# How to reverse added percentage to a number

Firstly sorry for my bad English.

Assume I have some values like this:

109
5450
926500
etc...


I know all of these values already added with 9% like this :

100 + 9         (9      is 9% of 100)   = 109
5000 + 450      (450    is 9% of 5000)  = 5450
850000 + 76,500 (76500 is 9% of 850000) = 926500


What I want?

I need a formula to give it a value then return the value without 9%

For instance:

I give it 109 and return me 100

or

I give it 5450 and return me 5000

Any ideas?

• Just multiply by $100/109$... – Parcly Taxel May 27 '17 at 7:56
• Note that I don't have 100. I only have 109 – Hamed Kamrava May 27 '17 at 7:57
• That's all you need to do. – Parcly Taxel May 27 '17 at 7:58
• I don't get that! please show me an example for 5450. How do I get 5000 from 5450 ? (Note that I only have 5450) – Hamed Kamrava May 27 '17 at 8:01
• $5450×100÷109=5000$ – Parcly Taxel May 27 '17 at 8:01

Expanding on what was said on the comments, multiplying by $\frac{100}{109}$ works for all values. The fact that you happen to have a $109$ in your example was just a mere coincidence.

The way it works is: you have a value $V$. $9$% of it is just $0.09V$. If you add it to the original value you get

$$V + 0.09V = 1V + 0.09V = (1+0.09)V = 1.09V$$

All the values you have are $1.09V$ and you want to find the $V$. All you have to do is divide by $1.09$.

For example, $5450/1.09 = 5000$. But dividing by $1.09$ is the same as multiplying by $100/109$.

As Parcly Taxel says, multiply the larger value by the fraction $100/109$ to get the smaller value.

Equivalently, divide by $1.09$. (This is a single step on any calculator.)

Edit: For your example, $5450/1.09=5000$.

• Worked like a charm. – Hamed Kamrava May 27 '17 at 8:04