Write what each number measures
A rate links unlike units, such as kilometres per hour or patients per clinician. A ratio compares quantities in a stated order. Add unit labels beside the values before calculating. This makes inverted rates and mismatched time periods visible.
- Quantity
- Unit
- Time period
- Required output unit
Choose scaling or the unitary method
If a ratio is 3:5 and the first quantity becomes 12, the scale factor is 4, so the second becomes 20. When the scale is not obvious, find the value for one part and multiply. Both methods preserve the same proportional relationship.
- Direct scale when the multiplier is clear
- One-part value for awkward totals
- Keep ratio order fixed
Worked example: convert before dividing
A vehicle travels 150 kilometres in 2 hours 30 minutes. Convert 30 minutes to 0.5 hours, giving 2.5 hours. The average speed is 150 ÷ 2.5 = 60 kilometres per hour. Treating 2 hours 30 minutes as 2.30 hours would produce the wrong rate.
- 30 minutes = 0.5 hours
- Total time = 2.5 hours
- Distance ÷ time = 60 km/h
Use dimensional cancellation
Arrange conversion factors so unwanted units cancel. To convert £ per kilogram into pence per 100 grams, convert pounds to pence and kilograms to ten lots of 100 grams. Tracking the unit path is safer than memorising isolated tricks.
- Write the starting unit
- Multiply by conversion factors
- Cancel units
- Check the requested final unit
Distinguish direct and inverse relationships
More items at a fixed price create a direct relationship. More workers completing a fixed job, under simplified equal-rate assumptions, can create an inverse relationship with time. Decide which variable should rise or fall before using a proportion.
- Predict direction first
- State what remains fixed
- Reject a result that moves the wrong way
Check scale and realism
A unit conversion can shift a value by 10, 100 or 1,000. Estimate the expected direction and size before calculating. If converting metres to centimetres, the numeric value must grow. This quick sense-check catches misplaced decimal points.
- Direction
- Power of ten
- Ratio order
- Final unit
Frequently asked questions
What is the difference between a ratio and a rate?
A ratio compares quantities; a rate usually compares quantities with different units.
Should I convert units before calculating?
Yes, make time, distance, mass or currency units compatible first.
How do I avoid reversing a ratio?
Write labels above both parts and preserve the order stated in the question.
How can I check a unit conversion?
Track cancelled units and predict whether the numeric value should become larger or smaller.
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