Solve proportions: word problems

key notes :

🔍 What is a Proportion?

👉 A proportion shows that two ratios are equal.
🧮 Example:

2/3 = 4/6

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🧩 Key Parts of a Proportion

• 🔢 Ratio: A comparison of two numbers (like 3:5 or 3/5)
• ⚖️ Proportion: Two equal ratios
• ✖️ Cross products: Multiply across to solve

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🧠 Steps to Solve Proportion Word Problems

1️⃣ Read carefully 📖

• Find what is given and what is unknown

2️⃣ Write the ratio ✍️

• Use fractions or “:” symbols

3️⃣ Set up a proportion ⚖️

• Make two ratios equal

4️⃣ Cross multiply ✖️

• Multiply diagonally

5️⃣ Solve for the unknown 🔍

• Divide to find the answer

6️⃣ Check your answer ✅

• Substitute back to see if it works

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📝 Example

🧃 If 3 bottles of juice cost ₹60, how much do 5 bottles cost?

Step 1️⃣ Write the proportion

3/60 = 5/x

Step 2️⃣ Cross multiply

3/x = 300

Step 3️⃣ Solve

x=100

✅ Answer: 5 bottles cost ₹100

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🌍 Where Do We Use Proportions?

• 🛒 Shopping (price comparison)
• 🍕 Recipes (scaling ingredients)
• 🚗 Speed & distance
• 📐 Maps and scale drawings

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⚠️ Common Mistakes to Avoid

❌ Mixing up numbers in ratios
❌ Forgetting to cross multiply
❌ Not checking the final answer

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🎯 Quick Tip

💡 Always keep units the same (rupees with rupees, km with km)

Learn with an example