# Reverse Percentage Calculations

## Reverse Percentage Calculations

Reverse percentage calculations are problems in which we are given a % of an amount and we have to find the original amount. This can only really be
done with a calculator as the calculations are quite complex. The best type of example for these calculations is a
sale in a shop. Have a look at the situation on the right. A shop currently has a sale of 30% and there is an item
with a reduced price of $235. The question is: What was the price of the item before the sale? To answer this
questions, we first have to look at how the new price was created. The new price (235) is equal to the old price x
0.7 (if you don’t understand why 0.7, have a look at the percentage increases and decreases page). The only
thing we have to do is to do the reverse operation of this expression which is 235/0.7. This then gives us the
original price of the item. It will not work if you just increase 235 by 30% as you are taking the 30% from a
different number. The answer would be wrong. Underneath, you will find a few examples of different reverse
percentage calculations (x = old/original price).
Learn More!
If you have looked at all the topics on percentages and you have understood everything then you should look for another topic that
interest you in our library. Please share this page if you like it or found it helpful!
Example 1
New Price = $85 Sale: 40%
In this example, we have identified that the new price
(85) = old price x 0.6. We have then used the reverse
operation to calculate the original price of the item.

Example 2
New Price = $275 Sale: 50%
In this example, we have identified that the new price
(275) = old price x 0.5. We have then done the reverse
operation to find the original price of the item.

Example 3
New Price = $139 Sale: 70%
In the last example, we have identified that the new price (139) = old price x 0.3. WE have used the reverse operation to
find the original price of the item.

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Chapter 4.3: Learning Outcomes
Students will be able to carry out reverse percentage calculations!
Students will be able to apply these skills to real life examples such as
items on sale in a store!

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