Adding and Subtracting Integers Practice Worksheet | 7th Grade PDF ... - Free Printable
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Step-by-step solution for: Adding and Subtracting Integers Practice Worksheet | 7th Grade PDF ...
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Step-by-step solution for: Adding and Subtracting Integers Practice Worksheet | 7th Grade PDF ...
Here is the complete solution to the "Adding and Subtracting Integers Practice" worksheet, with explanations for each section.
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## 🔢 Section A: Basic Integer Addition & Subtraction
Rule Recap:
- Adding a positive → move right on number line.
- Adding a negative → move left (same as subtracting).
- Subtracting a positive → move left.
- Subtracting a negative → move right (same as adding).
---
1) 2 – 7 = -5
Start at 2, subtract 7 → move 7 left → land on -5.
2) -4 + 8 = 4
Start at -4, add 8 → move 8 right → land on 4.
3) -2 + 12 = 10
Start at -2, add 12 → move 12 right → land on 10.
4) -7 – 4 = -11
Start at -7, subtract 4 → move 4 left → land on -11.
5) 9 – 10 = -1
Start at 9, subtract 10 → move 10 left → land on -1.
6) -7 + 4 = -3
Start at -7, add 4 → move 4 right → land on -3.
7) -8 – 11 = -19
Start at -8, subtract 11 → move 11 left → land on -19.
8) -15 + 1 = -14
Start at -15, add 1 → move 1 right → land on -14.
9) -12 + 14 = 2
Start at -12, add 14 → move 14 right → land on 2.
10) -10 + 23 = 13
Start at -10, add 23 → move 23 right → land on 13.
11) -6 – 11 = -17
Start at -6, subtract 11 → move 11 left → land on -17.
12) -12 – 17 = -29
Start at -12, subtract 17 → move 17 left → land on -29.
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## 🔄 Section B: Mixed Signs with Explicit +/- Notation
This section helps reinforce that `+ -` or `- +` can be simplified.
Key Rule:
- `a + (-b) = a - b`
- `a - (+b) = a - b`
- `a - (-b) = a + b`
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1) 2 + -6 = -4
Same as 2 - 6 = -4.
2) -9 – +9 = -18
Same as -9 - 9 = -18.
3) 4 + -3 = 1
Same as 4 - 3 = 1.
4) 3 – +8 = -5
Same as 3 - 8 = -5.
5) -2 + -4 = -6
Same as -2 - 4 = -6.
6) -5 – +5 = -10
Same as -5 - 5 = -10.
7) 3 – -4 = 7
Subtracting a negative → 3 + 4 = 7.
8) 8 – -5 = 13
8 + 5 = 13.
9) 10 – -6 = 16
10 + 6 = 16.
10) -7 – -3 = -4
-7 + 3 = -4.
11) -1 – -3 = 2
-1 + 3 = 2.
12) -6 – -2 = -4
-6 + 2 = -4.
---
## ⚖️ Section C: More Complex with Double Negatives
Focuses on simplifying expressions like `a - -b`.
---
1) -8 – -12 = 4
-8 + 12 = 4.
2) -8 + -10 = -18
-8 - 10 = -18.
3) -16 – +7 = -23
-16 - 7 = -23.
4) 27 + -5 = 22
27 - 5 = 22.
5) -17 – -3 = -14
-17 + 3 = -14.
6) -3 – -14 = 11
-3 + 14 = 11.
7) -17 + -9 = -26
-17 - 9 = -26.
8) -8 – +19 = -27
-8 - 19 = -27.
9) -54 – +24 = -78
-54 - 24 = -78.
10) -10 – -8 = -2
-10 + 8 = -2.
11) 9 – +20 = -11
9 - 20 = -11.
12) -18 – -33 = 15
-18 + 33 = 15.
---
## 🧩 Section D: Multi-step Expressions & Parentheses
Apply order of operations (PEMDAS): Parentheses first, then left-to-right for addition/subtraction.
---
1) 7 – +2 – -4 = ?
Simplify signs: 7 - 2 + 4
→ 5 + 4 = 9
2) -5 – -4 + -2 = ?
→ -5 + 4 - 2
→ (-5 + 4) = -1 → -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) = ?
Inside parentheses: 5 + 3 = 8
→ 2 + 8 = 10
7) -11 + (-8 – -2) = ?
Inside: -8 + 2 = -6
→ -11 + (-6) = -17
8) 7 – (-2 + -6) = ?
Inside: -2 - 6 = -8
→ 7 - (-8) = 7 + 8 = 15
9) (-4 + -2) + (4 – -9) = ?
First group: -4 - 2 = -6
Second group: 4 + 9 = 13
→ -6 + 13 = 7
10) 3 – ((-1 + -5) – 12) = ?
