Percentage Increase & Decrease

Percentage Increase & Decrease without a Calculator

You can increase and decrease a number by a certain percentage without a calculator using the same method that we use for calculating percentages of amounts. On the right, you can see and example in which 540 is increased by 36%. The way to do this is to find percentages which are easy to calculate such as 50%, 10%, 5% and 1% which you can then use to build any percentage of the number in question. The only difference to the example on the page about percentages of amounts is that this time we have to add 540 to 36% of 540 as we are increasing 540 by 36%. If we were to decrease 540 by 36%, we would subtract the sum of the different percentages we found from 540 instead of adding it. Using this method, you can easily decrease or increase a number by any percentage without a calculator. There are a couple of examples underneath to help you understand the method used. In this example, we found 10%, 5% and 1% (of 470) to calculate 16% which we then subtracted from 470 to decrease it by 16%. If you prefer to do complex multiplications instead of using this technique, you can do the calculator method which follows just without a calculator. Percentage Increase with a Calculator If you have access to a calculator to increase or decrease percentages, you can use a much easier method. This method involves transforming the percentage into a decimal which you can the multiply by the number to give you the percentage. There are two different procedures you can use depending on if you want your answer in one or two steps. Two step method: If you want to use the two step method, you can use the same calculator method as on the percentages of  amounts page. This involves converting the percentage into a decimal. For example, 16% becomes 0.16 (100% becomes 1). Next you have to multiply the decimal by the number you want to increase. If for example, I wanted to increase 540 by 18%, the expression would be 540 x 0.18. The last thing you have to do after you found the solution is to add it to the original number (540) as you are increasing. There is an example underneath that will make this clearer. Example: Increase 430 by 37% In this example, we have converted 37% into a decimal and multiplied it by the number. We have then taken the solution and added it to the original number to get the increased number. One step method: If you can, you should use this method instead of the one above as it is a lot faster. It works using the same concept which is to convert the percentage into a decimal. Let`s take the example I used in the two step method explanation again. We want to increase 540 by 18%. Instead of just simply converting the percentage to 0.18, we convert it but add a 1 which gives us 1.18. This is equivalent to 118%. It allows us to calculate the percentage increase in one step without having to calculate the percentage first and then adding it to the original number. Here is an example of this. Example: Increase 379 by 54% In this example, we have converted the percentage to a decimal and added a one so that we were able to increase by 54% in one step. Percentage Decrease with a Calculator Decreasing a number by a certain percentage with a  calculator is almost as easy as increasing. Again, there are two methods which allow us to get the solution in one or two steps. Of course, you should always try to use the shorter method. Two step method: In the two stop method we need to do two things to get our solution. Decreasing by using the two step method is very similar to increasing. Fist of all, we convert the decimal into a fraction and multiply it by the number we want to decrease. We then have to subtract the original number by the solution to get the decreased answer. Look at the example underneath to ensure that you understand this. Example: Decrease 180 by 83% In this example, we have converted the percentage into a fraction and multiplied it by 180. We have then subtracted 180 by the solution which gave us the decreased answer. One step method: The one step method is again a lot faster. To decrease a number by a certain percentage in one step, we have to find the “remaining percentage” after the decrease. So if the percentage you want to decrease a number by is 10%, the remaining percentage is 90%. You basically have to think about what remains when we decrease a number by 10% - 90% remains. So instead of calculating the decrease, we calculate the percentage of the whole number that will remain if we decrease the number by a percentage. You then just have to multiply the remaining percentage as a decimal by the number to get the decreased answer. The example underneath explains this. Example: Decrease 87 by 39% In this, example, we have found the remaining percentage of the number which would remain if we decreased it by 39% and the multiplied the number by this remaining percentage as a decimal. Reverse Percentage Calculations Now that you are familiar with percentage increase and decrease, you should try to do some reverse percentage calculations which also use the calculator methods above. Please share this page if you like it or found it helpful!
Example 1 Increase 368 by 76% In this example, we have found 50%, 10%, 5% and 1% (of 368) to calculate 76% which we then added to 368.
Example 2 Decrease 470 by 16% In this example, we found 10%, 5% and 1% (of 470) to calculate 16% which we then subtracted from 470 to decrease it by 16%.
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Chapter 4.2:  Learning Outcomes Students will be able to solve simple percentage problems without using the calculator! Students will be able to calculate percentages of amounts using a calculator!
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