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Adding Integers

RULE 1. If the addends have the same sign, add the two numbers and prefix their common sign.

(+62) + (+14) = +76 (-29) + (-13) = -42

RULE 2. If the addends have different signs, find the difference between the two numbers and prefix the sign of the number that is the greater distance from zero.

(+15) + (-8) = +7 (+9) + (-30) = -21

Some Practice Problems


1. (-5) + (-6) =
3. (-3) + (-6) =
5. (-2) + (-8) =
7. (-9) + (+10) =
9. (+12) + (+10) =
11. (-29) + (-11) =
13. (+42) + (-19) =
15. (+31) + (-56) =
17. -8 + 10 =
19. 75 + (-25) =
21. 73 + 47 =
23. 78 + (-30) =
25. 75 + (-25) =
27. 200 + 100 =
29. 355 + (-163) =
31. 34 + (-16) =
33. 72 + (-12) =
35. 1/2 + -1/2 =
37. 1/4 + (-1/2) =
39. 1/4 + -1/2 =
41. 16 + 16 =
43. 3 + (-8) + 7 =
45. 12 + 5 + (-8) + 20 + (-16) =
 2. (+9) + (-4) =
4. (-4) + (-4) =
6. (-7) + (+1) =
8. (-8) + (-5) =
10. (+13) + (-17) =
12. (-36) + (+24) =
14. (-33) + (+42) =
16. (+65) + (+15) =
18. 7 + (-18) =
20. 33 + (-22) =
22. 86 + (-58) =
24. 100 + 50 =
26. 150 + 50 =
28. 132 + (-181) =
30. 900 + 200 =
32. 14 + 43 =
34. 4 + 17 =
36. 7 + (-7) =
38. -1/4 + 1/4 =
40. 17 + 4 =
42. 2436 + (-1064) =
44. 11 + 5 + (-2) =
45. 12 + 5 + (-8) + 20 + (-16) =


Answer Key for Adding Integers

 

  1. –11
  2. 5
  3. –9
  4. –8
  5. –10
  6. –6
  7. 1
  8. –13
  9. 22
  10. –4
  11. –40
  12. –12
  13. 23
  14. 9
  15. –25
  16. 80
  17. 2
  18. -11
  19. 50
  20. –55
  21. –26
  22. 28
  23. –108
  24. –50
  25. –100
  26. 200
  27. –100
  28. –49
  29. 192
  30. 1100
  31. –50
  32. 57
  33. 60
  34. 13
  35. 0
  36. 0
  37. – 1/4
  38. 0
  39. –3/4
  40. –13
  41. 0
  42. 1372
  43. 2
  44. 14
  45. 13
Rules for Subtracting Integers

RULE 1. Because every subtraction problem can be rewritten as a corresponding addition problem, use the following rule: To subtract an integer, add its opposite.

1. (-8) – (+9) = The opposite of +9 is –9. Change sign to opposite: (-8) + (-9) = -17 using integer addition rules

RULE 1 examples:

1. (+7) – (+4) = (+7) + (-4) = +3

2. (+5) – (-6) = (+5) + (+6) = +11

3. (-3) – (+8) = (-3) + (-8) = -11

Alternate RULE 1. To subtract signed numbers:

    1. Change double negatives to a positive.
    2. Get a sum of terms with like signs and keep the given sign, using the sign in front of the number as the sign of the number.
    3. Find the difference when terms have different signs and use the sign of the larger numeral.

Alternate RULE 1 examples:

  1. 7 – (-5) = 7 + 5 = 12 (a. Change double negatives to positive, use integer addition rules)
  2. –5 – 9 = -14 (using the signs in front of the numbers, use only addition rules-signs are alike, add and keep the sign)
  3. 6 – 7 = -1 (using the signs in front of the numbers, use addition rules-signs are different, subtract and take the sign of the largest numeral)
  4. 6 – 7 + 3 – 4 – 2 = 9 – 13 = -4 (Get the sum of the terms with like signs, use addition rules)
Subtracting Integers

  1. 5 – (- 8) =
  2. –7 – (+8) =
  3. –9 – (+ 4) =
  4. 9 – (-2) =
  5. –1 – 6 =
  6. 1 – (-9) =
  7. –4 – 5 =
  8. 3 – 10 =
  9. –8 – (-4) =
  10. 4 – 6 =
  11. 8 – (-9) =
  12. –10 – 10 =
  13. 10 – (-10) =
  14. 10 – 10 =
  15. 25 – (-15) =
  16. –33 – (-49) =
  17. 8 – 7 =
  18. –6 – 8 =
  19. –3 – (-7) =
  20. 14 – (-6) =
  21. 5 – 11 =
  22. –8 – 6 =
  23. –11 – (-4) =
  24. 13 – (-16) =
  25. –6 – (-10) =
  26. –7 – 0 =
  27. 6 – 13 =
  28. –17 – 81 =
  29. 10 – (7 – 9) =
  30. 6 – (-9 +7) =
  31. 6 + (-8 – 7) =
  32. 14 – (18 – 40) =

 

Answer Key for Subtracting Integers

  1. 13
  2. –15
  3. –13
  4. 11
  5. –7
  6. 10
  7. –9
  8. –7
  9. –4
  10. –2
  11. 17
  12. –20
  13. 20
  14. 0
  15. 40
  16. 16
  17. 1
  18. –14
  19. 4
  20. 20
  21. –6
  22. –14
  23. –7
  24. 29
  25. 4
  26. –7
  27. –7
  28. –98
  29. 12
  30. 8
  31. –9
  32. 36