Work out the value for a single unit, then multiply up. If 4 pens cost 60 rupees, one pen costs 15, so 7 pens cost 105.
Why it is worth learning
A ratio can be set up backwards without you noticing. The unitary method is harder to reverse, because the middle step has a meaning you can say out loud.
Direct: 1 pen costs 60 ÷ 4. Inverse: 1 worker takes 6 × 10 = 60 days. Ask whether one worker should be faster or slower than six.
| Situation | Step down to one | Step up to what you want |
|---|---|---|
| 4 pens cost Rs 60. Find 7 pens | 1 pen: 60 ÷ 4 = Rs 15 | 7 pens: 7 × 15 = Rs 105 |
| 6 workers take 10 days. Find 15 | 1 worker: 6 × 10 = 60 days | 15 workers: 60 ÷ 15 = 4 days |
Write the middle step as a sentence, not a bare number. One pen costing 240 rupees when four cost 60 sounds absurd, and hearing that is the check.
Problems with two changes at once
Handle one change at a time. More workers shrinks the days; more walls grows them.
Ask whether the answer should be larger or smaller than the number you started with, and check that it is.
Ten machines fill ten times as many bottles, but ten people do not walk ten times as far. Read the situation before reaching for the arithmetic.
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