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Unitary Method of Solution (F)

Master the unitary method: find one, then many. Use proportional reasoning to solve time, cost, speed and recipe problems in GCSE Foundation Maths.

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Fascinating Fact:

In a print shop, 8 posters take 40 minutes, so 1 poster takes 40 ÷ 8 = 5 minutes. For 30 posters, time = 30 × 5 = 150 minutes.

In GCSE Maths (Foundation), the unitary method solves proportion problems by finding the value for a single unit first, then scaling up or down. It’s used for costs, recipes, speeds, maps, and best buys.

Key Terms

Unitary method: A step-by-step approach: find the value of one unit, then multiply to get many (or divide to get fractions of a unit).
Proportion: When two quantities increase or decrease at the same rate; their ratio stays constant.
Scale factor: The number you multiply or divide by to move between equivalent amounts.

Frequently Asked Questions (Click to see answers)

What is the unitary method in simple terms?

The unitary method means finding the value of one unit first, then using multiplication or division to get the required number of units.

How do I solve cost problems with the unitary method?

Divide the total cost by the quantity to get a one-unit price, then multiply by the new quantity. Example: 6 pens cost £9 → £1.50 each, so 14 pens cost £21.

How do I use the unitary method for speed, distance and time?

Find one unit of time or distance. If 180 km takes 3 h, that’s 60 km per hour. For 2.5 h, distance = 60 × 2.5 = 150 km.