Finding the Percentage Decrease

Finding percent decrease for a pair of numbers is very similar to finding percent increase, but the formula’s a little bit different. Once again, we will demonstrate on three different types of number pairs.

First, decimals, then fractions, then dollar amounts. In the first example, we have 3.6 and 2.0. To find percent decrease, we’ll take the first number, subtract the second number, and divide by the first number. So, what we have is 3.6-2.0 / 3.6.

Finding the Percentage Decrease - Percentage Increase Combined LessonsTemperature rises from 60F to 72F.  what is the percent increase?
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Population rises from 21,000 to 28,000. what is the percent increase?
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Revenues fall from $60 million to $54 million. what is the percent decrease?
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A $25 item now selling for $17.50 is discounted by what percent?
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Costs change from $240 to $320.  what is the percent change?
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Next Lesson: Finding the Percentage Increase

The following transcript is provided for your convenience.
We can simplify this by subtracting 2 from 3.6, and then we get 1.6/3.6. Now, if you reduce this fraction, what you wind up with is 4/9, whose percentage equivalent is 44.4%.

In the second example, we have 5/6 and 2/3. Once again, we’ll take the first number minus the second number over the first number. Now, we don’t have a common denominator yet, but we can convert the second number to a denominator of 6, and then we’ll add it. So, we’ll multiply this by 2/2, and what we wind up with is 5/6-4/6 / 5/6.

Now, 5/6-4/6 is just 1/6, so what we have is 1/6 / 5/6, or 1/6 times 6/5.

Now, this 6 is canceled here, and what we’re left with is just 1/5. The percentage equivalent for 1/5 is 20%.

In this final example, we have 200 and 30, $200 and $30. So, we’ll take once again the first number minus the second number divided by the first number. 200-30 is 170, so what we have is 170/200.

Now, since our denominator is already so close to 100, we’ll just convert it to 100, and then we’ll have our percentage figured out already. So, we’ll divide top and bottom by 2, 170/2 is 85, and 200/2 is 100. So, what we have is 85/100, which, by definition, is 85%.

The next lesson: Finding the Percentage Increase, both lessons are included in Practice Tests.