Adding & Subtracting Integers — Solutions

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1. Adding Integers

   1. −8 + 3 = −5
   2. −5 + (−4) = −9
   3. 6 + (−9) = −3
   4. −12 + 7 = −5
   5. −3 + (−8) = −11
   6. 4 + (−4) = 0
   7. −15 + 6 = −9
   8. −7 + (−5) = −12

2. Subtracting Integers

   1. 7 − (−3) = 10
   2. −4 − 6 = −10
   3. 2 − (−8) = 10
   4. −9 − (−4) = −5
   5. 0 − (−5) = 5
   6. −3 − (−3) = 0
   7. 11 − (−6) = 17
   8. −7 − 8 = −15

3. Mixed Addition and Subtraction

   1. −6 + (−2) − 3 = −11
   2. 4 − (−5) + (−7) = 2
   3. −3 − (−8) + (−2) = 3
   4. 10 + (−4) − (−1) = 7
   5. −9 − 3 + (−4) = −16
   6. 0 − (−6) + (−6) = 0
   7. −2 + (−7) − (−5) = −4
   8. 8 − (−3) + (−10) = 1

4. Temperature and Elevation Contexts

   1. −3 + 9 = 6°C
   2. 1850 − 1850 = 0 m (sea level)
   3. 4 − (−6) = 10°C fall
   4. −12 − 8 = −20 m
   5. 11 − (−7) = 18°C range
   6. 350 − 420 = −70 m (70 m below launch point)
   7. 4421 − (−86) = 4507 m
   8. −2 − 5 + 8 = 1°C

5. Find the Missing Integer

   1. n + (−3) = 5: n = 8
   2. −7 + n = −2: n = 5
   3. n − (−4) = 1: n = −3
   4. 6 + n = −3: n = −9
   5. n − 8 = −15: n = −7
   6. −5 + n = 0: n = 5
   7. n + (−6) = −10: n = −4
   8. 3 − n = 9: n = −6

6. Multi-Step Real-World Problems

   1. 45 − 60 + 30 − 25 = −$10 (overdrawn by $10)
   2. 2 + (−3) + 5 + (−2) + (−4) + 6 = 4°C
   3. −30 + 15 − 22 + 8 = −29 m
   4. 0 + 7 − 4 + 12 − 3 = 12 points
   5. −3 + 5 − 7 + 4 = Floor −1
   6. −120 + 85 + 200 − 65 = +$100 profit

7. Number Line Reasoning

   1. Start −4, move left 6: −4 − 6 = −10
   2. Start 3, move left 9: 3 − 9 = −6
   3. Start −8, move right 8: −8 + 8 = 0
   4. Start −5, move right 12: −5 + 12 = 7
   5. Start 0, left 7, then right 3: 0 − 7 + 3 = −4
   6. Start −2, left 4, then left 3: −2 − 4 − 3 = −9

8. Explain the Rule

   1. −5 + (−3) vs −5 − 3: Yes, they are equal. Adding a negative is the same as subtracting: both equal −8.
   2. 4 − (−6) vs 4 + 6: Yes, they are equal. Subtracting a negative is the same as adding: both equal 10.
   3. (−8) − (−8) vs 0: Yes. −8 − (−8) = −8 + 8 = 0. Any number minus itself equals zero.
   4. Student’s error: The error is applying “two negatives make a positive” to addition. The rule applies to multiplication/division. −3 + (−7) = −10 (both negative, so we add the magnitudes and keep the negative sign).

9. Patterns with Integers

   1. 10, 7, 4, 1, …: Next three: −2, −5, −8. Rule: subtract 3 each time.
   2. −20, −15, −10, −5, …: Next three: 0, 5, 10. Rule: add 5 each time.
   3. 8, 5, 2, −1, …: Next three: −4, −7, −10. Rule: subtract 3 each time.
   4. −3, −7, −11, −15, …: Next three: −19, −23, −27. Rule: subtract 4 each time.

10. Extended Problem Solving

    1. Dead Sea vs Everest: 8849 − (−430) = 8849 + 430 = 9279 m difference.
    2. Golfer’s total score: −3 + 2 + (−4) + (−1) = −6 (6 under par).
    3. Number line points A, B, C: A = −9. Moving right 7: B = −9 + 7 = −2. Distance from B to C: 5 − (−2) = 7 units. Yes, it is possible! B = −2.