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
What a learner can do afterwards
- 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
1 · Read
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.
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.
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.
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.
Two readings and eight practice questions were written for this proportional reasoning topic. The videos are linked from their original sources.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
16 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.