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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
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?