Increasing and Decreasing a Number by a Percentage


In this session we are going to learn how to increase and decrease an amount by a given percentage. We will need several examples to help us understand how to go about it. Keep in mind that, just like all other calculations involving percentages, this is equally simple, too. Below is our first example.

Example 1

  1. Increase $20 by 6%



To solve the above problem, the first thing we need to do is find the 6% of 20. Once we get our answer we are going to add it to the $20 dollars which is our main amount to get our 6% increase.

6 % of $20 = ____

In our previous lessons, we came up with a formula to solve such problems where we first converted the percent into a decimal number and multiplied them by the principal figure.

In this case convert 60% into a decimal number. First thing you need to do when converting a percentage to a decimal number is remove the percentage symbol and replace it with a decimal. The next step is to move the decimal point two places to the left and add a zero before the decimal point. You will therefore get 0.06 as your new decimal number. Multiply your new decimal number by the main number.

0.06 X 20 = 1.2

Add your answer to the $20

$1.2 + $20 = 21. 2

Therefore, a 6% increase from $20 gives us $21.20.

The above example is in a case where a principal number is being increased by a given percentage. We can equally reduce a number by a given percentage. The difference this time will be that, instead of adding we will be subtracting. Let us take a look at the next example.



Example 2

B) Decrease 20 lbs. by 5%

Just like in the example above, we start by finding 5% of the 20 lbs. We start by converting our percentage into a fraction and multiplying it by 20 lbs.

0.05 x 20 lbs. = 1 lbs.

Unlike in the above example where we added the result to the main number, when reducing a number by a percentage we subtract the result from the main number.
20 lbs. – 1 lbs. = 19 lbs.

Therefore, reducing 20 lbs. by 5% results to 19 lbs.

Example 3

  1. Increase 45ft by 80%

  2. Reduce your answer by 25%



We start by multiplying the principal length by the decimal number equivalent of the given percentage.

45 ft. X 0.8 = 36 ft.

Add your answer to the principal length to find your new increased length

45 ft. + 36 ft. = 81 ft.

Our new length becomes our new principal length with which we are going to work with on the next part of the example.

25% of 81 ft. =_________

0.25 X 81 ft. = 20.25 ft.

When decreasing an amount by a percentage, we subtract our answer from the principal length.

81 ft. - 20.25 ft. = 60.75 ft.

Our new reduced length becomes 60.75 ft.


Resource

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Browse Common Fractions
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