# Getting percentage difference between two numbers?

For example, if someone got a raise in salary and they were getting paid 80,000 and are now getting paid 85,000 how can you work out what percentage their raise was?

Percentage change : 100 % times the (Fractional change )

Fractional change : $\frac{85000-80000}{80000}$=$\frac{5000}{80000}$=$\dfrac{1}{16}$

Percentage change : $100\cdot\dfrac{1}{16}$% = $\dfrac{25}{4}$% = $6.25$%

• I realize on the first line you have to do original / difference to get the fraction, but I don't quite understand the formula on the second line. What is the dot after the 100 for? Commented Dec 16, 2014 at 11:32
• "$\cdot$" stands for multiplication or "times" it is 100 times $\frac{1}{16}$ Commented Dec 16, 2014 at 11:33
• and also the fractional change is difference or (change) / original Commented Dec 16, 2014 at 11:35
• I think you mean 100% times fractional change?
– BCLC
Commented Dec 16, 2014 at 12:23
• Ok, so basically it's difference / original * 100 ? Commented Dec 16, 2014 at 12:28

$100*\frac{new-original}{original}$

That will get the percent :)

Simple Algebraic intuition : Let the percentage be $x$. Now ask $what\ \%$ of $80000$ gets added to $80000$ to get $85000$. Express it in the form of an equation.

\begin{align} 80000+\left(\frac{x}{100}\times80000\right)&=85000 \\ \implies\ \ \ x&=\dfrac{85000-80000}{80000}\times100 \\ &=6.25 \end{align}