These questions ask you to reduce a comparison to a per-one rate, recognise equivalent rates or use a known rate to recover a total. Units are part of the calculation, not a label added afterwards.
Translate per into division
Read the requested unit phrase first. Quantity A per quantity B means divide A by B and keep the compound unit A per B. For example, 156 kilometres in 12 hours gives 156 divided by 12, or 13 kilometres per hour. The reciprocal, hours per kilometre, requires the reverse division and has a different numerical value.
| Signal | Method |
|---|---|
| A quantity per one container, person or time unit | Divide the total quantity by the number of containers, people or time units. |
| The reciprocal rate is requested | Reverse both the division and the unit order. For instance, 3 items per minute corresponds to one third of a minute per item. |
| A rate and a number of units are known | Multiply. A flow of 7 litres per minute for 9 minutes produces 63 litres because the minute units cancel. |
| A larger time or measurement unit is requested | Convert consistently after finding the rate, and keep exact values unless a rounding instruction is given. |
Use a unit check before accepting a calculation. If you divide a price by a mass, the result is money per unit of mass; if you divide the mass by the price, it is mass per unit of money. Both can be meaningful, but only one matches the wording.
Where mistakes happen
| Tempting route | How to reject it |
|---|---|
| Divide in one direction but write the units in the other | Carry the units through the fraction. The quantity divided goes before per, and the divisor goes after it. |
| Keep the same numerical value when reversing a rate | Reciprocal rates reverse the division as well as the words. Except for the special value one, the number must change. |
| Add or subtract quantities with unlike units | Distance minus time or volume plus duration has no unit-rate meaning. Use division to reduce a comparison to one unit. |
| Use a near time conversion | Convert with exact scale factors. Minutes become seconds by multiplying by 60, so a rounded-looking nearby value needs checking. |
Try it
A robot moves 96 m in 12 seconds at a steady rate. Enter its rate in m per second.
A 450 g bag of seeds costs 3.60 dollars. Which unit-rate statements are true? Select all that apply.
- The bag provides 125 g per dollar.
- The price is 0.008 dollars per g.
- The price is 8 dollars per kg.
- The bag provides 0.008 g per dollar.
- The price is 125 dollars per g.
A pump moves water at 6 litres per minute for 9 minutes. How much water does it move?
- 1.5 litres
- 15 litres
- 54 litres
- 63 litres