Percentage Calculations: Three Common Mistakes
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Start with the right base
A percentage compares an amount with a base. If an item costs $80 before a 25% discount, the discount is $20 and the new price is $60. The original $80 matters: changing the base changes the amount represented by the same percentage.
To find a percentage of a total, multiply the total by the rate and divide by 100. To find what percentage one amount represents of another, divide the part by the total and multiply by 100. Thus $20 is 25% of $80, but about 33.33% of $60.
A decrease and an increase do not cancel out
A 20% decrease takes 100 down to 80. Increasing 80 by 20% then gives 96, not 100. Returning to 100 requires a 25% increase because the gain of 20 is measured against the new base of 80.
Likewise, successive discounts of 20% and 10% amount to a 28% discount: 100 × 0.8 × 0.9 = 72. Simply adding the rates would incorrectly suggest a 30% discount.
Separate percentage points from relative change
If a rate rises from 10% to 12%, it increases by two percentage points. Its relative increase is 20%: (12 − 10) ÷ 10 × 100. Both statements describe the same change using different units.
Before sharing a result, state what is being compared and identify the base. Keep the intermediate decimals and round only the final answer to a useful precision.