Bounds, ratios and rates
Use measurement intervals and proportional reasoning instead of guessing an operation.
What you will learn
- Find bounds of products of positive measurements.
- Link ratios and recognise inverse proportion.
A rounded measurement is an interval
If a length is rounded to the nearest 0.1 cm, its true value lies within 0.05 cm of the stated measurement. The lower bound is included under the usual rounding convention; the upper endpoint is the limiting value. For a product of positive lengths, the upper bound uses both upper bounds.
Do not round intermediate bounds. If the question asks for the exact upper bound, give the full product rather than a three-significant-figure approximation.
Connect ratios through a shared quantity
To combine A:B and B:C, first make the B terms equal. Then join the ratios. Add the parts when a total is supplied; divide the total by that sum to find the value of one part.
Decide what stays constant
For identical workers or pumps, a fixed job requires a constant amount of worker-time or pump-time. More workers therefore mean less time. This is inverse proportion, provided each worker has the same constant rate and they do not interfere with one another.
Worked example
Three identical pumps fill a tank in 16 hours. How long do eight take at the same rate?
Show the worked solution
- The job takes 3 × 16 = 48 pump-hours.
- Divide the required work by eight pumps: 48/8 = 6.
Answer 6 hours
Common mistakes
- Do not multiply the time by the increase in the number of pumps.
- For positive lengths, using rounded values instead of endpoint bounds does not give an upper bound.
What can you explain now?
A:B = 2:3 and B:C = 6:5. If the total is 150, find C.
Compare with the explanation
50
The combined ratio is 4:6:5. There are 15 parts, each worth 10, so C is 50.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.