Percentages
Recovering the original from a decreased value
The backward form, used when you know the reduced price and the discount rate. Undefined when p is 1.
The Formula
Original = New / (1 - p)
The backward form, used when you know the reduced price and the discount rate. Undefined when p is 1.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| V1 | Known decreased value | number | The figure in hand after the cut — 90 in the standard case. |
| p | Decrease written as a decimal | decimal | 0.25 for a 25% decrease, leaving 0.75 as the divisor. |
| V0 | Recovered original value | number | 90 / 0.75 = 120, the figure the discount was applied to. |
What Each Symbol Means
V1number
Known decreased value
The figure in hand after the cut — 90 in the standard case.
pdecimal
Decrease written as a decimal
0.25 for a 25% decrease, leaving 0.75 as the divisor.
V0number
Recovered original value
90 / 0.75 = 120, the figure the discount was applied to.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate percent decrease page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Percent Decrease, filed under Math. Every number the guide produces comes from substituting into this one line.