--- title: "Calculating percentages" description: "Solve problems involving the calculation of percentages of amounts (e.g. 15% of 360) and the use of percentages for comparison" canonical: https://lightmysky.com/learn/mathematics/calculating-percentages-mt_PNSyfH56eQ source: https://lightmysky.com/learn/mathematics/calculating-percentages-mt_PNSyfH56eQ.md retrieved: 2026-10-19 --- > **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`. # Calculating percentages Solve problems involving the calculation of percentages of amounts (e.g. 15% of 360) and the use of percentages for comparison Subject: Mathematics · Area: Ratio & Proportion · Ages 10 to 11 Page: https://lightmysky.com/learn/mathematics/calculating-percentages-mt_PNSyfH56eQ ## Ready when they can - Calculate 15% of 360 by finding 10% and 5% and combining - Calculate and compare discount amounts from different original prices; subtract a discount from its original price to calculate a sale price and compare sale prices - Explain a strategy for finding any percentage of an amount using known percentage facts ## Lesson: Finding percentages of an amount Percent means out of one hundred. Find 1% by dividing an amount by 100. Any whole-number percentage is that many copies of the 1% amount. Useful shortcuts are 10% by dividing by 10, 5% by halving the 10% amount, 50% by halving the whole, and 25% by dividing the whole by 4. *(drawing: For an amount of 180, 10% is 18 and 5% is 9. Together they make 15%, or 27.)* **Example.** To find 15%, combine 10% and 5% of the same starting amount. For 180, divide by 10 to get 18. Half of 18 is 9, so that is 5%. Add 18 + 9 = 27. Doubling the 10% amount would give 20%, not 15%. **Example.** Compare discounts by calculating the money saved from each original price. Bag A costs £70 with 10% off, saving £7. Bag B costs £25 with 20% off: 10% is £2.50, so twice that is £5. Bag A saves more money despite its smaller percentage. To find how much more, subtract the smaller saving from the larger one. **Example.** A sale price is the original price minus the discount amount. A £120 item with 25% off has a discount of £120 ÷ 4 = £30. Subtract it: £120 − £30 = £90. When comparing shops, calculate both sale prices before choosing the cheaper one. **Example.** Build a percentage by counting known parts. For 45%, use four 10% parts and one 5% part. Add four copies of the 10% amount and one copy of the 5% amount. You can also subtract known parts: 50% minus 5% gives 45%. Check that your chosen percentages add or subtract to the requested percentage. **Recap.** Build any percentage from 10% and other known facts, and always calculate the actual amount before comparing discounts. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Decimals and fractions (age 10+)](https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-10-mt_4K1dr204Hi) - [Bar Models for Ratios](https://lightmysky.com/learn/mathematics/bar-models-for-ratios-mt_ePXg_XyCKU) - [Ratio and proportion vocabulary](https://lightmysky.com/learn/mathematics/ratio-and-proportion-vocabulary-mt_ESgc4YBw-a) - [Multiplying decimals by whole numbers](https://lightmysky.com/learn/mathematics/multiplying-decimals-by-whole-numbers-mt_SoDP1fSQEB) ## Opens up - [Percentages as fractions](https://lightmysky.com/learn/mathematics/percentages-as-fractions-mt_ALUrJpY0cZ) - [Pie charts and line graphs](https://lightmysky.com/learn/mathematics/pie-charts-and-line-graphs-mt_bESTSBB0wK) - [Percentages (age 12+)](https://lightmysky.com/learn/mathematics/percentages-age-12-mt_iEXqN48w3x) - [Efficiency, Sankey diagrams, and work done](https://lightmysky.com/learn/science/efficiency-sankey-diagrams-and-work-done-mt_JyfLtl_nhw)