Let's solve each of the integer addition problems step by step. The key rule to remember when adding integers is:
-
Same signs: Add the absolute values and keep the common sign.
-
Different signs: Subtract the smaller absolute value from the larger one, and take the sign of the number with the larger absolute value.
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Left Column:
1.
9 + (–11)
Different signs: |9| = 9, |–11| = 11 → 11 – 9 = 2 → negative (since –11 has larger absolute value)
= –2
2.
7 + (–11)
Different signs: 11 – 7 = 4 → negative
= –4
3.
–2 + 11
Different signs: 11 – 2 = 9 → positive
= 9
4.
–12 + 2
Different signs: 12 – 2 = 10 → negative
= –10
5.
8 + (–10)
Different signs: 10 – 8 = 2 → negative
= –2
6.
–6 + (–12)
Same signs: 6 + 12 = 18 → negative
= –18
7.
9 + (–9)
Same absolute values, opposite signs → cancel out
= 0
8.
11 + 4
Same signs: 11 + 4 = 15 → positive
= 15
9.
–12 + 10
Different signs: 12 – 10 = 2 → negative
= –2
10.
8 + 6
Same signs: 8 + 6 = 14 → positive
= 14
11.
–8 + 12
Different signs: 12 – 8 = 4 → positive
= 4
12.
1 + 11
Same signs: 1 + 11 = 12 → positive
= 12
13.
10 + (–3)
Different signs: 10 – 3 = 7 → positive
= 7
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Right Column:
1.
12 + 11
Same signs: 12 + 11 = 23 → positive
= 23
2.
–7 + 8
Different signs: 8 – 7 = 1 → positive
= 1
3.
–1 + 12
Different signs: 12 – 1 = 11 → positive
= 11
4.
–9 + (–2)
Same signs: 9 + 2 = 11 → negative
= –11
5.
6 + 8
Same signs: 6 + 8 = 14 → positive
= 14
6.
3 + (–11)
Different signs: 11 – 3 = 8 → negative
= –8
7.
11 + (–10)
Different signs: 11 – 10 = 1 → positive
= 1
8.
–12 + 6
Different signs: 12 – 6 = 6 → negative
= –6
9.
–4 + (–11)
Same signs: 4 + 11 = 15 → negative
= –15
10.
–1 + 4
Different signs: 4 – 1 = 3 → positive
= 3
11.
–12 + (–8)
Same signs: 12 + 8 = 20 → negative
= –20
12.
–10 + 10
Same absolute values, opposite signs → cancel out
= 0
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✔ Final Answers:
Left Column:
1. –2
2. –4
3. 9
4. –10
5. –2
6. –18
7. 0
8. 15
9. –2
10. 14
11. 4
12. 12
13. 7
Right Column:
1. 23
2. 1
3. 11
4. –11
5. 14
6. –8
7. 1
8. –6
9. –15
10. 3
11. –20
12. 0
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✔ Answer Key (All):
```
9 + (–11) = –2 12 + 11 = 23
7 + (–11) = –4 –7 + 8 = 1
–2 + 11 = 9 –1 + 12 = 11
–12 + 2 = –10 –9 + (–2) = –11
8 + (–10) = –2 6 + 8 = 14
–6 + (–12) = –18 3 + (–11) = –8
9 + (–9) = 0 11 + (–10) = 1
11 + 4 = 15 –12 + 6 = –6
–12 + 10 = –2 –4 + (–11) = –15
8 + 6 = 14 –1 + 4 = 3
–8 + 12 = 4 –12 + (–8) = –20
1 + 11 = 12 –10 + 10 = 0
10 + (–3) = 7
```
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Parent Tip: Review the logic above to help your child master the concept of addition of integers worksheet.