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# Integers

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### Integers

1. 1. INTEGERSINTEGERS
2. 2. What is anInteger?
3. 3. • An integer is a positive ornegative whole number,including 0.…-3, -2, -1, 0, 1, 2, 3…
4. 4. There are“4”IntegerOperations
5. 5. 4 Integer Operations• Addition +• Subtraction -• Multiplication x• Division ÷
6. 6. Rule #1 forAdding Integers (+)• The sum of two positive integers isalways positive.5 + 1 = 6
7. 7. Rule #2 forAdding Integers (+)• The sum of two negative integers isalways negative.-5 + (-1) = -6
8. 8. Rule #3 forAdding Integers (+)• The sum of a positive and a negativeinteger could be positive, negative, orzero.
9. 9. Rule #3 forAdding Integers Continued• When you add a positive and negativeinteger, you are really subtracting. Then,you give the answer the sign of thegreater absolute value.5 + (-1) = -4-5 + 1 = 4-5 + (-5) = 0
10. 10. Let’s Practice “Addition”1) 5 + 6 =2) -3 + (-2) =3) -6 + 5 =4) 8 + (-7) =5) -9 + 9 =
11. 11.  Let’s Check1) 5 + 6 = 112) -3 + (-2) = -53) -6 + 5 = -14) 8 + (-7) = 15) -9 + 9 = 0
12. 12. Rules forSubtracting Integers (-)• To subtract an integer, add itsopposite.• You will need to correctly change allsubtraction problems into additionproblems!
13. 13. How do youchange asubtractionproblem into anaddition problem?
14. 14. There are three steps:1. Keep the first integer the same.(Same)2. Change the subtraction sign into anaddition sign. (Change)3. Take the opposite of the number thatimmediately follows the newly placedaddition sign. (Change)
15. 15. Examples:5 – (-2) = 5 + 2 = 7-5 – 2 = -5 + (-2) = -7Think …Same, Change, Change
16. 16. Let’s Practice “Subtraction”1) 5 – 2 =2) -3 – 4 =3) -1 – (-2) =4) -5 – (-3) =5) 7 – (-6) =
17. 17.  Let’s Check1) 5 – 2 = 5 + (-2) = 32) -3 – 4 = -3 + (-4) = -73) -1 – (-2) = -1 + 2 = 14) -5 – (-3) = -5 + 3 = -25) 7 – (-6) = 7+ 6 = 13
18. 18. Rules forMultiplying Integers (x)• The product of two integers with thesame signs is POSITIVE.• The product of two integers withdifferent signs is NEGATIVE.
19. 19. Rules Summary forMultiplication• Positive x Positive = Positive• Negative x Negative = Positive• Positive x Negative= Negative• Negative x Positive = Negative
20. 20. Let’s Practice “Multiplication”1) 6 x (-3) =2) 3 x 3 =3) -4 x 5 =4) -6 x (-2) =5) -7 x (-8) =
21. 21.  Let’s Check1) 6 x (-3) = -182) 3 x 3 = 93) -4 x 5 = -204) -6 x (-2) = 125) -7 x (-8) = 56
22. 22. Did you know thatthe rules formultiplication anddivision are thesame?
23. 23. Guess what….They are!
24. 24. The rules for division are exactlythe same as those for multiplication.If we were to take the rules formultiplication and change themultiplication signs to division signs,we would have an accurate set ofrules for division.
25. 25. Rules forDividing Integers (÷)• The quotient of two integers withthe same signs is POSITIVE.• The quotient of two integers withdifferent signs is NEGATIVE.
26. 26. Rules Summary forDivision• Positive ÷ Positive = Positive• Negative ÷ Negative = Positive• Positive ÷ Negative= Negative• Negative ÷ Positive = Negative
27. 27. Let’s Practice “Division”1) 18 ÷ (-2) =2) -48 ÷ (-6) =3) -27 ÷ 9 =4) 64 ÷ 8 =5) 30 ÷ (-5) =
28. 28.  Let’s Check1) 18 ÷ (-2) = -92) -48 ÷ (-6) = 83) -27 ÷ 9 = -34) 64 ÷ 8 = 85) 30 ÷ (-5) = -6
29. 29. Let’s Review…
30. 30. What is an integer?
31. 31. ANSWER• An integer is a positive ornegative whole number,including 0.
32. 32. Can you give an exampleof an integer?
33. 33. ANSWER• …-3, -2, -1, 0, 1, 2, 3…
34. 34. What are the fouroperations?