--- title: "Percentage Change with Multipliers" description: "Use one multiplier for an increase or a decrease, chain multipliers for repeated changes, and divide by the multiplier to find the original amount." canonical: https://lightmysky.com/learn/mathematics/percentage-change-with-multipliers-mt_uqclfF4OBR source: https://lightmysky.com/learn/mathematics/percentage-change-with-multipliers-mt_uqclfF4OBR.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # 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. Subject: Mathematics · Area: Ratio & Proportion · Ages 15 to 16 Page: https://lightmysky.com/learn/mathematics/percentage-change-with-multipliers-mt_uqclfF4OBR ## Ready when they can - 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 ## Lesson: One number does the whole change 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. **Example.** 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. **Tip.** 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. **Recap.** Multiply by one number to change, divide by it to undo, never expect a rise and fall to cancel. ## Practice 20 questions on this page, each with its working shown. ## Needs first - [Standard Form](https://lightmysky.com/learn/mathematics/standard-form-mt_GbZZ2xjBTt) - [Percentages (age 12+)](https://lightmysky.com/learn/mathematics/percentages-age-12-mt_iEXqN48w3x) ## Opens up - [Compound Growth and Decay](https://lightmysky.com/learn/mathematics/compound-growth-and-decay-mt_xf5FQ2sugf)