--- title: "Percentages as fractions" description: "Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using p" canonical: https://lightmysky.com/learn/mathematics/percentages-as-fractions-mt_ALUrJpY0cZ source: https://lightmysky.com/learn/mathematics/percentages-as-fractions-mt_ALUrJpY0cZ.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`. # Percentages as fractions Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100% Subject: Mathematics · Area: Ratio & Proportion · Ages 11 to 13 Page: https://lightmysky.com/learn/mathematics/percentages-as-fractions-mt_ALUrJpY0cZ ## Ready when they can - Convert fluently between percentages, fractions, and decimals - Express one quantity as a percentage of another - Calculate percentage increases and decreases and interpret percentages greater than 100% ## Lesson: Percentages as fractions Percent means per hundred. A percentage compares an amount with a stated whole or starting amount. That reference amount is 100%. Keep track of which amount is the whole before converting, comparing or calculating a change. *(drawing: Seven tenths equal seventy hundredths, or 70%.)* **Example.** To change a percentage to a fraction, write its number over 100. Simplify by dividing numerator and denominator by the same common factor. For 18%, write 18/100 and divide both by 2 to get 9/50. To change a percentage to a decimal, divide by 100: 18% = 0.18. These methods also work above 100%. **Example.** To change a fraction to a percentage, make equivalent hundredths or divide its numerator by its denominator and multiply by 100. For 11/20, multiply both numbers by 5: 55/100 = 0.55 = 55%. To change any decimal to a percentage, multiply by 100 to find the number before the % sign. Small decimals can give percentages below 1%: 0.0015 × 100 = 0.15, so 0.0015 = 0.15%. **Example.** To express one quantity as a percentage of a whole, write part/whole. Simplify first if helpful, then make hundredths or divide and multiply by 100. If 13 of 50 tickets are used, 13/50 = 26/100 = 26%. The denominator is the total number of tickets, not the unused tickets. Percentages may be greater than 100%. They compare with the starting whole, rather than describing only parts inside it. For a positive starting amount, anything above 100% is more than that starting amount. For a starting amount of zero, multiplying by any percentage still gives zero. **Example.** To calculate an amount above 100%, keep the full starting amount and add the extra percentage. For 140% of £50, keep £50 and add 40%: four 10% parts of £5 make £20. The result is £70. Useful extra parts include 20% as one fifth and 25% as one quarter. Divide the starting amount by 5 or 4 to find them. **Example.** For percentage change, first find the increase or decrease. Divide that change by the positive original amount, then multiply by 100 to find the number before the % sign. The original is the reference whole. From £90 to £99, the increase is £9, so 9/90 × 100 = 10, giving a 10% increase. From £90 to £81, the decrease is also £9, giving a 10% decrease. Name the direction as well as the percentage. **Recap.** A percentage is a fraction out of 100, and the same amount can be written as a fraction, a decimal, or a percentage. ## Practice 20 questions on this page, each with its working shown. ## Needs first - [Moving between representations of a relationship](https://lightmysky.com/learn/mathematics/moving-between-representations-of-a-relationship-mt_9KmVWCuh5_) - [Proportional Reasoning Vocabulary](https://lightmysky.com/learn/mathematics/proportional-reasoning-vocabulary-mt_ATYLKt0je-) - [Calculating percentages](https://lightmysky.com/learn/mathematics/calculating-percentages-mt_PNSyfH56eQ) ## Opens up - [Percentages (age 12+)](https://lightmysky.com/learn/mathematics/percentages-age-12-mt_iEXqN48w3x) - [Fractions and percentages of amounts](https://lightmysky.com/learn/mathematics/fractions-and-percentages-of-amounts-mt_J339bO7qLe)