--- title: "Proportional Reasoning Vocabulary" description: "Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts" canonical: https://lightmysky.com/learn/mathematics/proportional-reasoning-vocabulary-mt_ATYLKt0je- source: https://lightmysky.com/learn/mathematics/proportional-reasoning-vocabulary-mt_ATYLKt0je-.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`. # Proportional Reasoning Vocabulary Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts Subject: Mathematics · Area: Ratio & Proportion · Ages 11 to 14 Page: https://lightmysky.com/learn/mathematics/proportional-reasoning-vocabulary-mt_ATYLKt0je- ## Ready when they can - Distinguish between 'direct proportion' and 'inverse proportion' with real-world examples - Use 'rate', 'speed', and 'density' correctly and explain what units they are measured in - Calculate using compound measures — e.g. work out the speed of a car that travels 120 miles in 2 hours ## Lesson: Proportional Reasoning: The Right Words You already compare amounts with ratios. Now it's time to learn the exact words mathematicians use for how two amounts behave together. When two quantities are in direct proportion, their ratio stays the same. Double one, and the other doubles too. *(drawing: Each apple costs $1, so the total cost grows right along with the number of apples. That's direct proportion.)* Not every relationship works that way. In inverse proportion, one quantity goes up while the other goes down, and for positive quantities their product stays the same. If more workers join a fixed job, and each worker works at the same steady rate, it takes fewer days to finish. *(drawing: Twice as many workers finish the job in half the time. That's inverse proportion.)* Here's how to keep the vocabulary straight. A rate compares two different kinds of quantities, like miles and hours. A unit rate is the amount for just one unit, such as 60 miles per hour. Speed and density are quantities measured in compound units: speed is distance divided by time, density is mass divided by volume. A scale factor tells you how much a map or drawing has been enlarged or shrunk. **Recap.** Direct proportion means the ratio of two amounts stays the same, inverse proportion means their product stays the same, and words like rate, unit rate, compound unit, and scale factor let you describe those relationships precisely. ## Practice 16 questions on this page, each with its working shown. ## Needs first - [Advanced Maths Vocabulary](https://lightmysky.com/learn/mathematics/advanced-maths-vocabulary-mt_3rTIyJDw7-) - [Ratio Notation](https://lightmysky.com/learn/mathematics/ratio-notation-mt_XWSGuFW7It) ## Opens up - [Scale drawings and maps](https://lightmysky.com/learn/mathematics/scale-drawings-and-maps-mt_1badik7iKJ) - [Proportion](https://lightmysky.com/learn/mathematics/proportion-mt_5mIcmKRCgA) - [Percentages as fractions](https://lightmysky.com/learn/mathematics/percentages-as-fractions-mt_ALUrJpY0cZ) - [Percentages (age 12+)](https://lightmysky.com/learn/mathematics/percentages-age-12-mt_iEXqN48w3x) - [Compound Units](https://lightmysky.com/learn/mathematics/compound-units-mt_kLQOzZYrd5) - [Dividing Quantities by Ratio](https://lightmysky.com/learn/mathematics/dividing-quantities-by-ratio-mt_nOCPx5qw0Z) - [Unit Conversions](https://lightmysky.com/learn/mathematics/unit-conversions-mt_tpT9brpI6D) - [One Quantity as a Fraction](https://lightmysky.com/learn/mathematics/one-quantity-as-a-fraction-mt_xAf2bu9wYK) - [Ratio Notation and Relationships](https://lightmysky.com/learn/mathematics/ratio-notation-and-relationships-mt_yK51ZnKA8m)