--- title: "Compound Units" description: "Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units" canonical: https://lightmysky.com/learn/mathematics/compound-units-mt_kLQOzZYrd5 source: https://lightmysky.com/learn/mathematics/compound-units-mt_kLQOzZYrd5.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`. # Compound Units Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units Subject: Mathematics · Area: Ratio & Proportion · Ages 11 to 14 Page: https://lightmysky.com/learn/mathematics/compound-units-mt_kLQOzZYrd5 ## Ready when they can - Calculate average speed given distance and time, converting between km/h and m/s if needed - Compare unit prices of two products sold in different quantities to find the better deal - Use the density formula to find mass, volume, or density given the other two values ## Lesson: Compound Units: Speed, Price, and Density Some units come from dividing one measurement by another. Speed is distance ÷ time. Unit price is cost ÷ quantity. Density is mass ÷ volume. These are called compound units. **Example.** A cyclist rides 30 km in 2 hours. Speed = distance ÷ time = 30 ÷ 2 = 15 km/h. To change km/h into metres per second, turn the distance into metres and the time into seconds: 18 km/h is 18,000 m in 3,600 s, and 18,000 ÷ 3,600 = 5 m/s. *(drawing: Oat flakes cost 60p per 100 g. Rice puffs cost 45p per 100 g. The lower bar is the better deal.)* **Example.** A rock has a mass of 150 g and a volume of 50 cm³. Density = mass ÷ volume = 150 ÷ 50 = 3 g/cm³. Turn it round to find a mass: a 40 cm³ piece of the same rock has mass 3 × 40 = 120 g. **Tip.** Check the units before you divide. If time is in minutes but you want km/h, convert it to hours first. The answer's units come from the division too, like km/h or g/cm³. **Recap.** Compound units come from dividing one measurement by another: speed, unit price, and density all follow amount ÷ amount, matched to the right units. ## Practice 15 questions on this page, each with its working shown. ## Needs first - [Simple formulae](https://lightmysky.com/learn/mathematics/simple-formulae-mt_3qrCtdoVAU) - [Proportional Reasoning Vocabulary](https://lightmysky.com/learn/mathematics/proportional-reasoning-vocabulary-mt_ATYLKt0je-) - [Proportion Graphs](https://lightmysky.com/learn/mathematics/proportion-graphs-mt_FspV_imUGK) - [Unit Conversions](https://lightmysky.com/learn/mathematics/unit-conversions-mt_tpT9brpI6D) ## Opens up - [Modelling Motion in a Straight Line](https://lightmysky.com/learn/mathematics/modelling-motion-in-a-straight-line-mt_no78_6w1rS) - [Reading Distance-Time Graphs](https://lightmysky.com/learn/science/reading-distance-time-graphs-mt_OUv-QXmW7_) - [Speed & Distance-Time Graphs](https://lightmysky.com/learn/science/speed-and-distance-time-graphs-mt_q-1a86ydgU) - [The Derivative as a Rate of Change](https://lightmysky.com/learn/mathematics/the-derivative-as-a-rate-of-change-mt_RqyLE3jrAW) - [Ratio Problems: Sharing, Changing and Combining](https://lightmysky.com/learn/mathematics/ratio-problems-sharing-changing-and-combining-mt_vJelayH4uv) - [Calculating with Bounds in Compound Measures](https://lightmysky.com/learn/mathematics/calculating-with-bounds-in-compound-measures-mt_zfMz7x8dlf)