Multi-step problems with percents

Key notes:

✅ Understand What Is Given

• Read the problem carefully.
• Identify:
  • The original value
  • The percentage
  • What is being asked (increase, decrease, discount, tax, profit, loss, etc.)

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🔄 Convert Percent to Decimal or Fraction

• Percent means “out of 100”
• Convert before calculating:
  • 25% = 0.25
  • 12.5% = 0.125
  • 150% = 1.5

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➕➖ Perform Steps in the Correct Order

Multi-step percent problems usually involve more than one operation:

• First: Find the percent of a number
• Next: Add or subtract (for increase or decrease)
• Sometimes: Repeat with a new percent

📌 Always solve step by step, not all at once.

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💸 Percent Increase Problems

Steps:

1. Find the increase amount
   → Increase = Original × Percent
2. Add to the original value

📘 Example idea:
Price increases by 10% → Add the increase to the original price.

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🏷️ Percent Decrease / Discount Problems

Steps:

1. Find the discount amount
   → Discount = Original × Percent
2. Subtract from the original value

📘 Used in:

• Discounts
• Sales
• Price reductions

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🧾 Problems with Tax or GST

• First calculate the tax amount
• Then add it to the original price

📌 Tax is always calculated on the original price, not the total.

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🔁 Successive Percent Changes

• When more than one percent change is applied:
  • Apply the first percent
  • Use the new value for the next percent
• Do not add the percentages directly.

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✏️ Use Equations When Helpful

• Let the unknown be x
• Write equations like:
  • Final value = Original ± (Percent × Original)

This helps in word problems.

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🔍 Check Your Answer

• Does the answer make sense?
  • Increase → final value should be greater
  • Decrease → final value should be less
• Recheck calculations to avoid small mistakes.

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🧠 Common Mistakes to Avoid

❌ Adding percentages directly
❌ Forgetting to convert percent to decimal
❌ Skipping steps
❌ Using the wrong base value

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⭐ Tip for Students

👉 Write each step clearly
👉 Label values (₹, %, units)
👉 Practice with real-life examples like shopping and bills

Learn with an example

let’s practice!