 + (-7) = 1 </li></ul><ul><li>-9 + 9 = 0 </li></ul>
  16. 16. Rules for Subtracting Integers (-) <ul><li>To subtract an integer, add its opposite. </li></ul><ul><li>You will need to correctly change all subtraction problems into addition problems! </li></ul>
  17. 17. How do you change a subtraction problem into an addition problem?
  18. 18. <ul><li>There are three steps : </li></ul><ul><li>1. Keep the first integer the same. (Same) </li></ul><ul><li>2. Change the subtraction sign into an addition sign. (Change) </li></ul><ul><li>3. Take the opposite of the number that immediately follows the newly placed addition sign. (Change) </li></ul>
  19. 19. Same
  20. 20. Change
  21. 21. Change
  22. 22. <ul><li>Examples: </li></ul><ul><li>5 – (-2) = 5 + 2 = 7 </li></ul><ul><li>-5 – 2 = -5 + (-2) = -7 </li></ul>Think … Same , Change , Change
  23. 23. Let’s Practice “Subtraction” <ul><li>1) 5 – 2 = </li></ul><ul><li>2) -3 – 4 = </li></ul><ul><li>3) -1 – (-2) = </li></ul><ul><li>4) -5 – (-3) = </li></ul><ul><li>5) 7 – (-6) = </li></ul>
  24. 24. <ul><li>Let’s Check </li></ul><ul><li>1) 5 – 2 = 5 + (-2) = 3 </li></ul><ul><li>2) -3 – 4 = -3 + (-4) = -7 </li></ul><ul><li>3) -1 – (-2) = -1 + 2 = 1 </li></ul><ul><li>4) -5 – (-3) = -5 + 3 = -2 </li></ul><ul><li>5) 7 – (-6) = 7+ 6 = 13 </li></ul>
  25. 25. Rules for Multiplying Integers (x) <ul><li>The product of two integers with the same signs is POSITIVE. </li></ul><ul><li>The product of two integers with different signs is NEGATIVE. </li></ul>
  26. 26. Rules Summary for Multiplication <ul><li>Positive x Positive = Positive </li></ul><ul><li>Negative x Negative = Positive </li></ul><ul><li>Positive x Negative= Negative </li></ul><ul><li>Negative x Positive = Negative </li></ul>
  27. 27. Let’s Practice “ Multiplication ” <ul><li>1) 6 x (-3) = </li></ul><ul><li>2) 3 x 3 = </li></ul><ul><li>3) -4 x 5 = </li></ul><ul><li>4) -6 x (-2) = </li></ul><ul><li>5) -7 x (-8) = </li></ul>
  28. 28. <ul><li>Let’s Check </li></ul><ul><li>1) 6 x (-3) = -18 </li></ul><ul><li>2) 3 x 3 = 9 </li></ul><ul><li>3) -4 x 5 = -20 </li></ul><ul><li>4) -6 x (-2) = 12 </li></ul><ul><li>5) -7 x (-8) = 56 </li></ul>
  29. 29. Did you know that the rules for multiplication and division are the same ?
  30. 30. Guess what…. They are!
  31. 31. <ul><li>The rules for division are exactly the same as those for multiplication. </li></ul><ul><li>If we were to take the rules for multiplication and change the multiplication signs to division signs, we would have an accurate set of rules for division. </li></ul>
  32. 32. Rules for Dividing Integers (÷) <ul><li>The quotient of two integers with the same signs is POSITIVE. </li></ul><ul><li>The quotient of two integers with different signs is NEGATIVE. </li></ul>
  33. 33. Rules Summary for Division <ul><li>Positive ÷ Positive = Positive </li></ul><ul><li>Negative ÷ Negative = Positive </li></ul><ul><li>Positive ÷ Negative= Negative </li></ul><ul><li>Negative ÷ Positive = Negative </li></ul>
  34. 34. Let’s Practice “Division” <ul><li>1) 18 ÷ (-2) = </li></ul><ul><li>2) -48 ÷ (-6) = </li></ul><ul><li>3) -27 ÷ 9 = </li></ul><ul><li>4) 64 ÷ 8 = </li></ul><ul><li>5) 30 ÷ (-5) = </li></ul>
  35. 35. <ul><li>Let’s Check </li></ul><ul><li>1) 18 ÷ (-2) = -9 </li></ul><ul><li>2) -48 ÷ (-6) = 8 </li></ul><ul><li>3) -27 ÷ 9 = -3 </li></ul><ul><li>4) 64 ÷ 8 = 8 </li></ul><ul><li>5) 30 ÷ (-5) = -6 </li></ul>
  36. 36. Let’s Review…
  37. 37. What is an integer?
  38. 38. ANSWER <ul><li>An integer is a positive or negative whole number, including 0. </li></ul>
  39. 39. Can you give an example of an integer?
  40. 40. ANSWER <ul><li>… -3, -2, -1, 0, 1, 2, 3… </li></ul>
  41. 41. What are the four operations?
  42. 42. ANSWER <ul><li>The four operations are: addition, subtraction, multiplication, and division. </li></ul>
  43. 43. How do you add integers?
  44. 44. ANSWER <ul><li>The sum of two positive integers is always positive. </li></ul><ul><li>The sum of two negative integers is always negative. </li></ul><ul><li>When you add a positive and negative integer, you are really subtracting. Then, you give the answer the sign of the greater absolute value. </li></ul>
  45. 45. How do you subtract integers?
  46. 46. ANSWER <ul><li>To subtract an integer, add its opposite. </li></ul><ul><li>Same, Change, Change </li></ul>
  47. 47. How do you multiply integers?
  48. 48. ANSWER <ul><li>If the signs are the same, your answer is always positive. </li></ul><ul><li>If the signs are different, your answer is always negative. </li></ul>
  49. 49. How do you divide integers?
  50. 50. ANSWER <ul><li>If the signs are the same, your answer is always positive. </li></ul><ul><li>If the signs are different, your answer is always negative. </li></ul><ul><li>*Multiplication and Division Rules are the same! </li></ul>
  51. 51. The End -7 15 -8 3 6 10 -9
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