How to Find a Percentage of a Quantity Mentally
Break awkward percentages into friendly ones such as 10% + 5% or 50% − 1%.
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Topic archive
Category: Percentages & Ratios
The Ratio Rule That Prevents Most Unit Mistakes
Before simplifying a ratio, make sure both quantities use the same unit. That one habit prevents a large class of mistakes.
Read the explanation →Percentage Points vs Percentage Change: The Difference in One Example
If a rate rises from 20% to 25%, the increase is 5 percentage points but 25% in relative terms. Those are different statements.
Read the explanation →Why 15% Off and 15% Back Does Not Return to the Starting Price
A percentage decrease and the same percentage increase act on different starting amounts. Here is the quickest way to see the difference.
Read the explanation →A Fast Way to Turn Common Fractions into Percentages
Some fractions are worth memorising because they appear everywhere in percentage work and mental maths.
Read the explanation →Best Buy Questions: Use a Unit Rate, Not a Guess
Turn each option into a price per one item, per 100 g, or per litre so the comparison is fair.
Read the explanation →How to Share an Amount in a Given Ratio
Add the ratio parts, find the value of one part, then build each share from there.
Read the explanation →Can You Use Percentage Change Across Zero?
When a value crosses zero, the usual percentage-change formula still computes something, but the result often needs careful interpretation.
Read the explanation →How to Find the Original Price Before VAT Was Added
If a bill already includes VAT, divide by the VAT multiplier to recover the original amount before tax.
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