Complete addition and subtraction sentences with integers
Key note :–
| 🔍 What Are Integers? |
- Integers are whole numbers and their negatives, including zero.
Examples: –5, –2, 0, 3, 8
| ➕➖ Addition and Subtraction of Integers |
✅ Rule #1: Adding Integers
| Case | Rule | Example | Result |
|---|---|---|---|
| ➕ Both Positive | Add normally | (+6) + (+4) | +10 |
| ➖ Both Negative | Add, keep negative sign | (–3) + (–7) | –10 |
| ➕➖ One Positive, One Negative | Subtract and take sign of bigger number | (–8) + (+5) | –3 |
| ✅ Rule #2: Subtracting Integers |
🔁 Turn Subtraction into Addition
Change “–” to “+” and flip the sign of the second number.
Examples:
| Original | Convert | Answer |
|---|---|---|
| 9 – (–4) | 9 + 4 | 13 |
| –5 – (+3) | –5 + (–3) | –8 |
| –10 – (–6) | –10 + 6 | –4 |
| ✍️ How to Complete Integer Sentences |
You’re given part of a number sentence. Your job is to find the missing number.
✅ Steps to Solve:
- Understand if it’s addition or subtraction.
- Apply rules for integers.
- Use inverse operations to find the missing number.
- Check your answer by plugging it back in.
| 📌 Example 1: |
___ + (–5) = –9
➤ Think: What number added to –5 gives –9?
➤ Use inverse operation: –9 – (–5) = ?
➤ –9 + 5 = –4
✅ Answer: –4
| 📌 Example 2: |
7 – ___ = 10
➤ Think: 7 minus what equals 10?
➤ Reverse it: 7 – ? = 10 → not possible!
➤ Try: What added to 7 gives 10?
➤ 7 + 3 = 10, so subtraction would be: 7 – (–3) = 10
✅ Answer: –3
| 📌 Example 3: |
___ – (–6) = 9
➤ Change to: ___ + 6 = 9
➤ Now subtract: 9 – 6 = 3
✅ Answer: 3
| 📝 Practice Problems (Complete the blanks): |
- ___ + (–4) = –10
- 12 – ___ = 8
- ___ – (–5) = 11
- –3 + ___ = –7
- ___ – (+2) = –6
✅ Answers:
- –6
- 4
- 6
- –4
- –4
| 🎯 Key Takeaways: |
✅ Use number line if needed
✅ Always check using the reverse operation
✅ Be careful with double negatives
✅ Practice makes perfect!
Learn with an example
➡️ Type the integer that makes the following addition number sentence true:
_____+ -5 = -9
You want to find the number that makes the addition number sentence true.
Later on, you’ll learn another way of solving problems like this, but for now, there is a helpful shortcut that you can use. Look at the two numbers and ignore their signs. They are 5 and 9. Now find their sum and difference. To find the sum, add 5 and 9 to get 14. To compute the difference, subtract the smaller number, 5, from the larger number, 9, to get 4.
Now you have two numbers to try: 14 and 4. If you make these two numbers negative, you’ll have another two numbers to try: -14 and -4. The correct answer will be one of these four numbers.
Try 14:
14 + -5 = 9
Try 4:
4 + -5 = -1
Try -14:
-14 + -5 = -19
Try -4:
-4 + -5 = -9
The number -4 makes the number sentence true, so the correct answer is -4.
➡️ Type the integer that makes the following subtraction number sentence true:
-7 −____= -15
You want to find the number that makes the subtraction number sentence true.
Later on, you’ll learn another way of solving problems like this, but for now, there is a helpful shortcut that you can use. Look at the two numbers and ignore their signs. They are 7 and 15. Now find their sum and difference. To find the sum, add 7 and 15 to get 22. To compute the difference, subtract the smaller number, 7, from the larger number, 15, to get 8.
Now you have two numbers to try: 22 and 8. If you make these two numbers negative, you’ll have another two numbers to try: -22 and -8. The correct answer will be one of these four numbers.
Try 22:
-7 − 22 = -29
Try 8:
-7 − 8 = -15
Try -22:
–7 − –22 = 15
Try -8:
-7 − -8 = 1
The number 8 makes the number sentence true, so the correct answer is 8.
➡️ Type the integer that makes the following addition number sentence true:
____+ -6 = -8
You want to find the number that makes the addition number sentence true.
Later on, you’ll learn another way of solving problems like this, but for now, there is a helpful shortcut that you can use. Look at the two numbers and ignore their signs. They are 6 and 8. Now find their sum and difference. To find the sum, add 6 and 8 to get 14. To compute the difference, subtract the smaller number, 6, from the larger number, 8, to get 2.
Now you have two numbers to try: 14 and 2. If you make these two numbers negative, you’ll have another two numbers to try: -14 and -2. The correct answer will be one of these four numbers.
Try 14:
14 + -6 = 8
Try 2:
2 + -6 = -4
Try -14:
-14 + -6 = -20
Try -2:
-2 + -6 = -8
The number -2 makes the number sentence true, so the correct answer is -2.
Try some practice problems!
