Practice adding and subtracting integers with this educational worksheet.
Worksheet titled "Adding and Subtracting Integers" with math problems involving positive and negative numbers, colorful geometric background.
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Step-by-step solution for: Adding and Subtracting Integers worksheet for 3
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Show Answer Key & Explanations
Step-by-step solution for: Adding and Subtracting Integers worksheet for 3
Absolutely! Let’s solve each problem step by step, following the rules for adding and subtracting integers.
---
1. Adding two numbers with the same sign: Add their absolute values and keep the sign.
- Example: `(-8) + (-2) = -10`
2. 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.
- Example: `3 + (-8) = -5` (because 8 > 3, and -8 is negative)
3. Subtracting a number: Change the subtraction to addition of the opposite.
- Example: `6 - (-4) = 6 + 4 = 10`
- Example: `(-9) - (-4) = (-9) + 4 = -5`
---
Now let’s solve all the problems row by row:
---
- `3 + (-8)` → Different signs → |8| - |3| = 5, sign of -8 → -5
- `(-9) - (-4)` → = (-9) + 4 → Different signs → |9| - |4| = 5, sign of -9 → -5
- `7 - 5` → Simple subtraction → 2
---
- `6 - (-4)` → = 6 + 4 → 10
- `(-4) - (-2)` → = (-4) + 2 → Different signs → |4| - |2| = 2, sign of -4 → -2
- `(-4) - 10` → = (-4) + (-10) → Same sign → 4+10=14, negative → -14
---
- `6 - 5` → 1
- `(-2) - 5` → = (-2) + (-5) → Same sign → 2+5=7, negative → -7
- `(-2) - 7` → = (-2) + (-7) → Same sign → -9
---
- `(-8) + (-2)` → Same sign → 8+2=10, negative → -10
- `8 + 6` → 14
- `(-9) + 10` → Different signs → |10| - |9| = 1, sign of 10 → 1
---
- `8 + (-10)` → Different signs → |10| - |8| = 2, sign of -10 → -2
- `2 - (-10)` → = 2 + 10 → 12
- `8 - 5` → 3
---
- `8 - (-2)` → = 8 + 2 → 10
- `1 - (-7)` → = 1 + 7 → 8
- `4 + 2` → 6
---
- `(-2) + 6` → Different signs → |6| - |2| = 4, sign of 6 → 4
- `(-4) - 4` → = (-4) + (-4) → Same sign → -8
- `9 - (-7)` → = 9 + 7 → 16
---
- `(-1) - 0` → Any number minus 0 is itself → -1
- `7 - 5` → 2
- `(-5) + (-10)` → Same sign → 5+10=15, negative → -15
---
- `(-1) - (-2)` → = (-1) + 2 → Different signs → |2| - |1| = 1, sign of 2 → 1
- `(-5) - (-6)` → = (-5) + 6 → Different signs → |6| - |5| = 1, sign of 6 → 1
- `9 - (-9)` → = 9 + 9 → 18
---
- `7 - 4` → 3
- `(-2) + 5` → Different signs → |5| - |2| = 3, sign of 5 → 3
- `(-4) - (-10)` → = (-4) + 10 → Different signs → |10| - |4| = 6, sign of 10 → 6
---
## 🎯 Final Answer Sheet (All Solved):
```
3 + (-8) = -5 (-9) - (-4) = -5 7 - 5 = 2
6 - (-4) = 10 (-4) - (-2) = -2 (-4) - 10 = -14
6 - 5 = 1 (-2) - 5 = -7 (-2) - 7 = -9
(-8) + (-2) = -10 8 + 6 = 14 (-9) + 10 = 1
8 + (-10) = -2 2 - (-10) = 12 8 - 5 = 3
8 - (-2) = 10 1 - (-7) = 8 4 + 2 = 6
(-2) + 6 = 4 (-4) - 4 = -8 9 - (-7) = 16
(-1) - 0 = -1 7 - 5 = 2 (-5) + (-10) = -15
(-1) - (-2) = 1 (-5) - (-6) = 1 9 - (-9) = 18
7 - 4 = 3 (-2) + 5 = 3 (-4) - (-10) = 6
```
✔ All problems solved correctly using integer operation rules!
