Integer Rules cheat sheet for addition, subtraction, multiplication, and division with clear examples and helpful tips.

It looks like you've uploaded an image of a handwritten or printed educational chart titled "Integer Rules", which explains how to perform arithmetic operations (addition, subtraction, multiplication, and division) with integers (positive and negative numbers). Let's go through the content, clarify it, and explain each rule in detail.

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🔷 1. Addition Rules

#### ✔ Same Signs: KEEP THEM
- When adding two numbers with the same sign (both positive or both negative), keep the sign and add their absolute values.
- Example:
- (+5) + (+3) = +8
- (-4) + (-2) = -6

#### ✘ Different Signs: SUBTRACT and KEEP the LARGER SIGN
- When adding 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:
- (+6) + (-2) = +4 → 6 > 2, so keep the positive sign.
- (-7) + (+3) = -4 → 7 > 3, so keep the negative sign.

> 💡 Tip: Think of it as "fighting" — the bigger number wins and takes the sign.

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🔷 2. Subtraction Rules

The rule is:
"Keep, Change, Change"

This means:
1. Keep the first number as it is.
2. Change the subtraction sign to addition.
3. Change the sign of the second number.

Then follow the addition rules.

#### Example:
- (+5) − (+3) → Keep: +5, Change: − → +, Change: +3 → −3
→ (+5) + (−3) = +2

- (−4) − (−2) → Keep: −4, Change: − → +, Change: −2 → +2
→ (−4) + (+2) = −2

> 🔄 So subtraction becomes addition! This makes it easier to handle.

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🔷 3. Multiplication and Division Rules

These follow the same pattern:

| Rule | Result |
|------|--------|
| (+) × (+) = (+) | Positive × Positive = Positive |
| (−) × (−) = (+) | Negative × Negative = Positive |
| (+) × (−) = (−) | Positive × Negative = Negative |
| (−) × (+) = (−) | Negative × Positive = Negative |

Same for division:
- (+) ÷ (+) = (+)
- (−) ÷ (−) = (+)
- (+) ÷ (−) = (−)
- (−) ÷ (+) = (−)

#### Mnemonic:
> "Same signs = Positive"
> "Different signs = Negative"

#### Examples:
- (−6) × (−3) = +18
- (−10) ÷ (+2) = −5
- (+7) × (−2) = −14

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✔ Summary Table

| Operation | Rule |
|---------|------|
| Addition – Same Sign | Add, keep the sign |
| Addition – Different Signs | Subtract, keep the larger sign |
| Subtraction | Keep, Change, Change → turn into addition |
| Multiplication/Division | Same signs → positive; different signs → negative |

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🎯 Why These Rules Matter

Understanding these integer rules helps with:
- Solving algebraic equations
- Working with real-world problems (e.g., temperature changes, bank balances)
- Building a foundation for more advanced math (like pre-algebra and calculus)

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📝 Final Note

Your chart is correct and well-organized! It’s a great study tool. Just remember:

> "Keep, Change, Change" is your magic phrase for subtraction.
> "Same signs = positive, different signs = negative" applies to multiplication/division.

Let me know if you'd like practice problems or a quiz based on this! 😊