Negative Numbers Worksheets - Printable Worksheet on Negative ... - Free Printable

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 arithmetic.

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🔢 Section A: Basic Addition and Subtraction

We’ll go through each problem:

1) $ 2 - 7 = -5 $
→ Subtracting a larger number from a smaller one gives a negative result: $ 2 - 7 = -(7 - 2) = -5 $

2) $ -4 + 8 = 4 $
→ Adding a positive to a negative: $ -4 + 8 = 8 - 4 = 4 $

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

4) $ -7 - 4 = -11 $
→ Subtracting a positive is like adding a negative: $ -7 - 4 = -11 $

5) $ 9 - 10 = -1 $
→ $ 9 - 10 = -(10 - 9) = -1 $

6) $ -7 + 4 = -3 $
→ $ -7 + 4 = -(7 - 4) = -3 $

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

8) $ -15 + 1 = -14 $
→ $ -15 + 1 = -(15 - 1) = -14 $

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

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

11) $ -8 - 11 = -19 $
→ Same as #7: $ -8 - 11 = -19 $

12) $ -12 - 17 = -29 $
→ $ -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) = -4 $
→ $ 2 - 6 = -4 $

2) $ -9 - (+9) = -9 - 9 = -18 $
→ Subtracting a positive means adding a negative: $ -9 - 9 = -18 $

3) $ 4 + (-3) = 1 $
→ $ 4 - 3 = 1 $

4) $ 3 - (+8) = 3 - 8 = -5 $
→ Subtracting 8 from 3 → $ -5 $

5) $ -2 + 4 = 2 $
→ $ -2 + 4 = 2 $

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

7) $ 3 - (-4) = 3 + 4 = 7 $
→ Subtracting a negative is like adding: $ 3 + 4 = 7 $

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 $

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

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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 = -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 $

✔ Section C Answers:
1) 4 2) 2 3) -22 4) 22 5) -14 6) 11 7) -26 8) -27 9) -78 10) -2 11) -11 12) 15

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🔢 Section D: Multi-Step Expressions (Order of Operations)

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) = 2 + 2 = 4 $

7) $ -11 + (-8 - 2) = -11 + (-10) = -11 - 10 = -21 $

8) $ 7 - (2 + (-6)) = 7 - (2 - 6) = 7 - (-4) = 7 + 4 = 11 $

9) $ (4 + (-2)) + (4 - 9) = (4 - 2) + (-5) = 2 - 5 = -3 $

10) $ 3 - ((-1 + (-5)) - 12) $
Step-by-step:
- First: $ -1 + (-5) = -6 $
- Then: $ -6 - 12 = -18 $
- Then: $ 3 - (-18) = 3 + 18 = 21 $

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

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

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

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

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📝 Key Concepts Recap:

- Adding a negative is the same as subtracting:
$ a + (-b) = a - b $

- Subtracting a negative is the same as adding:
$ a - (-b) = a + b $

- Always simplify inside parentheses first, then follow order of operations.

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