Grow or shrink any value by a percentage, with the multiplier shortcut shown.
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The Coddy math course teaches the method itself - you work each step on an interactive board and get told exactly where a move went wrong.
To increase 60 by 25%, first work out what 25% of 60 is - a quarter of 60 is 15 - and then add it on: 60 + 15 = 75. Decreasing works the same way with a subtraction at the end: 60 - 15 = 45. Two steps, and the first one is the ordinary percentage-of question from the page next door.
There is also a one-step route, and it is the one worth graduating to: increasing by 25% is multiplying by 1.25, because you keep the whole (100%) and add the quarter (25%) in the same move. Decreasing by 25% is multiplying by 0.75. This page shows both routes on every calculation - the two-step version explains, the multiplier version scales, and they always agree.
The multiplier is also the key to the reverse question. A price that became 75 after a 25% increase was not 75 minus 25%: undoing a rise means dividing by 1.25, which takes you back to exactly 60. Subtracting the same percent lands at 56.25 - close, wrong, and the single most common percentage mistake in the wild.
The percentage of the value, as on the percentage calculator: 25% of 60 is 25/100 × 60 = 15.
Increase: 60 + 15 = 75. Decrease: 60 - 15 = 45. The direction is the only difference between the two.
Increase by 25% = × (1 + 25/100) = × 5/4. Decrease by 25% = × 3/4. One step, and the form every spreadsheet formula and compound-interest calculation uses.
Each percentage change and the single multiplication it is. The decrease column is not the increase column backwards - that asymmetry is the point.
| Change | Multiplier | 60 becomes |
|---|---|---|
| +5% | 1.05 | 63 |
| +10% | 1.1 | 66 |
| +12.5% | 1.125 | 67.5 |
| +20% | 1.2 | 72 |
| +25% | 1.25 | 75 |
| +50% | 1.5 | 90 |
| +100% | 2 | 120 |
| -5% | 0.95 | 57 |
| -10% | 0.9 | 54 |
| -20% | 0.8 | 48 |
| -25% | 0.75 | 45 |
| -50% | 0.5 | 30 |
60 + 25%25% of 60 is 15, and 60 + 15 = 75. In one move: 60 × 1.25 = 75. Both routes are shown on every answer, because the two-step one explains what happened and the multiplier is the one you will actually use at speed.
60 - 25%The same part - 15 - taken off instead of added on: 60 - 15 = 45, or 60 × 0.75 in one step. Note the multiplier is 0.75, not -1.25: a decrease keeps three quarters, it does not multiply by a negative.
48 + 12.5%12.5% is exactly 1/8, so the part is 48/8 = 6 and the answer is 54. Recognising the eighth turns a decimal-looking problem into whole-number arithmetic - the fraction column of the cheat sheet is there for exactly this.
75 after +25%If 75 is the price AFTER a 25% increase, the original was 75 ÷ 1.25 = 60. Taking 25% off 75 instead gives 56.25 - a different number, because that 25% is measured against 75 rather than the original. Undo a multiplication with a division, always.
Work out the percentage of it and add it on: 25% of 60 is 15, so 60 becomes 75. Or in one step, multiply by (1 + p/100): 60 × 1.25 = 75. Both give the same answer; the two-step route explains, the multiplier route scales.
The same two steps with a subtraction: 25% of 60 is 15, and 60 - 15 = 45. As one multiplication it is × (1 - p/100) - here × 0.75. A decrease keeps a fraction of the value; it never multiplies by a negative.
An increase of p% keeps everything you had (100%) and adds p% more, so the new value is (100 + p)% of the old - one multiplication by (1 + p/100). It is faster, it chains correctly when changes compound, and it is the only sane way to undo a change: divide by the multiplier.
Divide by the multiplier. After a 25% rise the price is 1.25 times the original, so the original is the new price ÷ 1.25. Subtracting 25% from the new price is the classic error - it measures the percent against the wrong base and lands below the true original.
Because the second percent has a different base. 100 up 10% is 110; 110 down 10% is 99. As multipliers: 1.1 × 0.9 = 0.99, a 1% loss. Percent changes compound - which is also why they cannot be added across periods.
Yes - they are all this exact operation under different names. Adding 20% VAT is × 1.2; a 15% tip is × 1.15; a year of 4% interest is × 1.04, and n years of it is × 1.04ⁿ because the changes compound. Type the value and the rate, and the working is the same.
