A 2:5 ratio: two parts, or a share of the whole?
“Two to five” does not always mean that the first share is 40% of the total. Five may describe only the second share, making seven parts altogether. Naming both sides prevents that confusion.
Name both sides and keep their order
A ratio compares quantities in a stated order: A:B is not B:A. Convert comparable measurements to the same unit before simplifying; 2 metres to 50 centimetres is not the ratio 2:50.
Reducing 20:50 to 2:5 preserves the relationship. Scaling multiplies both sides by the same factor; adding the same number to both sides generally changes it.
References: OpenStax — Ratios, rates and unit prices
The whole contains all the parts
Splitting a total in a 2:5 ratio creates 7 parts. The first share is 2/7 of the total and the second is 5/7. The fraction 2/5 instead compares the first share with the second.
Divide the total by the combined part count to find one part, then allocate it. If money or indivisible objects require rounding, check that the final shares still add to the original total.
Scaling is different from splitting
When you know the desired first quantity, find the factor that takes the original first part to it, then apply that factor to the second part. No total is needed; it follows from the two scaled quantities.
Proportion is a mathematical model, not permission to enlarge every recipe or industrial process without review. Use it where a linear relationship is a sound assumption for the task.
Worked example: paper for two activities
To distribute 350 sheets in a 2:5 ratio, divide 350 by 7 to get 50 sheets per part. The first activity receives 100 and the second 250, totalling 350.
For a separate task, suppose the first activity needs 80 sheets while the same ratio is retained. The scale is 80 ÷2 =40, so the second needs 5 ×40 =200. The total is now 280; 80 was the first share, not the whole.