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Learn to calculate and interpret the percentage change between two values.
If a 40, you saved $10—but what 'slice' of the original price is that? Understanding percent change is like having a superpower to track how the world grows, shrinks, and shifts around you.
The percent of change is a ratio that compares the amount of change to the original amount. It tells us how much a value has increased or decreased relative to where it started. We always express this change as a percentage. If the new value is greater than the original, it is a percent increase. If the new value is less than the original, it is a percent decrease. The most important rule to remember is that we always divide by the original value, never the new one.
A pair of sneakers originally costs 100. What is the percent increase?
1. Find the amount of change: . 2. Set up the ratio: . 3. Simplify the fraction: . 4. Convert to a decimal: . 5. Convert to a percent: .
The price increased by .
Quick Check
If a value moves from 50 to 40, is this a percent increase or a percent decrease?
Answer
It is a percent decrease because the new value is smaller than the original.
To solve any percent change problem, you can use this universal formula:
By using the absolute value (the positive difference) in the numerator, you find the 'amount of change.' Then, by dividing by the original amount, you see what portion of the start has changed. Finally, multiplying by 100 turns that decimal into a percentage. This works for everything from store discounts to tracking how many people live in your city.
A small town had 8,000 residents in 2010. By 2020, the population was 6,000. Find the percent decrease.
1. Find the amount of change: . 2. Divide by the original: . 3. Simplify: . 4. Convert to percent: .
The population decreased by .
Quick Check
In the formula, why do we always divide by the original value instead of the new value?
Answer
Because the percent of change measures how much the starting amount has shifted; the original value is our 'baseline' or 100% point.
Sometimes you know the percentage and the original value, and you need to find the new value. For a percent increase, you add the change to the original (). For a decrease, you subtract it (). This is common in inflation calculations, where prices rise over time, or depreciation, where items like cars lose value as they get older.
A laptop originally priced at 15\%10\%$ 'restocking fee' to the new sale price. What is the final price?
1. Find the sale price: . 2. Calculate: . 3. Find the fee: of is . 4. Add the fee to the sale price: .
The final price is .
A shirt was 25. What is the percent increase?
Which value always goes in the denominator when calculating percent change?
A 10% increase followed by a 10% decrease results in the exact same original price.
Review Tomorrow
In 24 hours, try to explain to a friend why a 50% increase followed by a 50% decrease doesn't bring you back to your starting number.
Practice Activity
Look at a receipt or a store flyer today. Pick an item on sale and calculate the percent decrease based on the original and sale prices.