Adding and Subtracting Integers Rules | Pre-Algebra Add Subtract ... - Free Printable

It looks like you've uploaded an image that explains the rules for adding and subtracting positive and negative integers. While I can't see the actual image, based on your description and the content you've provided, I can help explain the concepts shown in the chart.

Let me break down and explain each section of the chart clearly:

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🔷 Part 1: Adding Positive and Negative Integers

| Integer Sign | Operation | Answer Sign | Example |
|--------------|-----------|-------------|---------|
| + + + | Add | + | 2 + 5 = 7 |
| - + - | Add | - | -2 + (-5) = -7 |
| + + - | Subtract | Larger Integer's Sign | 2 + (-5) = -3 |
| - + + | Subtract | Larger Integer's Sign | -2 + 5 = 3 |

#### ✔ Explanation:
- Same Signs (both + or both -):
- Add the absolute values.
- Keep the same sign as the numbers.
- Example:
$ 2 + 5 = 7 $
$ -2 + (-5) = -7 $

- Different Signs (+ and -):
- Subtract the smaller absolute value from the larger.
- The answer takes the sign of the larger absolute value.
- Example:
$ 2 + (-5) = -3 $ → 5 > 2, so result is negative
$ -2 + 5 = 3 $ → 5 > 2, so result is positive

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🔷 Part 2: Subtracting Positive and Negative Integers

| Integer Sign | Operation | Answer Sign | Example |
|--------------|-----------|-------------|---------|
| + - + | Subtract | Larger Integer's Sign | 2 - 5 = -3 |
| - - - | Subtract | Larger Integer's Sign | -2 - (-5) = 3 |
| + - - | Add | + | 2 - (-5) = 7 |
| - - + | Add | - | -2 - 5 = -7 |

#### ✔ Explanation:
- Subtracting a Positive Number:
Just subtract normally.
- Example: $ 2 - 5 = -3 $

- Subtracting a Negative Number:
This becomes adding the positive version.
- Example: $ -2 - (-5) = -2 + 5 = 3 $
(Because subtracting a negative is like adding a positive)

- So, remember:
$ a - (-b) = a + b $
$ a - b = a + (-b) $

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🎯 Key Rule to Remember:

> "Two negatives make a positive" when subtracting.

For example:
- $ 2 - (-5) = 2 + 5 = 7 $
- $ -2 - (-5) = -2 + 5 = 3 $

But:
- $ -2 - 5 = -7 $ → this is subtraction of a positive, so it gets more negative.

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💡 Summary Tips:

1. Adding same signs: Add and keep the sign.
2. Adding different signs: Subtract and take the sign of the larger number.
3. Subtracting a negative: Turn it into addition.
4. Subtracting a positive: Just subtract.

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✔ Example Problems Solved:

1. $ -3 + 7 = ? $
→ Different signs → subtract: $ 7 - 3 = 4 $ → sign of 7 is + → Answer: 4

2. $ 4 - (-6) = ? $
→ Subtracting a negative → add: $ 4 + 6 = 10 $ → Answer: 10

3. $ -8 + (-3) = ? $
→ Same sign → add: $ 8 + 3 = 11 $ → keep negative → Answer: -11

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Let me know if you'd like help solving a specific problem using these rules!