Percent change is always measured against the original amount, not the new one.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
How to find it
Work out the change, divide by the original, then write it as a percent.
The multiplier shortcut
A 20% rise multiplies by 1.2. A 20% fall multiplies by 0.8.
Up then down does not return
A 10% rise then a 10% fall does not give the original, because the second is of a bigger number.
Change is measured against the starting value
A rise from 40 to 50 is an increase of 10, and 10 out of the original 40 is 25%. The denominator is always the original amount, not the new one. Using the new value gives 20%, which answers a different question.
The calculation
Percent change is (change ÷ original) × 100. A drop from 50 to 40 is a change of 10 out of 50, which is 20%. Notice the rise and the fall between the same two numbers give different percentages — because the base differs.
The multiplier method
A 25% increase multiplies by 1.25; a 20% decrease multiplies by 0.8. Working with multipliers is faster and handles several changes in a row cleanly. It also makes reversing a change a simple division.
Increases and decreases do not cancel
Raise 100 by 10% to get 110, then lower it by 10% and you get 99, not 100. The second percentage applies to a bigger base. This is why a 50% loss needs a 100% gain to recover, and it surprises people with real money at stake.
Step 2: Try It Yourself
Tap and try it out.
Before: 10
After: 12
The factor is more than 1, so the bar got longer.
Step 3: Watch an Example
One step at a time.
Watch Ana Find a Percent Increase
A price rises from 40 pounds to 50.
- Step 1
She finds the change: 50 − 40 = 10.
Step 4: Your Turn
Practice makes it stick.
The Sale
Problem 1 of 3
A 60 pound coat is reduced by 25%. What is the new price?
pounds
The Rise
Problem 2 of 3
A price rises from 80 to 100. What is the percent increase?
percent
The Tax
Problem 3 of 3
A 200 pound item has 20% tax added. What is the total?
pounds
Up and Down
1 of 4
A 50 pound item rises 10%. New price?
2 of 4
A 90 pound item falls 20%. New price?
3 of 4
From 20 to 25. Percent increase?
4 of 4
From 50 to 40. Percent decrease?
Step 5: Quick Check
Show what you know.
Question 1 of 2
A 120 pound item falls 25%. New price?
Question 2 of 2
Percent change is divided by which amount?
What You Learned
- Percent change is the change divided by the original.
- A rise multiplies by more than 1, a fall by less.
- Up 10% then down 10% does not return to the start.