Percent of Change

📈 Percent of Change

Part 1 of 5 — Concept Introduction

Have you ever seen a sign that says "30% off!" or read a headline like "Population up 12% this year"? Those numbers are all about percent of change — how much something grew or shrank compared to where it started.

Percent of change tells us how much a quantity increased or decreased, written as a percentage of the original amount.

The Formula

$\text{Percent of Change} = \frac{\text{Amount of Change}}{\text{Original Amount}} \times 100\%$

The amount of change is just the difference between the new value and the old value:

$\text{Amount of Change} = \text{New} - \text{Original}$

🔑 Big idea: Always divide by the original amount — the number you started with — not the new amount.

Two Kinds of Change

Every percent of change is either an increase or a decrease.

• A percent increase happens when the new amount is bigger than the original (population growth, a raise, rising temperature).
• A percent decrease happens when the new amount is smaller than the original (a sale, a price cut, weight loss).

A First Worked Example

A shirt costs $20. The price rises to $25. What is the percent change?

• Step 1 — Amount of change: $25 - 20 = 5$ dollars.
• Step 2 — Divide by the original: $\frac{5}{20} = 0.25$.
• Step 3 — Convert to a percent: $0.25 \times 100\% = 25\%$.

Because the price went up, this is a 25% increase. ✅

Concept Check 🎯

📝 Worked Examples

Part 2 of 5 — Worked Examples

The same three steps work for both increase and decrease. The only difference is the order you subtract so the amount of change comes out positive.

Example 1: Percent Increase (Population)

A town's population was 8,000 last year. This year it is 8,800. Find the percent increase.

• Step 1 — Amount of change: $8800 - 8000 = 800$ people.
• Step 2 — Divide by the original: $\frac{800}{8000} = 0.1$.
• Step 3 — Convert to a percent: $0.1 \times 100\% = 10\%$.

The population had a 10% increase. 🎉

Example 2: Percent Decrease (Sale)

A jacket normally costs $80 but is on sale for $60. Find the percent decrease.

• Step 1 — Amount of change: $80 - 60 = 20$ dollars (the price dropped by $20).
• Step 2 — Divide by the original: $\frac{20}{80} = 0.25$.
• Step 3 — Convert to a percent: $0.25 \times 100\% = 25\%$.

The price had a 25% decrease. 🏷️

💡 For a decrease, subtract $\text{New}$ from $\text{Original}$ so the change stays positive, then divide by the original just like always.

Your Turn 🧮

Maria scored 72 on her first test and 90 on her second test. Find the percent increase, one step at a time.

1. What is the amount of change (new − original)? (Type a single number.)

2. Divide that change by the original score. What decimal do you get? (Type it like $0.25$.)

3. Convert that decimal to a percent. What is the percent increase? (Type just the number, like $25$.)

🧭 Guided Practice

Part 3 of 5 — Guided Practice

Work through each one with the three steps: find the change, divide by the original, multiply by 100.

Increase or Decrease? 🔍

For each situation, decide whether it is a percent increase or a percent decrease.

🌎 Application & Word Problems

Part 4 of 5 — Real-World Practice

Percent of change shows up constantly in everyday life:

• Shopping: "Save 25%!" means the price had a 25% decrease.
• Sports & stats: A player's points might go up 40% from last season.
• News: Gas prices, populations, and ticket sales are often reported as percent changes.

When you read a word problem, look for the two amounts — the one you started with (original) and the one you ended with (new). Decide which is bigger, then run the three steps.

🛒 Tip: The phrase "on sale for" or "marked down to" usually signals a decrease, while "raised to" or "grew to" signals an increase.

Word Problem 🧮

A video game originally costs $60. During a holiday sale it is marked down to $45. Find the percent decrease step by step.

1. What is the amount of change (original − new)? (Type a single number.)

2. Divide that change by the original price. What decimal do you get? (Type it like $0.25$.)

3. What is the percent decrease? (Type just the number, like $25$.)

Apply It 🎯

🏆 Review & Challenge

Part 5 of 5 — Putting It All Together

You now have a complete toolkit for percent of change. Here is a quick summary:

Remember:

• Always divide by the original amount.
• A bigger new value means a percent increase; a smaller new value means a percent decrease.
• A percent increase can be more than 100% (if a value more than doubles), but a percent decrease can never be more than 100%.

Ready for the final challenge? Let's go! 🚀

Final Challenge 🎯

Mix of increase and decrease — read each one carefully.