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Level 5Grade 5skill: unitary_method· 7 min read

The Unitary Method: the Value of One

In short: The unitary method solves "this many cost this much" problems in two moves: divide the total to find the value of one unit, then multiply that value by the count you actually want. Find one, then keep going — one is a bridge, not the answer.

How the unitary method works

Almost every "if this many cost this much, what about that many" question hides one small fact: the value of a single unit. The unitary method is just the habit of finding that value first, then building back up to whatever you were actually asked for.

It is always the same two moves. First you divide the total by the number of units you were given, which tells you what one unit is worth. Then you multiply that per-one value by the new number of units. Divide down to one, multiply up to many.

The reason it never lets you down is that the per-one value stays fixed. If eight notebooks cost $96, one notebook is $12 whether you go on to buy three of them or thirty. That fixed "per one" number is the bridge between the amount you know and the amount you want.

  1. Spot the fact you are given: some number of units and their total value (8 notebooks → $96).
  2. Divide the total by that number of units to find the value of ONE unit (96 ÷ 8 = $12).
  3. Multiply the value of one unit by the new count you are asked about (12 × 5 = $60).
  4. Check the units and the size: more units should cost more, fewer should cost less.

Why finding "one" always works Why it works

Down to one
To get the value of a single unit, divide the total by how many units you have.

60 stickers shared across 5 sheets → 60 ÷ 5 = 12 stickers on each sheet.

Up to many
Multiply the value of one unit by the new count you want.

12 stickers per sheet × 9 sheets = 108 stickers.

One stays fixed
The per-one value does not change when the count changes — that is the whole reason the method is safe.

Whether you order 4 samosas or 40 at $8 each, one samosa is still $8.

Here is the one insight worth keeping: one is a bridge, not a destination. It is tempting to compute the value of one and stop, as if that were the answer. It almost never is — it is the stepping stone you multiply from.

Worked examples

7 identical markers cost $91. What do 4 markers cost? = $52
  1. Value of one marker: 91 ÷ 7 = $13
  2. Value of four markers: 13 × 4 = $52
A car travels 240 km on 8 litres of fuel. How far can it go on 5 litres? = 150 km
  1. Distance on one litre: 240 ÷ 8 = 30 km
  2. Distance on five litres: 30 × 5 = 150 km
9 identical bricks weigh 3600 g altogether. What do 4 bricks weigh? (Watch the size of your answer.) = 1600 g
  1. Weight of one brick: 3600 ÷ 9 = 400 g
  2. Weight of four bricks: 400 × 4 = 1600 g
6 concert tickets cost $450. What do 11 tickets cost? (Here the number you want is bigger than the number you were given — the method still works.) = $825
  1. Cost of one ticket: 450 ÷ 6 = $75
  2. Cost of eleven tickets: 75 × 11 = $825

Common mistakes

Losing track of magnitude when scaling

✗ $600

The student found one notebook correctly at $12, then wrote 12 × 5 = 600 — a tenfold magnitude slip. Five notebooks at $12 each cannot cost $600.

Fix: 12 × 5 = 60, not 600. Sanity-check the size: five notebooks should cost a bit more than four, nowhere near $600.

place_value_slip

Finding one and forgetting to scale up

✗ $12

The student divided perfectly, got $12 for one notebook, and stopped there — answering the value of one when the question asked for five. Finding one unit is only half the method; the count you were asked for still needs building up.

Fix: Reread the question after finding one. It asked for 5 notebooks, so finish the job: 12 × 5 = $60.

partial_computation

Practice

Work each one in two moves: divide to find the value of one unit, then multiply up to the count you are asked for. Multiply your quotient back to check it, and make sure the size of your answer makes sense.

Related skills

First, make sure of

Frequently asked questions

What exactly is the unitary method?

It is a two-step way to solve "this many cost this much, so what about that many" problems. You first divide to find the value of a single unit, then multiply that value by the number of units you actually want.

Why do I divide first and then multiply?

Dividing the total by the number of units gives you the value of one unit — the per-one amount that stays the same no matter how many you buy. Once you know what one is worth, multiplying by any new count scales straight up to the answer.

What is the most common mistake with the unitary method?

Stopping after you find the value of one. That number is a stepping stone, not the answer. Always reread the question and multiply the per-one value by the count you were actually asked about.

How can I check my answer quickly?

Two checks. Multiply your quotient back (8 × 12 should give the original 96) to catch division slips, and glance at the size — more units should cost more, fewer should cost less.

Does the method still work when the number I want is bigger than the number I'm given?

Yes. Finding the value of one works the same way whether you scale down or up. If 6 tickets cost $450, one ticket is $75, so 11 tickets cost 75 × 11 = $825.