Oct 21, 2015 · 4 min read
By the end of this article you’ll have the tools to calculate percentages mentally. So leave that calculator at home and take the challenge! But first we need to add another technique to our arsenal.
To calculate 1% of a number, move the decimal point two positions left.
Here are some illustrative examples:
Let’s quickly look at why the 1% Trick works by taking 1% of 250 long-hand.
Begin by rewriting 1 percent as 1/100 and performing the multiplication.
Whenever we divide by 100, we move the decimal point two places left.
Therefore, you can always move the decimal point two places left to find 1 percent.
Alright, you’re set! Now let’s try some problems.
One percent (1%) means 1 per 100.
1% of this line is shaded green: it is very small isn't it?
|50% means 50 per 100 (50% of this box is green)|
|25% means 25 per 100 (25% of this box is green)|
|100% means all. Example:100% of 80 is 100100 × 80 = 80|
|50% means half. Example:
50% of 80 is 50100 × 80 = 40
|5% means 5/100ths. Example:
5% of 80 is 5100 × 80 = 4
Use the slider and try some different numbers
(What is 40% of 80? What is 10% of 200? What is 90% of 10?)
Because “Percent” means “per 100” think:
“this should be divided by 100”
- So 75% really means 75100
- And 100% is 100100, or exactly 1 (100% of any number is just the number, unchanged)
- And 200% is 200100, or exactly 2 (200% of any number is twice the number)
A Percent can also be expressed as a Decimal or aFraction
Read more about this at Decimals, Fractions and Percentages.
Some Worked Examples
- 25% = 25100
- And 25100 × 80 = 20
- So 25% of 80 is 20
15% = 15100
|And 15100 × 200||= 15 × 200100|
|= 15 × 2|
|= 30 apples|
30 apples are bad
- As a fraction, 10200 = 0.05
- As a percentage it is: 10200 x 100 = 5%
- 5% of those apples are bad
Example: A Skateboard is reduced 25% in price in a sale. The old price was $120.
Find the new price.
- First, find 25% of $120:
- 25% = 25100
- And 25100 × $120 = $30
- 25% of $120 is $30
- So the reduction is $30
- Take the reduction from the original price
- $120 − $30 = $90
- The Price of the Skateboard in the sale is $90
This little rule can make some calculations easier:
x% of y = y% of x
- 8% of 50 is the same as 50% of 8
- And 50% of 8 is 4
- So 8% of 50 is also 4
“Percent” comes from the latin Per Centum. The latin word Centum means 100, for example a Century is 100 years.
My Dictionary says “Percentage” is the “result obtained by multiplying a quantity by a percent”. So 10 percent of 50 apples is 5 apples: the 5 apples is the percentage.
But in practice people use both words the same way.
Copyright © 2018 MathsIsFun.com
How to Calculate Percentages
By Ashley Watters, Abshier House
Calculating percentages can be an easy task. There are numerous percentage calculators online that can help with task by simply searching for “percentage calculator.” However, there may be a time when (however, unlikely it sounds) you may need to be able to calculate percentages without any digital assistance.
Before you can calculate a percentage, you should first understand exactly what a percentage is.
The word percentage comes from the word percent. If you split the word percent into its root words, you see “per” and “cent.
” Cent is an old European word with French, Latin, and Italian origins meaning “hundred”. So, percent is translated directly to “per hundred.” If you have 87 percent, you literally have 87 per 100.
If it snowed 13 times in the last 100 days, it snowed 13 percent of the time.
The numbers that you will be converting into percentages can be given to you in 2 different formats, decimal and fraction. Decimal format is easier to calculate into a percentage. Converting a decimal to a percentage is as simple as multiplying it by 100. To convert .87 to a percent, simply multiple .87 by 100.
.87 × 100=87
Thus, resulting in 87 percent.
Percent is often abbreviated with the % symbol. Presenting your answer as 87% or 87 percent is acceptable.
If you are given a fraction, convert it to a percentage by dividing the top number by the bottom number. If you are given 13/100, you would divide 13 by 100.
- 13 ÷ 100 = .13
- Then, follow the steps above for converting a decimal to a percent.
- .13 × 100 = 13
- Thus getting 13%.
- The more difficult task comes when you need to know a percentage when you are given numbers that don’t fit so neatly into 100.
Most of the time, you will be given a percentage of a given number. For example, you may know that 40 percent of your paycheck will go to taxes and you want to find out how much money that is. To calculate the percentage of a specific number, you first convert the percentage number to a decimal.
This process is the reverse of what you did earlier. You divide your percentage by 100. So, 40% would be 40 divided by 100 or .40.
40 ÷ 100 = .40
Once you have the decimal version of your percentage, simply multiply it by the given number. In this case, the amount of your paycheck. If your paycheck is $750, you would multiply 750 by .40.
750 × .40 = 300
Your answer would be 300. You are paying $300 in taxes.
Let’s try another example. You need to save 25 percent of your paycheck for the next 6 months to pay for an upcoming vacation. If your paycheck is $1500, how much should you save?
- Start by converting 25 percent to a decimal.
- 25 ÷ 100 = .25
- Now, multiply the decimal by the amount of your paycheck, or 1500.
- 1500 × .25 = 375
- You need to save $375 from each paycheck.
How to Calculate Percentages
Visualize what a percentage represents. A percentage is an expression of part of the whole. Nothing is represented by 0%, and the whole amount is 100%. Everything else is somewhere in between!
- 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”.
The percentage symbol is merely a format. In statistics, percentages are often left in their base form of 0 – 1, where 1 represents the whole. We merely multiply a decimal by a factor of 100% to format the answer.
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%.
