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Core ideas
- x% of N = x × N / 100
- Percentage change = (new − old) / old × 100
- Successive change: a% then b% gives a + b + ab/100 (use signs)
- Fraction shortcuts: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/8 = 12.5%, 1/10 = 10%
Worked example
A price rises 20% and then falls 20%. Net change = 20 − 20 − (20×20)/100 = −4%.
Common mistakes
- Applying the second percentage to the original value instead of the changed value.
- Mixing "percent" and "percentage points".