Percentage Change with Multipliers
Use one multiplier for an increase or a decrease, chain multipliers for repeated changes, and divide by the multiplier to find the original amount.
What a learner can do afterwards
- Write a 15 percent rise as a multiplier of 1.15
- Find the original price from a sale price and the discount
- Explain why a 20 percent rise then a 20 percent fall does not return to the start
1 · Read
One multiplier does a whole percentage change for you. A 15% rise means you keep all 100% and add 15%, so multiply by 1.15. A 20% fall leaves 80%, so multiply by 0.80. Above 1 grows, below 1 shrinks.
A coat costs 68 pounds after 15% off. Off means the multiplier is 0.85, so 68 pounds is 0.85 of the original. Undo it by dividing: 68 divided by 0.85 = 80, so the coat was 80 pounds. Finding the start always means dividing by the multiplier.
Chain changes by multiplying their multipliers. A 20% rise then a 20% fall gives 1.20 times 0.80 = 0.96, which sits 4% below the start. The fall bites a bigger number, so a rise and a fall never cancel back home.
Name the multiplier before you touch the calculator. Rise: 100% plus the percent. Fall: 100% minus it. If you know the new value, divide by that same multiplier to walk back to the start.
Multiply by one number to change, divide by it to undo, never expect a rise and fall to cancel.
More to read
Key ideas: Percent increase and decrease
## Percent increase and percent decrease
A percent increase happens when a value gets bigger. You compare how much it went up to the amount you started with.
Percent increase = (new value - original value) / original value x 100%
A percent decrease happens when a value gets smaller. You compare how much it went down to the amount you started with.
Percent decrease = (original value - new value) / original value x 100%
For a rise of 15%, just multiply the original amount by 1.15. For a fall of 20%, multiply by 0.80. That one multiplication does the whole job of finding the new value, so you don't need two separate steps.
If you know the new value and the multiplier, you can also work backward. Divide the new value by the multiplier to find the original amount before the change happened.
How to Calculate Percent Change: Formula & Examples
Looking at how much something changed in percent, rather than just in raw numbers, gives you a clearer picture of how big the change really is.
To find a percent increase, subtract the original value from the new value. Divide that difference by the original value, then multiply by 100 to get a percentage.
To find a percent decrease, subtract the new value from the original value instead. Divide by the original value and multiply by 100.
Once you know the percent, you can turn it into a multiplier. Add the percent to 100% for an increase, or subtract it from 100% for a decrease, then write that as a decimal. A 15% increase becomes 1.15. A 20% decrease becomes 0.80.
This multiplier trick is handy because it lets you go straight from an original amount to a new amount (or back again) with a single multiplication or division, instead of doing the percent calculation every time.
Key Terms
Here are some words that show up a lot when you're working with percentage change.
Percent: a ratio out of 100.
Percent increase: how big the increase is, compared to the original amount.
Percent decrease: how big the decrease is, compared to the original amount.
Discount: an amount taken off the original price, based on a discount rate. If a discount rate is 20%, the multiplier for the sale price is 0.80.
Mark-up: an amount added to the wholesale price, based on a mark-up rate. If a mark-up rate is 15%, the multiplier for the new price is 1.15.
Knowing these terms helps you spot right away whether a problem wants a multiplier above 1 (for an increase, like a mark-up) or below 1 (for a decrease, like a discount).
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