Student & Academic · Cheatsheet

Percentages and Ratios Cheatsheet

Calculate percentage shares, increases, discounts, and ratios. Use worked examples to distinguish percentage points from relative percentage changes.

37 commands 7 sections

Start with the right quantity

25% = 0.25 = 1/4 Divide the percentage number by 100
50% = 0.5 = 1/2 Half of the whole
75% = 0.75 = 3/4 Three quarters of the whole
0.08 × 100% = 8% Convert a decimal to a percentage
3/5 × 100% = 60% Divide the numerator by the denominator, then multiply by 100%

New = original × (1 + p / 100) Increase a value by p percent
80 increased by 15% = 92 Calculate 80 × 1.15
New = original × (1 - p / 100) Decrease a value by p percent
80 reduced by 15% = 68 Calculate 80 × 0.85
Original = final / (1 + p / 100) Reverse an increase when the divisor is nonzero
Original = final / (1 - p / 100) Reverse a decrease below 100%

Change % = (new - old) / old × 100% Use a positive original value for the usual increase interpretation
From 40 to 50 = 25% increase Calculate (50 - 40) / 40 × 100%
From 50 to 40 = 20% decrease Use 50 as the original value for the reverse change
From 20% to 25% = 5 percentage points Subtract the two percentage values
From 20% to 25% = 25% relative increase Calculate (25 - 20) / 20 × 100%
20% off, then 10% off = 28% off Multiply 0.8 × 0.9; successive discounts do not add