Technique
Unitary method: find one unit, then scale
Arithmetic • Ratio and Proportion
Statement
If units of a good cost , then one unit costs and units cost , provided the rate does not change with the quantity bought.
How to use it
- 1Divide by the given quantity to reach one unit, then multiply by the quantity wanted; never scale directly between two unequal bulk amounts.
- 2When several goods are linked by 'the cost of kg of equals that of kg of ', apply the move once per link and walk the chain.
- 3Carry the rate as a fraction rather than a decimal when the divisions are not exact, so nothing is rounded mid-chain.
Worked example
If pens cost Rs. , what do pens cost?
Step-by-step
- 1
Why: Dividing the bulk price by the quantity gives the price of one pen.
- 2
Answer
Rs.
Watch out
It assumes a constant rate. Bulk discounts, slab tariffs and a fixed charge added on top of a per-unit rate all break the proportionality, and then the unit price is not the same at every quantity.
Also known as
unitary method, rate per unit, cost of one then cost of many, price per kg, conversion chain