Practice Negative Number and Addition and Subtraction Worksheet ... - Free Printable

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 $
→ Subtract 7 from 2: go 7 units left from 2 → $-5$

2) $ -4 + 8 = 4 $
→ Start at -4, move 8 right → $+4$

3) $ -2 + 12 = 10 $
→ Start at -2, move 12 right → $+10$

4) $ -7 - 4 = -11 $
→ Subtract 4 from -7 → $-11$

5) $ 9 - 10 = -1 $
→ Subtract 10 from 9 → $-1$

6) $ -7 + 4 = -3 $
→ Add 4 to -7 → $-3$

7) $ -8 - 11 = -19 $
→ Subtract 11 from -8 → $-19$

8) $ -15 + 1 = -14 $
→ Add 1 to -15 → $-14$

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

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

11) $ -6 - 11 = -17 $
→ Subtract 11 from -6 → $-17$

12) $ -12 - 17 = -29 $
→ Subtract 17 from -12 → $-29$

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## ✔ Section B

1) $ 2 + (-6) = -4 $
→ Same as $2 - 6 = -4$

2) $ -9 - (+9) = -18 $
→ Subtracting +9 is like subtracting 9 → $-9 - 9 = -18$

3) $ 4 + (-3) = 1 $
→ $4 - 3 = 1$

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

5) $ -2 + (-4) = -6 $
→ Adding two negatives: $-2 - 4 = -6$

6) $ -5 - (+5) = -10 $
→ Subtract 5 from -5 → $-10$

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

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 $

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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)

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

2) $ -5 - (-4) + (-2) = -5 + 4 - 2 = -1 - 2 = -3 $

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

4) $ -3 - (-9) + (-9) = -3 + 9 - 9 = 6 - 9 = -3 $

5) $ 18 + (-3) - (-4) = 18 - 3 + 4 = 15 + 4 = 19 $

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)) = (-6) + (4 + 9) = -6 + 13 = 7 $

10) $ 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) -3
3) 5
4) -3
5) 19
6) 10
7) -17
8) 15
9) 7
10) 21

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✔ Summary:
The key is remembering that:
- Subtracting a negative = adding a positive
- Adding a negative = subtracting a positive

Use number lines or think in terms of debts and gains to visualize!

Let me know if you'd like this formatted as a printable answer sheet!