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Mathematics › 🔄 Grade 7 › Percent Increase and Decrease
🔄 Grade 7 · Lesson 5 of 14

Percent Increase and Decrease

A price tag stretches or shrinks by a percent of its original self — the trick is knowing which number is 'the original.'

Grade 7Middle school
Percent Increase and Decrease — illustration
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The big idea: Percent change always compares an amount of change to the original amount, not the new one. Whether it's a discount, a markup, a tip, or a population change, the same formula applies: find how much something changed, divide by what it started at, and convert to a percent. A shortcut multiplier — multiply by (1 + rate) for an increase or (1 − rate) for a decrease — gets you the new amount directly.
🎯 By the end, you'll be able to
  • Calculate the amount of change given a percent increase or decrease
  • Compute a new amount after a percent change using a multiplier
  • Find the percent change given an original and a new amount
  • Distinguish percent increase from percent decrease in real-world contexts
📎 You should already know
  • Converting between percents, decimals, and fractions
  • Multiplying decimals

Change, measured against the start

Sales, tax, tips, discounts, population growth, a stock price move — all of these describe a quantity changing by a percent. But percent of what? Percent change is always measured against the original amount — the value before the change happened.

🔑 Percent change compares to the original
Percent change is the amount something changed by, divided by its original value, then written as a percent. It does not matter how big the new value is — the original is always the denominator.
\[ \text{percent change} = \dfrac{\text{new} - \text{original}}{\text{original}} \times 100\% \]
A positive result is a percent increase; a negative result is a percent decrease.

A shortcut: the multiplier

If you already know the percent rate and want the new amount directly, skip straight to a multiplier. For an increase, multiply the original by (1 + rate); for a decrease, multiply by (1 − rate), where the rate is written as a decimal.

\[ \text{new amount} = \text{original} \times (1 \pm r) \]
Use + r for an increase (like a markup) and − r for a decrease (like a discount).
🎮 Elastic Price Tag LIVE
Stretch or shrink a price by a percent and see increase/decrease as a fraction of the original.

Markups, discounts, and everything between

A store marks up a wholesale price to set a retail price — that's a percent increase. A discount or sale takes a percent off the regular price — that's a percent decrease. The same formula handles a rising population, a shrinking savings account, or a growing plant — anything that changes by a fixed percent of where it started.

📝 Worked example: A $80 jacket is marked up by 15%. What is the new price?
  1. Write the rate as a decimal: 15% = 0.15.
  2. Use the multiplier for an increase: 1 + 0.15 = 1.15.
  3. New price = 80 × 1.15.
✓ The new price is <strong>$92</strong>.
📝 Worked example: A price drops from $50 to $40. What is the percent decrease?
  1. Find the amount of change: 50 − 40 = 10.
  2. Divide by the original amount: 10 ÷ 50 = 0.20.
  3. Convert to a percent: 0.20 × 100%.
✓ The price decreased by <strong>20%</strong>.
⚠️ Always divide by the original, not the new amount
A common mistake is dividing the amount of change by the new value instead of the original. For the $50-to-$40 example, dividing 10 by 40 gives 25% — the wrong answer. The original amount, $50, is always the one underneath.

Check your understanding

1. A $40 shirt is marked up by 25%. What is the new price?
New price = 40 × (1 + 0.25) = 40 × 1.25 = $50.
2. A $120 item is discounted by 30%. What is the new price?
New price = 120 × (1 − 0.30) = 120 × 0.70 = $84.
3. A price rises from $60 to $75. What is the percent increase?
Change = 75 − 60 = 15. Percent = 15 ÷ 60 = 0.25 = 25%.
4. Percent change should always be calculated relative to which value?
Percent change is always the amount of change divided by the original (starting) amount.
5. A population drops from 500 to 400. What is the percent decrease?
Change = 500 − 400 = 100. Percent = 100 ÷ 500 = 0.20 = 20%.
✅ Key takeaways
  • Percent change compares the amount something changed by to its original value, not the new one.
  • Percent change = (new − original) ÷ original × 100%.
  • A shortcut: new amount = original × (1 + rate) for an increase, or × (1 − rate) for a decrease.
  • Markups are percent increases; discounts are percent decreases — same formula, opposite direction.
  • Dividing by the new amount instead of the original is the most common mistake — always use the original as the denominator.