Practice worksheet for adding and subtracting negative numbers, divided into four sections with 12 problems each.

Let's solve each section of the worksheet step by step and explain the reasoning behind each answer. This worksheet focuses on adding and subtracting negative numbers, which is a foundational concept in mathematics.

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Section A: Basic Addition and Subtraction

We'll go through each problem:

1) 2 - 7
= 2 + (-7) = -5

2) -4 + 8
= 4 less than zero, then add 8 → move 8 units right from -4 → +4

3) -2 + 12
= -2 + 12 = 10

4) -7 - 4
= -7 + (-4) = -11

5) 9 - 10
= 9 + (-10) = -1

6) -7 + 4
= -7 + 4 = -3

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

8) -15 + 1
= -15 + 1 = -14

9) -12 + 14
= -12 + 14 = 2

10) -10 + 23
= -10 + 23 = 13

11) -8 - 11
= -8 + (-11) = -19

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

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

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Section B: More Practice with Negatives

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

2) -9 - (-4)
Subtracting a negative is like adding:
= -9 + 4 = -5

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

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

5) -2 + 4
= 2 more than -2 → 2

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

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

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

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

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

11) -1 - 3
= -1 + (-3) = -4

12) -6 - 2
= -6 + (-2) = -8

✔ Section B Answers:
1) -4
2) -5
3) 1
4) -5
5) 2
6) -10
7) 7
8) 13
9) 16
10) -10
11) -4
12) -8

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Section C: Larger Numbers & Mixed Operations

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

2) -8 + 10
= 2

3) -15 - (+7)
= -15 - 7 = -22

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

5) -17 - 3
= -17 + (-3) = -20

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

7) -17 + 9
= -8

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

9) -54 + 24
= -30

10) -10 - 8
= -18

11) 9 - (-20)
= 9 + 20 = 29

12) -18 - 33
= -18 + (-33) = -51

✔ Section C Answers:
1) 4
2) 2
3) -22
4) 22
5) -20
6) 11
7) -8
8) -27
9) -30
10) -18
11) 29
12) -51

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Section D: Multi-step Problems (Order of Operations)

These involve multiple operations or parentheses.

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

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)
First do inside brackets: 5 - 3 = 2
Then: 2 + 2 = 4

7) -11 + (-8 - 2)
Inside: -8 - 2 = -10
Then: -11 + (-10) = -21

8) 7 - (2 - 6)
Inside: 2 - 6 = -4
Then: 7 - (-4) = 7 + 4 = 11

9) (4 + 2) + (4 - 9)
First: 4 + 2 = 6
Second: 4 - 9 = -5
Then: 6 + (-5) = 1

10) 3 - ((-1 + 5) - 12)
Step-by-step:
- Innermost: -1 + 5 = 4
- Then: 4 - 12 = -8
- Finally: 3 - (-8) = 3 + 8 = 11

✔ Section D Answers:
1) 1
2) -11
3) 5
4) -21
5) 11
6) 4
7) -21
8) 11
9) 1
10) 11

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✔ Final Answer Summary:

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

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

#### Section C:
1) 4
2) 2
3) -22
4) 22
5) -20
6) 11
7) -8
8) -27
9) -30
10) -18
11) 29
12) -51

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

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🔍 Key Concepts Explained:

- Adding a negative number: Same as subtraction.
Example: 5 + (-3) = 5 - 3 = 2

- Subtracting a negative number: Same as addition.
Example: 5 - (-3) = 5 + 3 = 8

- Order of operations: Always simplify inside parentheses first, then work left to right.

- Negative numbers on number line: Moving left for subtraction, right for addition.

This practice helps build fluency with integers — essential for algebra and beyond!

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