Percent Change

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"Prices are down 25%."


"Wages have increased by 13%."


You may hear phrases like this all the time, but could you calculate the new figure?


In some cases, you will be given the original number and the new number, and asked to calculate the percent change. To do this, subtract the old number from the new number, and then divide the difference by the old number.  Multiply by 100 (or move the decimal point two places to the right) to convert the decimal into a percentage.


Let's look at an example. The price of a shirt has increased from $20 to $24. What is the percent change? First, we subtract the old price from the new: 24 − 20 = 4. We divide this difference by the original price, 4 ÷ 20 = 0.2, and then multiply by 100 to reach the solution: 20%. 


But what if the number is decreasing? The process remains the same. Returning to our shirt, imagine the price fell by $4 instead. In this case, the percent change would be calculated like this:

  • 16 − 20 = -4 (Don't worry about the negative in this problem, it just means that the change is a decrease.)
  • -4 ÷ 20 = -0.2, or 20%
Notice that the percent change is the same no matter whether the original amount increases or decreases, if it does so by the same amount.  

Another way you might see this concept is when the percent change and either the original or new value are given, and you must calculate the missing value. Consider this example: a book that previously cost $14 has been discounted by 25%. How much does it cost now? To solve, convert 25% into a decimal and multiply it by the original cost: 0.25 × 14 = 3.5. A book that was $14 has been discounted $3.50. So, to find the new price, just subtract the amount of the discount from the original price: $14 − $3.50 = $10.50. Simple, right?  


Here are a few practice questions to help you get the hang of it!