How to Calculate Percentages

Percentages are all around us—from 3.4% APR to 80% off clearance. It is helpful to know what they are, what they mean, and how to calculate them. It is not as difficult as you might think, and the way to do it is shown simply below.

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Method 1 Calculating the Percentage of a Whole

1. 1
Know what a percentage is. A percentage is a way to express a number as a part of a whole. To calculate a percentage, we look at the whole as equal to 100%. For example, say you have 10 apples (=100%). If you eat 2 apples, then you have eaten 2/10 × 100% = 20% of your apples and you are left with 80% of your original apples.
• The term "percent" in English comes from the Italian per cento or the French pour cent, which literally mean per hundred.
2. 2
Determine the value of the whole. For instance, let's say we have a jar containing 1199 red marbles and 485 blue marbles, making it 1684 marbles in total. In this case, 1684 makes up a whole jar of marbles, and will be set equal to 100%.
3. 3
Find the value that you want to turn into a percentage. Let's say we want to find out the percentage of the jar that is taken up by the 485 blue marbles.
4. 4
Put the two values into a fraction. In our example, we need to find out what percent 485 (number of blue marbles) is of 1684 (total number of marbles). Therefore the fraction in this case is 485/1684.
5. 5
Convert the fraction into a decimal. To turn 485/1684 into a decimal, divide 485 by 1684. This comes to 0.288.
6. 6
Convert the decimal into a percent. Multiply the result obtained in the step above by 100. For this example, 0.288 multiplied by 100 equals 28.8 or 28.8%.
• A simple way to multiple a decimal by 100 is to move the decimal to the right two places.

Method 2 Working Backwards From a Percentage

1. 1
Know when you need to work backwards. Sometimes you're given the percentage of an amount and need to know the numerical value of the percent. Examples include calculating taxes, tips, and loan interest.
2. 2
Know the initial numbers you're working with. Say you borrowed money from a friend who is going to charge you interest. The amount borrowed was initially \$15 and the interest rate is 3% per day. These are the only two numbers you need for the calculation.
3. 3
Convert the percent into a decimal. Multiply the percent by .01 or simply move the decimal to the left two places. This turns 3% into .03.
4. 4
Multiply your initial total by the new decimal. In this case, multiply 15 by .03. This comes to 0.45. In this example, \$0.45 is the amount of interest accrued each day that you do not pay your friend back.

Method 3 Calculating Discounts

1. 1
Know the price and the discount amount. This is a very simple way to calculate a discounted price, but you must begin with an accurate percent off. Double check what your item is on sale for.
2. 2
Find the opposite of the discount percent. The opposite of a percent is 100% minus the percent you are working with. If you want to buy a shirt that is 30% off, the opposite of this is 70%.
3. 3
Convert the opposite percent into a decimal. To convert a percent into a decimal, multiply it by .01 or move the decimal two places to the left. In this example, 70% becomes .7
4. 4
Multiply the price by the new decimal. If the shirt you want is \$20, multiply 20 by .7. This comes to 14. This means the shirt is on sale for \$14.

Tips

• A visual representation of what percentage means can be shown with pie charts. A pie represents 100%. Pieces of the pie represent percentages of the whole pie that are less than 100% or the whole pie.

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Categories: Mathematics