Mathématiques

The Percentage Multiplier

1.15 adds 15%, 0.85 takes it off, 1.025 adds 2.5%. The conversion table, why a 15% rise then a 15% cut leaves you 2.25% down, and how to reverse either.

Percentage multiplier

A percentage multiplier is the single number an amount is multiplied by to apply a percentage change, such as 1.15 for a 15% increase.

Aussi appelé: Decimal multiplier, The multiplier method
Où les élèves le rencontrent: Grade 8 mathematics, and used throughout GCSE and IGCSE percentage change, compound interest, depreciation and reverse percentage questions.

La réponse en bref
A percentage multiplier is the single number that applies a percentage change in one multiplication: 1.15 for a 15% increase, 0.85 for a 15% decrease, 1.025 for 2.5% up. Increases are 1 plus the decimal, decreases are 1 minus it, and repeated changes multiply together.

Un exemple

240 increased by 15%: 240 × 1.15 = 276

The 1 keeps the original amount and the 0.15 adds the extra 15%, so one multiplication does both jobs. Working out 15% of 240 and then adding it on gives the same 276, in two steps instead of one — and the multiplier version is the one that survives being repeated.

The conversion table

Turn the percentage into a decimal, then add it to 1 for an increase or subtract it from 1 for a decrease. The only place this trips people is percentages that are not whole numbers, where 2.5% becomes 0.025 rather than 0.25.

Repeated changes are where multipliers earn their place. Applying the same change n times means raising the multiplier to the power n, which turns a year-by-year table into a single calculation.

Increase by 15% → × 1.15
Decrease by 15% → × 0.85
Increase by 2.5% → × 1.025
Decrease by 2.5% → × 0.975
Increase by 100% → × 2
Decrease by 100% → × 0
Increase by 5% each year for 3 years → × 1.05³ = × 1.157625

Why 15% on and 15% off does not bring you back

Start with 240 and add 15%: 240 × 1.15 = 276. Now take 15% off that: 276 × 0.85 = 234.60. You are 5.40 short of where you started, and no arithmetic slip has occurred.

The reason is that the 15% was added to 240 and then removed from 276, and 15% of the larger figure is more than 15% of the smaller one. The combined multiplier says it in one line: 1.15 × 0.85 = 0.9775, which is a fall of 2.25%. The same thing happens with any pair of equal-sized rises and falls.

Going backwards

To undo a percentage change you divide by its multiplier rather than applying the opposite one. A price of 276 after a 15% rise came from 276 ÷ 1.15 = 240. A price of 234.60 after a 15% discount came from 234.60 ÷ 0.85 = 276.

This is the whole of reverse percentages, and it is why questions that give you a price 'after VAT' or 'after a 20% discount' are one division rather than a puzzle. The trap they are testing is whether you take 15% off the new figure instead — which, as the previous section shows, lands somewhere else.

The net fall left by a 15% rise followed by a 15% cut, since 1.15 × 0.85 = 0.9775: 2.25%The net fall left by a 15% rise followed by a 15% cut, since 1.15 × 0.85 = 0.9775

Questions fréquentes

What is the multiplier for a 15% decrease?

0.85, because you are keeping 85% of the original. Take the percentage as a decimal, 0.15, and subtract it from 1. The quick sense check is that the multiplier for any decrease must be less than 1, and the multiplier for any increase must be more than 1.

How do I write 2.5% as a multiplier?

2.5% is 0.025, so the multiplier for an increase is 1.025 and for a decrease 0.975. The common error is writing 1.25, which would be a 25% increase — ten times too much. Dividing by 100 rather than moving the decimal point by eye avoids it.

What multiplier do I use for compound interest over several years?

The annual multiplier raised to the number of years. At 5% a year for 3 years, that is 1.05³ = 1.157625, so 8,000 becomes 8,000 × 1.157625 = 9,261. Depreciation works identically with a multiplier below 1: losing 20% a year for 4 years is × 0.8⁴.

Why doesn't adding 15% then taking 15% off return the original amount?

Because the two percentages are calculated from different amounts. Adding 15% to 240 gives 276, and 15% of 276 is larger than 15% of 240, so more comes off than went on. The overall multiplier is 1.15 × 0.85 = 0.9775, leaving you 2.25% below where you started.

Dernière mise à jour 21 août 2026