Mathematics · Arithmetic
Percentages laboratory: choose the right base
Five paths with editable examples: groups A and B, fractions, change and inverse formulas, successive changes and returning to the initial value.
Read the full explanation1 / 5
Groups and rates
Group A is a% of the population and b% of prisoners. Do not confuse its share among prisoners with its within-group rate. All data are hypothetical teaching examples.
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Fraction → %
Enter a fraction and observe the ratio, conversion and explicit multiplication by 100%.
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Change and inverses
Choose the unknown. V is the initial value, N the final value and P the signed change number: P = −3.8 means a 3.8% decrease.
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Successive changes
The second change applies to the value already changed, not the initial base. Compare the result with the simple sum of the percentages.
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Return to the start
Follow the 2014 method: find the reciprocal, convert it to a percentage with × 100%, then subtract 100%. Try −10% and +5%, also checked using the Excel formula.
Displayed results are rounded; calculations use unrounded values. In the birth problem the input figures are also rounded: the reconstructed value is not the exact official count.