Do the ratios form a proportion: word problems

Key notes:

🔢 What is a Ratio?

➡️ A ratio compares two quantities using:

• Colon 👉 3 : 5
• Fraction 👉 3/5
• Words 👉 3 to 5

✨ Example:
🖍️ Red pencils : Blue pencils = 4 : 6

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⚖️ What is a Proportion?

➡️ A proportion says two ratios are equal.

📌 Written as:
👉 a : b = c : d
👉 a/b = c/d

✨ Example:
🍎 2 apples : 4 apples = 4 apples : 8 apples ✔️

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✅ How to Check if Ratios Form a Proportion

🔁 Cross Multiply!

👉 If a × d = b × c, then it IS a proportion 🎉

🧮 Example:
3 : 5 and 6 : 10
➡️ 3 × 10 = 30
➡️ 5 × 6 = 30
✔️ Yes! They form a proportion 👍

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❌ When Do Ratios NOT Form a Proportion?

🚫 If cross products are not equal, it is NOT a proportion.

🧮 Example:
4 : 7 and 8 : 15
➡️ 4 × 15 = 60
➡️ 7 × 8 = 56
❌ Not equal → Not a proportion

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📖 Proportion Word Problems – Key Clues

🔍 Look for words like:

• per
• for every
• same rate
• same speed
• same cost

✨ Example:
🚗 A car travels 60 km in 2 hours and 90 km in 3 hours.
➡️ 60 : 2 = 30
➡️ 90 : 3 = 30
✔️ Same ratio → Proportion 🚀

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🧠 6. Real-Life Examples

🏫 Class strength
💰 Money & shopping
⏱️ Speed & time
📦 Cost per item

✨ Example:
🛒 5 notebooks cost ₹100
🛒 10 notebooks cost ₹200
➡️ 5 : 100 = 10 : 200 ✔️

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📝 7. Steps to Solve Word Problems

1️⃣ Write the two ratios
2️⃣ Convert them to fractions
3️⃣ Cross multiply
4️⃣ Compare the results
5️⃣ Decide ✔️ or ❌

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🌟 8. Remember!

💡 Equal ratios = Proportion
💡 Unequal ratios = Not a proportion
💡 Cross multiplication is the key 🔑

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🎉📚 Learning Tip:
👉 Always check the units (km, hours, rupees, items) before comparing ratios!