Comprehensive worksheet designed to help students master the rules of adding and subtracting negative integers.

Let's solve each section of the worksheet step by step, explaining the rules and reasoning behind operations involving negative numbers.

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🔷 Rules to Remember:

1. Adding a negative number is the same as subtracting a positive number:
- $ a + (-b) = a - b $
2. Subtracting a negative number is the same as adding a positive number:
- $ a - (-b) = a + b $
3. When signs are the same, add and keep the sign.
4. When signs are different, subtract and take the sign of the larger absolute value.

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## ✔ Section A

1) $ 2 - 7 = -5 $
→ Subtracting 7 from 2 goes below zero.

2) $ -4 + 8 = 4 $
→ $ 8 - 4 = 4 $, positive because 8 > 4

3) $ -2 + 12 = 10 $
→ $ 12 - 2 = 10 $

4) $ -7 - 4 = -11 $
→ Subtracting a positive makes it more negative

5) $ 9 - 10 = -1 $
→ 10 is bigger than 9, so result is negative

6) $ -7 + 4 = -3 $
→ $ 7 - 4 = 3 $, but since -7 is larger in magnitude, answer is negative

7) $ -8 - 11 = -19 $
→ $ -8 - 11 = -(8+11) = -19 $

8) $ -15 + 1 = -14 $
→ Adding 1 to -15 moves one step toward zero

9) $ -12 + 14 = 2 $
→ $ 14 - 12 = 2 $

10) $ -10 + 23 = 13 $
→ $ 23 - 10 = 13 $

11) $ -6 - 11 = -17 $
→ $ -(6 + 11) = -17 $

12) $ -12 - 17 = -29 $
→ $ -(12 + 17) = -29 $

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## ✔ Section B

1) $ 2 + (-6) = 2 - 6 = -4 $

2) $ -9 - (+9) = -9 - 9 = -18 $

3) $ 4 + (-3) = 4 - 3 = 1 $

4) $ 3 - (+8) = 3 - 8 = -5 $

5) $ -2 + (-4) = -2 - 4 = -6 $

6) $ -5 - (+5) = -5 - 5 = -10 $

7) $ 3 - (-4) = 3 + 4 = 7 $
→ Subtracting a negative becomes addition

8) $ 8 - (-5) = 8 + 5 = 13 $

9) $ 10 - (-6) = 10 + 6 = 16 $

10) $ -7 - (-3) = -7 + 3 = -4 $

11) $ -1 - (-3) = -1 + 3 = 2 $

12) $ -6 - (-2) = -6 + 2 = -4 $

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## ✔ Section C

1) $ -8 - (-12) = -8 + 12 = 4 $

2) $ -8 + (-10) = -8 - 10 = -18 $

3) $ -16 - (+7) = -16 - 7 = -23 $

4) $ 27 + (-5) = 27 - 5 = 22 $

5) $ -17 - (-3) = -17 + 3 = -14 $

6) $ -3 - (-14) = -3 + 14 = 11 $

7) $ -17 + (-9) = -17 - 9 = -26 $

8) $ -8 - (+19) = -8 - 19 = -27 $

9) $ -54 - (+24) = -54 - 24 = -78 $

10) $ -10 - (-8) = -10 + 8 = -2 $

11) $ 9 - (+20) = 9 - 20 = -11 $

12) $ -18 - (-33) = -18 + 33 = 15 $

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## ✔ Section D (Multi-step problems)

We simplify step by step.

1) $ 7 - (+2) - (-4) = 7 - 2 + 4 = 5 + 4 = 9 $

2) $ -5 - 4 + (-2) = -5 - 4 - 2 = -11 $

3) $ 4 + (-6) - (-7) = 4 - 6 + 7 = -2 + 7 = 5 $

4) $ -3 - 9 + (-9) = -3 - 9 - 9 = -21 $

5) $ 18 + (-3) - 4 = 18 - 3 - 4 = 15 - 4 = 11 $

6) $ 2 + (5 - (-3)) = 2 + (5 + 3) = 2 + 8 = 10 $

7) $ -11 + (-8 - (-2)) = -11 + (-8 + 2) = -11 + (-6) = -17 $

8) $ 7 - (-2 + (-6)) = 7 - (-2 - 6) = 7 - (-8) = 7 + 8 = 15 $

9) $ (-4 + (-2)) + (4 - 9) = (-4 - 2) + (-5) = -6 - 5 = -11 $

10) $ 3 - ((-1 + (-5)) - 12) = 3 - ((-1 - 5) - 12) = 3 - ((-6) - 12) = 3 - (-18) = 3 + 18 = 21 $

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✔ Final Answers:

#### Section A
1) -5
2) 4
3) 10
4) -11
5) -1
6) -3
7) -19
8) -14
9) 2
10) 13
11) -17
12) -29

#### Section B
1) -4
2) -18
3) 1
4) -5
5) -6
6) -10
7) 7
8) 13
9) 16
10) -4
11) 2
12) -4

#### Section C
1) 4
2) -18
3) -23
4) 22
5) -14
6) 11
7) -26
8) -27
9) -78
10) -2
11) -11
12) 15

#### Section D
1) 9
2) -11
3) 5
4) -21
5) 11
6) 10
7) -17
8) 15
9) -11
10) 21

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