Add and subtract rational numbers

Key notes:

🔢 What Are Rational Numbers?

• Rational numbers are numbers that can be written as a fraction 🥧
• Example: 1/2, -3/4, 5, -8, 0.25 ( = 1/4 )
• They include positive, negative, fractions, and decimals! 🌟

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➕ Adding Rational Numbers with the Same Sign

Add normally and keep the same sign ✔️

Example:

• 3/5 + 2/5 = 5/5 = 1 😄
• -4 + -2 = -6

💡 Same side = team up! 🤝

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🔄 Adding Rational Numbers with Different Signs

Subtract the smaller value from the bigger value

Keep the sign of the larger number

Example:

• 7 – 10 = -3
• -5 + 12 = 7

💡 Opposites try to cancel each other! ⚡⚡

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➖ Subtracting Rational Numbers

Change subtraction to addition of the opposite ✨

Example:

• 4 – 7 = 4 + (-7) = -3
• -3 – 5 = -3 + (-5) = -8

💡 Subtracting becomes adding the opposite! 🔁

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🍰 Adding & Subtracting Fractions

📌 If denominators are the same:

Add/subtract numerators only!

• 3/8 + 2/8 = 5/8
• 7/9 – 4/9 = 3/9 = 1/3

📌 If denominators are different:

Find LCM (Least Common Multiple) 🎯

Convert to equivalent fractions

Add/subtract numerators

• 1/4 + 1/6 → LCM = 12
• 3/12 + 2/12 = 5/12

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🧊 Adding & Subtracting Decimals

Line up the decimal points

Add or subtract normally

• 3.75 + 2.1 = 5.85
• 6.4 – 3.25 = 3.15

🖊️ Keep decimals in the right place! 📍

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🎯 Opposites and Zero Pair

A number and its opposite always add to 0

• 5 + (-5) = 0
• -8 + 8 = 0

💥 They cancel each other! 🚫

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🧮 Key Rule to Remember

✔️ Addition → Follow sign rules
✔️ Subtraction → Add the opposite
✔️ Fractions → Use LCM
✔️ Decimals → Align decimal points

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🌟 Real-life Examples

Temperature changes 🌡️

• -3°C + 7°C = 4°C

Money profit & loss 💰

• ₹500 – ₹800 = -₹300