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

Let's solve each problem step by step, explaining the rules of negative numbers, addition, and subtraction as we go.

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🔹 Key Rules to Remember:

1. Adding a negative number is the same as subtracting a positive:
- $ a + (-b) = a - b $
2. Subtracting a negative number is the same as adding a positive:
- $ a - (-b) = a + b $
3. When adding or subtracting integers:
- Same signs: Add absolute values, keep the sign.
- Different signs: Subtract smaller from larger, take the sign of the larger absolute value.

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## ✔ Section A

1) $ 2 - 7 = -5 $
(Start at 2, move 7 left on number line → -5)

2) $ -4 + 8 = 4 $
(Go from -4 up 8 → 4)

3) $ -2 + 12 = 10 $
(From -2 up 12 → 10)

4) $ -7 - 4 = -11 $
(From -7, go 4 more left → -11)

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

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

7) $ -8 - 11 = -19 $
(Add negatives: -8 + (-11) = -19)

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

9) $ -12 + 14 = 2 $
(14 - 12 = 2; positive wins)

10) $ -10 + 23 = 13 $
(23 - 10 = 13; positive wins)

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 = adding)

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’ll 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 = 19 $

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

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

8) $ 7 - (-2 + (-6)) $
Inside: $ -2 + (-6) = -8 $
Then: $ 7 - (-8) = 7 + 8 = 15 $

9) $ (-4 + (-2)) + (4 - (-9)) $
Left: $ -4 - 2 = -6 $
Right: $ 4 - (-9) = 4 + 9 = 13 $
Total: $ -6 + 13 = 7 $

10) $ 3 - ((-1 + (-5)) - 12) $
Step 1: $ -1 + (-5) = -6 $
Step 2: $ -6 - 12 = -18 $
Step 3: $ 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) 19
6) 10
7) -17
8) 15
9) 7
10) 21

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✔ All solved! Let me know if you'd like this in printable format or need explanations for any specific problem.