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).
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).
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.
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%.
• A simple way to multiply a decimal by 100 is to move the decimal to the right
3 Simple Ways to Calculate Percentages (Math)
How to calculate percentages is easier than you think. Learning this can help you to easily calculate tips at restaurants and how to use percentages to easily calculate sales prices when shopping.
If you’re not sure how to perform any of those handy calculations, or if you’re just in need of a general percentage refresher, check out our guide on how to calculate percentages below.
TABLE OF CONTENTS
1. Calculating the Percentage of a Whole
To calculate a percentage, the whole amount must be known. This is in addition to the percentage or portion amount. You may be asked “what percentage of W is P,” where W is the whole amount and P is the portion amount. Or the question may be “how much is X percent of W,” where X represents a percentage figure.
1. What is a percentage?
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. What is 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. Turn the value into percentage
Let’s say we want to find out the percentage of the jar that is taken up by the 485 blue marbles.
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. Convert the fraction to a decimal
To turn 485/1684 to a decimal, divide 485 by 1684. This comes to 0.288.
Formula: 485/1684 = 0.288
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%.
Formula: 0.288 x 100 = 28.8 or 28.8%
A simple way to multiply a decimal by 100 is to move the decimal to the right two places.
2. Reverse Percentage
You may come across a question that will ask you to work backward and find the original price of something after the price has increased. If you are given a quantity after a percentage increase or decrease, you may need to find the original amount.
1. When to do reverse percentage?
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. Initial numbers
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. 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.
Formula: 3% x .01 = .03
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.
Formula: 0.3 x 15 = .45 (amount of interest accrued)
3. Calculating Discounts
Doing your shopping but want to save money by picking discounted items? Learning how to solve discount percentages will help you learn if you are actually saving money or wasting money.
1. 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. 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%.
Formula: 100% – 30% (discount) = 70 %
3. Convert the opposite percent to a decimal
To convert a percent to a decimal, multiply it by .01 or move the decimal two places to the left. In this example, 70% becomes .7.
Formula: 70% x .01 = .7
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.
Formula: $20 (item price) x .7 = 14 (discounted item price)
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Find a percentage or work out the percentage given numbers and percent values. Use percent formulas to figure out percentages and unknowns in equations. Add or subtract a percentage from a number or solve the equations.
How to Calculate Percentages
There are many formulas for percentage problems. You can think of the most basic as X/Y = P x 100. The formulas below are all mathematical variations of this formula.
Let's explore the three basic percentage problems. X and Y are numbers and P is the percentage:
- Find P percent of X
- Find what percent of X is Y
- Find X if P percent of it is Y
Read on to learn more about how to figure percentages.
1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y
Example: What is 10% of 150?
- Convert the problem to an equation using the percentage formula: P% * X = Y
- P is 10%, X is 150, so the equation is 10% * 150 = Y
- Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10
- Substitute 0.10 for 10% in the equation: 10% * 150 = Y becomes 0.10 * 150 = Y
- Do the math: 0.10 * 150 = 15
- Y = 15
- So 10% of 150 is 15
- Double check your answer with the original question: What is 10% of 150? Multiply 0.10 * 150 = 15
2. How to find what percent of X is Y. Use the percentage formula: Y/X = P%
Example: What percent of 60 is 12?
- Convert the problem to an equation using the percentage formula: Y/X = P%
- X is 60, Y is 12, so the equation is 12/60 = P%
- Do the math: 12/60 = 0.20
- Important! The result will always be in decimal form, not percentage form. You need to multiply the result by 100 to get the percentage.
- Converting 0.20 to a percent: 0.20 * 100 = 20%
- So 20% of 60 is 12.
- Double check your answer with the original question: What percent of 60 is 12? 12/60 = 0.20, and multiplying by 100 to get percentage, 0.20 * 100 = 20%
3. How to find X if P percent of it is Y. Use the percentage formula Y/P% = X
Example: 25 is 20% of what number?
- Convert the problem to an equation using the percentage formula: Y/P% = X
- Y is 25, P% is 20, so the equation is 25/20% = X
- Convert the percentage to a decimal by dividing by 100.
- Converting 20% to a decimal: 20/100 = 0.20
How to Quickly Calculate Percentages
How to calculate percentages can be easier than you may realize. Keep reading for some simple tricks.
Long time math fans may remember our first foray into the world of percentages way back in the 12th and 13th episodes of the podcast. In those shows we learned what percentages are, how they’re related to fractions, how to use percentages to easily calculate tips at restaurants, and how to use percentages to easily calculate sales prices when shopping.
If you’re not sure how to perform any of those handy calculations, or if you’re just in need of a general percentage refresher, I highly recommend taking a look at those earlier shows and getting yourself up to speed. Why? Because once you’re caught up, you’ll be ready to step up and learn how to become a true percentage-calculating machine. Which is exactly what we’re going to turn you into today.
See Also: 3 Frequently Asked Questions About Percentages
Recap: What Are Percentages?
To make sure we’re all on the same page, let’s kick things off by taking a minute to recap a few key facts about percentages.
Let’s start with the most important question: What are percentages? Perhaps the most illuminating thing to know is that the word “percent” is really just the phrase “per cent” squashed together.
And since “cent” here means 100 (as in “century”), we see that the word “percent” just means “per 100.” In other words, 10% means “10 per 100,” which is the same as the fraction 10/100 or 1/10.
This turns out to be great news since it makes lots of percentages easy to calculate. In particular, it’s easy to calculate 10% of any number since that’s just 1/10 of the number. Why is that so helpful? Because it means that you can quickly calculate 10% of a number simply by moving its decimal point 1 position to the left.