## Monday, July 20, 2020

Knowing how to calculate percentages will help you not only score well on a math test but in the real world as well. They are used for calculating tips in restaurants, finding out the nutritional content of your food, or even determining statistics of your favorite sports team. Regardless of how you plan to use the knowledge, calculating percentages is fundamental and quite easy overall.

## Steps

### Calculating the Percentage of a Whole

1. Visualize what a percentage represents. A percentage is an expression of part of the whole. 0% represents nothing, and 100% represents the entire amount. Everything else is somewhere in between![1]
• For example, say you have 10 apples. If you eat 2 apples, then you have eaten 2 out of the whole 10 apples (2 / 10 × 100% = 20% eaten). If 10 apples is 100% and you ate 20%, then 100% - 20% = 80% of the apples remain.
• The term "percent" in English comes from the Latin per centum, meaning “through 100” or “for 100”.
2. Determine the value of the whole. In some cases, you will be given the value for part of the whole and the whole. Other times, you might get two parts that make up the whole. It is important to distinguish what the percentage is “of.” 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, i.e. 100%.[2]
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 blue marbles. Then the percentage of the whole we are looking for is 485 (the number of blue marbles) of 1684 (the whole amount).[3]
4. Put the two values into a fraction. The part goes on top of the fraction (numerator), and the whole goes on the bottom (denominator). Therefore the fraction in this case is 485/1684 (part/whole).[4]
5. Convert the fraction into a decimal. Percentages are best calculated from the decimal form. To turn 485/1684 into a decimal, divide 485 by 1684 using a calculator or pencil and paper. This comes to 0.288.[5]
6. Convert the decimal into a percent. Multiply the result obtained in the step above by 100% (per 100 = per cent). For this example, 0.288 multiplied by 100% equals 28.8%.[6]

### Working Backwards From a Percentage

1. Identify the given numbers you're working with. Say you borrowed money from a friend who is going to charge you daily 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.[7]
2. Convert the percentage into a decimal. Working backward from before, divide the percentage by 100%, or you can multiply by 0.01 (they’re the exact same). 3%/100% = 3/100 = 0.03. [8]
3. Re-word the problem with your new values. It helps to reword your problem with the new value(s) now in the form of “X of Y is Z.” X is the decimal form of your percent, “of” means to multiply, Y is the whole amount, and Z is the answer. So, 0.03 x \$15 is \$0.45.[9]
• In this example, \$0.45 is the amount of interest accrued each day that you do not pay your friend back.
• If you need to further calculate the total due after 1 day, you would add the amount you borrowed to the amount of the interest times the number of days. So \$15 + (\$0.45 x 1 day) = \$15.45.

### Calculating Discounts

1. Write down the original price and the discount percentage. The original price is usually the big number that retailers will mark through or make especially large so you know how good of a “deal” you’re getting.[10]
• Be sure to also pay attention to whether the discounted percentage applies to a single item or the total.
2. Find the opposite of the discount percentage. This trick lets you perform 1 calculation instead of 2! The opposite of a percent is 100% minus the percent you are working with, i.e. the amount of the item you are still paying for. If you want to buy a shirt that is 30% off, the opposite of this is 70%, meaning you would have to pay 70% of the original price.[11]
3. Convert the opposite percent into a decimal. To convert a percent into a decimal, divide by 100%, multiply times 0.01, or move the decimal two places to the left. In this example, 70%/100% = 70/100 = 7/10 = 0.7.[12]
4. Multiply the original price by the new decimal. If the shirt you want is \$20, multiply \$20 by 0.7. This comes to \$14, meaning the shirt is now on sale for \$14.[13]
5. Calculate your savings afterward to feel better. Once you get home, it can be a good idea to check your receipts, not only to make sure the discounts were applied correctly but to see how much you saved altogether. Here, you can simply subtract the sale price from the original price (\$20 - \$14 = \$6 saved)!

## Tips

• x% of y is the same as y% of x. For example, 10% of 30 = 3 = 30% of 10.[14]

## Quick Summary

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