Percent Change

Grade 6 · ratios · 100 practice problems · read aloud

🔊 Listen to this explanation

What is Percent Change? 📈📉

Percent change is a way to measure how much something has increased or decreased, expressed as a percentage. It's super useful in real life for comparing prices, tracking growth, or seeing how much your test scores improve!

How to Calculate Percent Change

  1. Find the Change: Subtract the old value from the new value. (New - Old)
  2. Divide by the Original: Take your answer from step 1 and divide it by the original (old) value.
  3. Convert to a Percent: Multiply your answer from step 2 by 100.

Formula: Percent Change = [(New Value - Old Value) / Old Value] × 100

Visual Examples

Example 1: Price Increase

A video game was $50. Now it's $65. What is the percent increase?

  1. Change: $65 - $50 = $15
  2. Divide: $15 / $50 = 0.30
  3. Convert: 0.30 × 100 = 30% increase 🎮

Example 2: Test Score Decrease

You scored 80 on your first test and 72 on your second. What is the percent decrease?

  1. Change: 72 - 80 = -8
  2. Divide: -8 / 80 = -0.10
  3. Convert: -0.10 × 100 = 10% decrease ✏️

Common Mistakes to Avoid

  • Dividing by the wrong number: Always divide by the original (old) value, not the new one.
  • Forgetting the percent sign: After multiplying by 100, don't forget to write the % symbol!
  • Mixing up increase/decrease: A negative answer means a decrease. A positive answer means an increase.

Tips & Tricks

  • Remember the order with the phrase: "Change Over Original." The "change" goes on top, the "original" is on the bottom.
  • Estimate first! If a price goes from $10 to $15, that's about half again as much, so you know the answer should be close to 50%.

How to Practice

Look for percent changes in your everyday life! Practice with:

  • Sale ads in the newspaper or online.
  • Your own grades or sports statistics.
  • The growth of a plant you are measuring.

Try this: If you have 20 marbles and you get 5 more, what is the percent increase? (Answer: 25%)

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 A store increased the price of a $120 item by 25%, then applied a 15% discount. What is the final price?

Hint: First calculate the increased amount, then apply the discount to that new amount. Remember to work with the changed values at each step.

Show the answer

Answer: 127.50

  1. Start with the original price. Original price = 120
  2. Apply the 25% price increase. A 25% increase means the new price is: 120 + (25% of 120) 25% of 120 = 25/100 * 120 = 0.25 * 120 = 30 So increased price = 120 + 30 = 150
  3. Apply the 15% discount to the increased price. A 15% discount means you pay 85% of the price. 85% of 150 = 85/100 * 150 = 0.85 * 150 0.85 * 150 = 127.50
  4. State the final price. Final price = 127.50 So the item's final price after the increase and then the discount is 127.50.

Let's solve this step by step.

2 A store increases the price of a $120 item by 25%, then applies a 15% discount. What is the final price?

Hint: First calculate the increased amount, then apply the discount to the new price. Remember to work with percentages carefully.

Show the answer

Answer: 127.50

  1. Original price** The item starts at $120. --- **
  2. Apply the 25% increase** A 25% increase means the new price is: Original price + 25% of original price = 120 + (25/100) * 120 = 120 + 0.25 * 120 = 120 + 30 = 150 So after the increase, the price is $150. --- **
  3. Apply the 15% discount** A 15% discount means you pay 85% of the price. 85% of 150 = (85/100) * 150 = 0.85 * 150 = 127.50 --- **
  4. Final answer** The final price after both changes is $127.50.

Let's go step by step. --- **

3 A $1500 computer is discounted by 20%, then the sale price is increased by 15%. What is the final price?

Hint: First find the discounted amount, then calculate the new price after the increase. Remember to work with percentages of the current price at each step.

Show the answer

Answer: $1380

  1. Calculate the 20% discount on the original price 20% of $1500 = 0.20 × 1500 = $300
  2. Find the sale price after discount $1500 - $300 = $1200
  3. Calculate the 15% increase on the sale price 15% of $1200 = 0.15 × 1200 = $180
  4. Find the final price after increase $1200 + $180 = $1380 The final price is $1380.

4 A $1500 computer is discounted by 20%, then the sale price is increased by 10%. What is the final price?

Hint: First find the discounted amount, then calculate the new price after the increase using that result.

Show the answer

Answer: $1320

  1. Calculate the 20% discount on $1500 20% of $1500 = 0.20 × 1500 = $300
  2. Find the sale price after discount $1500 - $300 = $1200
  3. Calculate the 10% increase on the sale price 10% of $1200 = 0.10 × 1200 = $120
  4. Find the final price after increase $1200 + $120 = $1320 The final price is $1320.

5 A store increases the price of a $1200 laptop by 15%, then applies a 10% discount. What is the final price?

Hint: First calculate the price after the percentage increase, then apply the percentage decrease to that new amount. Remember that percentages are applied sequentially, not added together.

Show the answer

Answer: 1242

  1. Start with the original price. Original price = 1200
  2. Apply the 15% price increase. 15% of 1200 = (15/100) * 1200 = 0.15 * 1200 = 180 New price after increase = 1200 + 180 = 1380
  3. Apply the 10% discount to the increased price. 10% of 1380 = (10/100) * 1380 = 0.10 * 1380 = 138 Price after discount = 1380 - 138 = 1242
  4. Final answer. The final price after the increase and then the discount is 1242. Explanation: We first increase the original price by 15%, then take 10% off the new price, not the original. The order matters because the discount is applied after the increase.

Let's solve this step-by-step.

6 A store increased the price of a $1200 laptop by 15%, then applied a 10% discount. What is the final price?

Hint: First calculate the price after the percentage increase, then apply the percentage decrease to that new amount. Remember to work with the updated values at each step.

Show the answer

Answer: 1242

  1. Start with the original price** Original price = 1200 --- **
  2. Apply the 15% increase** 15% of 1200 = (15/100) × 1200 = 0.15 × 1200 = 180 New price after increase = 1200 + 180 = 1380 --- **
  3. Apply the 10% discount on the increased price** 10% of 1380 = (10/100) × 1380 = 0.10 × 1380 = 138 Price after discount = 1380 − 138 = 1242 --- **
  4. Final answer** Final price = 1242 --- **Reasoning check:** You could also compute it as: 1200 × (1 + 0.15) × (1 − 0.10) = 1200 × 1.15 × 0.90 = 1200 × 1.035 = 1242 Both methods give the same result.

Let's go step-by-step. --- **

Practise this topic — 10 free problems, no signup →