Let me know if you’d like this in a printable format or want to check your own answers against this key!
---
📌 Key Rules to Remember:
1. Adding two numbers with the same sign: Add their absolute values and keep the sign.
- Example: `(-8) + (-2) = -10`
2. 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.
- Example: `3 + (-8) = -5` (because 8 > 3, and -8 is negative)
3. Subtracting a number: Change the subtraction to addition of the opposite.
- Example: `6 - (-4) = 6 + 4 = 10`
- Example: `(-9) - (-4) = (-9) + 4 = -5`
---
Now let’s solve all the problems row by row:
---
✔ Row 1:
- `3 + (-8)` → Different signs → |8| - |3| = 5, sign of -8 → -5
- `(-9) - (-4)` → = (-9) + 4 → Different signs → |9| - |4| = 5, sign of -9 → -5
- `7 - 5` → Simple subtraction → 2
---
✔ Row 2:
- `6 - (-4)` → = 6 + 4 → 10
- `(-4) - (-2)` → = (-4) + 2 → Different signs → |4| - |2| = 2, sign of -4 → -2
- `(-4) - 10` → = (-4) + (-10) → Same sign → 4+10=14, negative → -14
---
✔ Row 3:
- `6 - 5` → 1
- `(-2) - 5` → = (-2) + (-5) → Same sign → 2+5=7, negative → -7
- `(-2) - 7` → = (-2) + (-7) → Same sign → -9
---
✔ Row 4:
- `(-8) + (-2)` → Same sign → 8+2=10, negative → -10
- `8 + 6` → 14
- `(-9) + 10` → Different signs → |10| - |9| = 1, sign of 10 → 1
---
✔ Row 5:
- `8 + (-10)` → Different signs → |10| - |8| = 2, sign of -10 → -2
- `2 - (-10)` → = 2 + 10 → 12
- `8 - 5` → 3
---
✔ Row 6:
- `8 - (-2)` → = 8 + 2 → 10
- `1 - (-7)` → = 1 + 7 → 8
- `4 + 2` → 6
---
✔ Row 7:
- `(-2) + 6` → Different signs → |6| - |2| = 4, sign of 6 → 4
- `(-4) - 4` → = (-4) + (-4) → Same sign → -8
- `9 - (-7)` → = 9 + 7 → 16
---
✔ Row 8:
- `(-1) - 0` → Any number minus 0 is itself → -1
- `7 - 5` → 2
- `(-5) + (-10)` → Same sign → 5+10=15, negative → -15
---
✔ Row 9:
- `(-1) - (-2)` → = (-1) + 2 → Different signs → |2| - |1| = 1, sign of 2 → 1
- `(-5) - (-6)` → = (-5) + 6 → Different signs → |6| - |5| = 1, sign of 6 → 1
- `9 - (-9)` → = 9 + 9 → 18
---
✔ Row 10:
- `7 - 4` → 3
- `(-2) + 5` → Different signs → |5| - |2| = 3, sign of 5 → 3
- `(-4) - (-10)` → = (-4) + 10 → Different signs → |10| - |4| = 6, sign of 10 → 6
---
## 🎯 Final Answer Sheet (All Solved):
```
3 + (-8) = -5 (-9) - (-4) = -5 7 - 5 = 2
6 - (-4) = 10 (-4) - (-2) = -2 (-4) - 10 = -14
6 - 5 = 1 (-2) - 5 = -7 (-2) - 7 = -9
(-8) + (-2) = -10 8 + 6 = 14 (-9) + 10 = 1
8 + (-10) = -2 2 - (-10) = 12 8 - 5 = 3
8 - (-2) = 10 1 - (-7) = 8 4 + 2 = 6
(-2) + 6 = 4 (-4) - 4 = -8 9 - (-7) = 16
(-1) - 0 = -1 7 - 5 = 2 (-5) + (-10) = -15
(-1) - (-2) = 1 (-5) - (-6) = 1 9 - (-9) = 18
7 - 4 = 3 (-2) + 5 = 3 (-4) - (-10) = 6
```
✔ All problems solved correctly using integer operation rules!
Let me know if you’d like this in a printable format or want to check your own answers against this key!
Parent Tip: Review the logic above to help your child master the concept of combining integers worksheet.