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Welcome to our Math lesson on Percentage Decrease, this is the third lesson of our suite of math lessons covering the topic of Percentage Increase and Decrease, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
As we mentioned at the beginning of this tutorial, percentage decrease is the inverse of percentage increase of an amount. Thus, to obtain the value of a given percentage decrease, we must subtract the new percentage from the old one. Mathematically, we have
For example, if there is a 30% discount on the price of an item, the new price will be 70% of the original (since the original price represents the whole, which when written as a percentage gives 100%). Here, the discount represents the percentage decrease while the new price is expressed as a percentage of the original.
On the other hand, when we know the new and the old values expressed in numbers and not in percentages, we can use the formula
An item cost $125 but after a discount, it became $90. What is the percentage decrease of this item?
We can use two approaches to solve this exercise. The first is to express the new price as a percentage of the original (old percentage), which on the other hand represents the percentage of the whole (100%). Hence since,
and giving that
we obtain
Thus,
This result can be obtained using a shorter approach, i.e. by directly using the formula
that yields
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