Practice Negative Number and Addition and Subtraction Worksheet ... - Free Printable
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Step-by-step solution for: Practice Negative Number and Addition and Subtraction Worksheet ...
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Step-by-step solution for: Practice Negative Number and Addition and Subtraction Worksheet ...
Absolutely! Let's solve all the problems in this worksheet step by step, explaining the rules for adding and subtracting negative numbers as we go.
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## 🔢 Key Rules to Remember:
1. Adding a negative number is the same as subtracting its positive counterpart.
- e.g., `5 + (-3) = 5 - 3 = 2`
2. Subtracting a negative number is the same as adding its positive counterpart.
- e.g., `5 - (-3) = 5 + 3 = 8`
3. When adding two numbers with different signs, subtract the smaller absolute value from the larger one, and keep the sign of the number with the larger absolute value.
- e.g., `-7 + 4 = -(7 - 4) = -3`
4. When adding two negative numbers, add their absolute values and keep the negative sign.
- e.g., `-3 + (-5) = -8`
5. Order of operations (BIDMAS/BODMAS) applies: Brackets first, then addition/subtraction left to right (unless brackets change order).
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# ✔ Section A
1) `2 - 7` → Start at 2, move 7 left → -5
2) `-4 + 8` → Start at -4, move 8 right → 4
3) `-2 + 12` → Start at -2, move 12 right → 10
4) `-7 - 4` → Start at -7, move 4 more left → -11
5) `9 - 10` → Start at 9, move 10 left → -1
6) `-7 + 4` → Start at -7, move 4 right → -3
7) `-8 - 11` → Start at -8, move 11 left → -19
8) `-15 + 1` → Start at -15, move 1 right → -14
9) `-12 + 14` → Start at -12, move 14 right → 2
10) `-10 + 23` → Start at -10, move 23 right → 13
11) `-6 - 11` → Start at -6, move 11 left → -17
12) `-12 - 17` → Start at -12, move 17 left → -29
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# ✔ Section B
*(Note: These include expressions like `+ -` or `- +`, which are equivalent to subtraction or addition respectively)*
1) `2 + -6` → Same as `2 - 6` → -4
2) `-9 - +9` → Same as `-9 - 9` → -18
3) `4 + -3` → Same as `4 - 3` → 1
4) `3 - +8` → Same as `3 - 8` → -5
5) `-2 + -4` → Same as `-2 - 4` → -6
6) `-5 - +5` → Same as `-5 - 5` → -10
7) `3 - -4` → Same as `3 + 4` → 7
8) `8 - -5` → Same as `8 + 5` → 13
9) `10 - -6` → Same as `10 + 6` → 16
10) `-7 - -3` → Same as `-7 + 3` → -4
11) `-1 - -3` → Same as `-1 + 3` → 2
12) `-6 - -2` → Same as `-6 + 2` → -4
---
# ✔ Section C
*(Here we have double negatives and mixed signs — apply rules carefully)*
1) `-8 - -12` → Same as `-8 + 12` → 4
2) `-8 + -10` → Same as `-8 - 10` → -18
3) `-16 - +7` → Same as `-16 - 7` → -23
4) `27 + -5` → Same as `27 - 5` → 22
5) `-17 - 3` → Straightforward subtraction → -20
6) `-3 - -14` → Same as `-3 + 14` → 11
7) `-17 + -9` → Same as `-17 - 9` → -26
8) `-8 - +19` → Same as `-8 - 19` → -27
9) `-54 - +24` → Same as `-54 - 24` → -78
10) `-10 - -8` → Same as `-10 + 8` → -2
11) `9 - +20` → Same as `9 - 20` → -11
12) `-18 - -33` → Same as `-18 + 33` → 15
---
# ✔ Section D
*(These involve multiple operations — work left to right unless brackets dictate otherwise)*
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)`
→ Inside bracket: `5 + 3 = 8`
→ `2 + 8` → 10
7) `-11 + (-8 - -2)`
→ Inside bracket: `-8 + 2 = -6`
→ `-11 + (-6) = -11 - 6` → -17
8) `7 - (-2 + -6)`
→ Inside bracket: `-2 - 6 = -8`
→ `7 - (-8) = 7 + 8` → 15
9) `(-4 + -2) + (4 - -9)`
→ First bracket: `-4 - 2 = -6`
→ Second bracket: `4 + 9 = 13`
→ `-6 + 13` → 7
10) `3 - ((-1 + -5) - 12)`
→ Innermost: `-1 - 5 = -6`
→ Then: `-6 - 12 = -18`
→ Finally: `3 - (-18) = 3 + 18` → 21
---
# 📝 Final Answers Summary:
## 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) -20 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
---
✔ All problems solved! Practice these rules until they become second nature — especially the “double negative becomes positive” rule. Great job working through this!