Innermost: -1 - 5 = -6
Then: -6 - 12 = -18
Then: 3 - (-18) = 3 + 18 = 21
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## ✔ Final Answer Key:
1) -5 2) 4 3) 10 4) -11 5) -1 6) -3
7) -19 8) -14 9) 2 10) 13 11) -17 12) -29
1) -4 2) -18 3) 1 4) -5 5) -6 6) -10
7) 7 8) 13 9) 16 10) -4 11) 2 12) -4
1) 4 2) -18 3) -23 4) 22 5) -14 6) 11
7) -26 8) -27 9) -78 10) -2 11) -11 12) 15
1) 9 2) -3 3) 5 4) -3 5) 19
6) 10 7) -17 8) 15 9) 7 10) 21
---
Let me know if you’d like a printable version or step-by-step visual number line diagrams for any problem! 😊
---
## 🔢 Section A: Basic Integer Addition & Subtraction
Rule Recap:
- Adding a positive → move right on number line.
- Adding a negative → move left (same as subtracting).
- Subtracting a positive → move left.
- Subtracting a negative → move right (same as adding).
---
Section A Solutions:
1) 2 – 7 = -5
Start at 2, subtract 7 → move 7 left → land on -5.
2) -4 + 8 = 4
Start at -4, add 8 → move 8 right → land on 4.
3) -2 + 12 = 10
Start at -2, add 12 → move 12 right → land on 10.
4) -7 – 4 = -11
Start at -7, subtract 4 → move 4 left → land on -11.
5) 9 – 10 = -1
Start at 9, subtract 10 → move 10 left → land on -1.
6) -7 + 4 = -3
Start at -7, add 4 → move 4 right → land on -3.
7) -8 – 11 = -19
Start at -8, subtract 11 → move 11 left → land on -19.
8) -15 + 1 = -14
Start at -15, add 1 → move 1 right → land on -14.
9) -12 + 14 = 2
Start at -12, add 14 → move 14 right → land on 2.
10) -10 + 23 = 13
Start at -10, add 23 → move 23 right → land on 13.
11) -6 – 11 = -17
Start at -6, subtract 11 → move 11 left → land on -17.
12) -12 – 17 = -29
Start at -12, subtract 17 → move 17 left → land on -29.
---
## 🔄 Section B: Mixed Signs with Explicit +/- Notation
This section helps reinforce that `+ -` or `- +` can be simplified.
Key Rule:
- `a + (-b) = a - b`
- `a - (+b) = a - b`
- `a - (-b) = a + b`
---
Section B Solutions:
1) 2 + -6 = -4
Same as 2 - 6 = -4.
2) -9 – +9 = -18
Same as -9 - 9 = -18.
3) 4 + -3 = 1
Same as 4 - 3 = 1.
4) 3 – +8 = -5
Same as 3 - 8 = -5.
5) -2 + -4 = -6
Same as -2 - 4 = -6.
6) -5 – +5 = -10
Same as -5 - 5 = -10.
7) 3 – -4 = 7
Subtracting a negative → 3 + 4 = 7.
8) 8 – -5 = 13
8 + 5 = 13.
9) 10 – -6 = 16
10 + 6 = 16.
10) -7 – -3 = -4
-7 + 3 = -4.
11) -1 – -3 = 2
-1 + 3 = 2.
12) -6 – -2 = -4
-6 + 2 = -4.
---
## ⚖️ Section C: More Complex with Double Negatives
Focuses on simplifying expressions like `a - -b`.
---
Section C Solutions:
1) -8 – -12 = 4
-8 + 12 = 4.
2) -8 + -10 = -18
-8 - 10 = -18.
3) -16 – +7 = -23
-16 - 7 = -23.
4) 27 + -5 = 22
27 - 5 = 22.
5) -17 – -3 = -14
-17 + 3 = -14.
6) -3 – -14 = 11
-3 + 14 = 11.
7) -17 + -9 = -26
-17 - 9 = -26.
8) -8 – +19 = -27
-8 - 19 = -27.
9) -54 – +24 = -78
-54 - 24 = -78.
10) -10 – -8 = -2
-10 + 8 = -2.
11) 9 – +20 = -11
9 - 20 = -11.
12) -18 – -33 = 15
-18 + 33 = 15.
---
## 🧩 Section D: Multi-step Expressions & Parentheses
Apply order of operations (PEMDAS): Parentheses first, then left-to-right for addition/subtraction.
---
Section D Solutions:
1) 7 – +2 – -4 = ?
Simplify signs: 7 - 2 + 4
→ 5 + 4 = 9
2) -5 – -4 + -2 = ?
→ -5 + 4 - 2
→ (-5 + 4) = -1 → -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) = ?
Inside parentheses: 5 + 3 = 8
→ 2 + 8 = 10
7) -11 + (-8 – -2) = ?
Inside: -8 + 2 = -6
→ -11 + (-6) = -17
8) 7 – (-2 + -6) = ?
Inside: -2 - 6 = -8
→ 7 - (-8) = 7 + 8 = 15
9) (-4 + -2) + (4 – -9) = ?
First group: -4 - 2 = -6
Second group: 4 + 9 = 13
→ -6 + 13 = 7
10) 3 – ((-1 + -5) – 12) = ?
Innermost: -1 - 5 = -6
Then: -6 - 12 = -18
Then: 3 - (-18) = 3 + 18 = 21
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## ✔ Final Answer Key:
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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Let me know if you’d like a printable version or step-by-step visual number line diagrams for any problem! 😊
Parent Tip: Review the logic above to help your child master the concept of subtracting integers worksheet.
