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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?

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3 Answers 3

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Percentage change : 100 % times the (Fractional change )

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

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

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  • $\begingroup$ 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? $\endgroup$
    – Brett
    Commented Dec 16, 2014 at 11:32
  • $\begingroup$ "$\cdot$" stands for multiplication or "times" it is 100 times $\frac{1}{16}$ $\endgroup$ Commented Dec 16, 2014 at 11:33
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    $\begingroup$ and also the fractional change is difference or (change) / original $\endgroup$ Commented Dec 16, 2014 at 11:35
  • $\begingroup$ I think you mean 100% times fractional change? $\endgroup$
    – BCLC
    Commented Dec 16, 2014 at 12:23
  • $\begingroup$ Ok, so basically it's difference / original * 100 ? $\endgroup$
    – Brett
    Commented Dec 16, 2014 at 12:28
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$100*\frac{new-original}{original}$

That will get the percent :)

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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.

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

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