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.
2 · Watch
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8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.