Let me know if you’d like a printable answer key or further explanations! 😊
---
## 🔢 Key Rules to Remember:
1. Adding a negative number is the same as subtracting its positive counterpart.
- e.g., `5 + (-3) = 5 - 3 = 2`
2. Subtracting a negative number is the same as adding its positive counterpart.
- e.g., `5 - (-3) = 5 + 3 = 8`
3. When adding two numbers with different signs, subtract the smaller absolute value from the larger one, and keep the sign of the number with the larger absolute value.
- e.g., `-7 + 4 = -(7 - 4) = -3`
4. When adding two negative numbers, add their absolute values and keep the negative sign.
- e.g., `-3 + (-5) = -8`
5. Order of operations (BIDMAS/BODMAS) applies: Brackets first, then addition/subtraction left to right (unless brackets change order).
---
# ✔ Section A
1) `2 - 7` → Start at 2, move 7 left → -5
2) `-4 + 8` → Start at -4, move 8 right → 4
3) `-2 + 12` → Start at -2, move 12 right → 10
4) `-7 - 4` → Start at -7, move 4 more left → -11
5) `9 - 10` → Start at 9, move 10 left → -1
6) `-7 + 4` → Start at -7, move 4 right → -3
7) `-8 - 11` → Start at -8, move 11 left → -19
8) `-15 + 1` → Start at -15, move 1 right → -14
9) `-12 + 14` → Start at -12, move 14 right → 2
10) `-10 + 23` → Start at -10, move 23 right → 13
11) `-6 - 11` → Start at -6, move 11 left → -17
12) `-12 - 17` → Start at -12, move 17 left → -29
---
# ✔ Section B
*(Note: These include expressions like `+ -` or `- +`, which are equivalent to subtraction or addition respectively)*
1) `2 + -6` → Same as `2 - 6` → -4
2) `-9 - +9` → Same as `-9 - 9` → -18
3) `4 + -3` → Same as `4 - 3` → 1
4) `3 - +8` → Same as `3 - 8` → -5
5) `-2 + -4` → Same as `-2 - 4` → -6
6) `-5 - +5` → Same as `-5 - 5` → -10
7) `3 - -4` → Same as `3 + 4` → 7
8) `8 - -5` → Same as `8 + 5` → 13
9) `10 - -6` → Same as `10 + 6` → 16
10) `-7 - -3` → Same as `-7 + 3` → -4
11) `-1 - -3` → Same as `-1 + 3` → 2
12) `-6 - -2` → Same as `-6 + 2` → -4
---
# ✔ Section C
*(Here we have double negatives and mixed signs — apply rules carefully)*
1) `-8 - -12` → Same as `-8 + 12` → 4
2) `-8 + -10` → Same as `-8 - 10` → -18
3) `-16 - +7` → Same as `-16 - 7` → -23
4) `27 + -5` → Same as `27 - 5` → 22
5) `-17 - 3` → Straightforward subtraction → -20
6) `-3 - -14` → Same as `-3 + 14` → 11
7) `-17 + -9` → Same as `-17 - 9` → -26
8) `-8 - +19` → Same as `-8 - 19` → -27
9) `-54 - +24` → Same as `-54 - 24` → -78
10) `-10 - -8` → Same as `-10 + 8` → -2
11) `9 - +20` → Same as `9 - 20` → -11
12) `-18 - -33` → Same as `-18 + 33` → 15
---
# ✔ Section D
*(These involve multiple operations — work left to right unless brackets dictate otherwise)*
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)`
→ Inside bracket: `5 + 3 = 8`
→ `2 + 8` → 10
7) `-11 + (-8 - -2)`
→ Inside bracket: `-8 + 2 = -6`
→ `-11 + (-6) = -11 - 6` → -17
8) `7 - (-2 + -6)`
→ Inside bracket: `-2 - 6 = -8`
→ `7 - (-8) = 7 + 8` → 15
9) `(-4 + -2) + (4 - -9)`
→ First bracket: `-4 - 2 = -6`
→ Second bracket: `4 + 9 = 13`
→ `-6 + 13` → 7
10) `3 - ((-1 + -5) - 12)`
→ Innermost: `-1 - 5 = -6`
→ Then: `-6 - 12 = -18`
→ Finally: `3 - (-18) = 3 + 18` → 21
---
# 📝 Final Answers Summary:
## 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) -20 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
---
✔ All problems solved! Practice these rules until they become second nature — especially the “double negative becomes positive” rule. Great job working through this!
Let me know if you’d like a printable answer key or further explanations! 😊
Parent Tip: Review the logic above to help your child master the concept of worksheet subtracting negative numbers.
