The question “how to calculate percentages” begins to overcome schoolchildren in the 5th grade. It is then that such a topic appears in mathematics. It seems that fifth graders are not given challenging tasks. Then why do so many people have problems with these tasks? Perhaps everything is hidden in a misunderstanding of the essence of this concept.
The basis of everything is understanding the meaning
This is the key to all tasks on this topic. If a person can determine one percent, then he can determine thirteen, eighty-nine and one hundred and thirty-five. At least four hundred and twenty...
And this is a hundredth of the total number discussed in the problem. Moreover, it can be specified explicitly, but sometimes it is only discussed indirectly.
What situations exist?
Find out the percentage of a number
That is, a certain value is known and you need to calculate how much x% of it will be. This is the main task in the topic. So how do you calculate the percentage of a number? You need to create a proportion; the first line will contain the known data, and the second line will contain the data you are looking for. Now you need to multiply the known value by the desired percentage and divide by 100%.
If we write it down briefly, we get the following proportion:
known number - 100%,
the required number is x%.
From this record you can create a formula:
sought = (known * x%) / 100%.
The result is obtained by multiplying two known quantities crosswise and dividing by the one that is left without a pair.
If in a problem the total number is the sum of several, then the question arises of how to calculate the percentage of the sum. There are two ways to do this:
Find out the number using a known percentage
In this situation, the part of the number and the corresponding % are known. To find out how to correctly calculate percentages, you will need to use the already recorded proportion. Only the first line will contain the required number, and the second line will contain the known one:
sought = (known * 100%) / x%.
Find out the percentage of one number from another
Given two values, you need to calculate what percentage the larger or smaller will be. Typically, such tasks contain information about the plan being exceeded or, conversely, about a decrease in quantity compared to an earlier value.
Again, proportion is required. It is customary to take the value with which it is being compared as 100%.
the first value is 100%,
second value - x%,
x = (second value * 100%) / first value.
Find out the percentage when nothing is known about the total number
Such problems state that some number is a known percentage and another is an unknown percentage. This is what needs to be calculated. How to calculate interest in this case? Using proportion again:
the first number is the known %,
second number - x%,
x = (second * known%) / first.
Assignments with more complex questions
Find out by what percentage the numbers differ
There are two possible options here. The first is when you need to compare more with less. And find how many percent the second is less. In this situation, the question of how to calculate percentages comes down to understanding what to choose as 100%. The one that is bigger. And then the proportion will look like this:
higher number - 100%,
smaller number - x%,
x = (smaller * 100%) / greater.
But this is not the answer. It will require subtracting the found x value from 100%.
The second option is when the smaller number is compared with the larger one. It takes the smaller value to be 100%. The proportion looks like this:
smaller number - 100%,
the larger number is x%,
x = (larger * 100%) / smaller.
To calculate the final value, you need to find out how much x% - 100% will be.
Find out the result of increasing a number by a known percentage
In such tasks you need to find the answer that will be obtained after increasing the known one by a certain percentage value from it. In this case, the proportion will look like this:
known number - 100%,
the required number is 100 + x%,
sought = (known * (100 + x%)) / 100%.
Find out the result of reducing a number by a known percentage
known number - 100%,
the required number is 100 - x%,
sought = (known * (100 - x%)) / 100%.
Calculator as an assistant in calculating percentages
It can be used in two ways. The first is when all the actions described above are carried out step by step on the device screen. Everything is simple here. You just need to not get confused with the order of actions. In general, the calculator will simply replace a person in the moment of practical calculation.
In the second method, he will do everything himself. For example, you can select the engineering view of the calculator on your computer and enter the entire formula with brackets and necessary actions into it at once. After pressing the “=” key, the answer will be displayed in the window.
It happens that the calculation option is simple, when you need to find out the percentage of a known value. Then you can use a special function, which is indicated by the “%” button.
To do this, you need to enter a known value on the calculator. Then press the multiplication sign. Then the number of percentages and the “%” button. The answer will immediately appear on the screen.
They will prevent you from getting confused. Moreover, you will be able to answer any question about how to calculate a percentage from a sum or difference; you will no longer have to think about it - everything will be solved automatically.
- Always go to specific quantities. A percentage is something faceless. But kilograms, pupils and boxes are quite tangible and understandable. This is what we should strive for.
- Read the terms and conditions very carefully. Because there are situations when interest is taken several times and from different amounts.
- Check the answer. Is it really final? Or maybe it's just an intermediate value.
How to calculate the percentage of the amount, you need to know in many cases (when calculating state duties, loans, etc.). We will tell you how to calculate percentages of an amount using a calculator, proportions and known ratios.
How to find out the percentage of the amount in the general case?
After this there are two options:
- If you want to find out what percentage another amount is from the original, you just need to divide it by the 1% amount obtained earlier.
- If you need an amount that is, say, 27.5% of the original, you need to multiply the amount of 1% by the required amount of interest.
How to calculate a percentage of an amount using a proportion?
But you can do it differently. To do this, you will have to use knowledge about the method of proportions, which is taught as part of the school mathematics course. It will look like this.
Let us have A - the main amount equal to 100%, and B - the amount whose relationship with A as a percentage we need to find out. We write down the proportion:
(X in this case is the number of percent).
According to the rules for calculating proportions, we obtain the following formula:
X = 100 * V / A
If you need to find out how much the amount B will be if the number of percentages of the amount A is already known, the formula will look different:
B = 100 * X / A
Now all that remains is to substitute known numbers into the formula - and you can make the calculation.
How to calculate the percentage of an amount using known ratios?
Finally, you can use a simpler method. To do this, just remember that 1% as a decimal is 0.01. Accordingly, 20% is 0.2; 48% - 0.48; 37.5% is 0.375, etc. It is enough to multiply the original amount by the corresponding number - and the result will indicate the amount of interest.
In addition, sometimes you can use simple fractions. For example, 10% is 0.1, that is, 1/10; therefore, finding out how much 10% is is simple: you just need to divide the original amount by 10.
Other examples of such relationships would be:
- 12.5% - 1/8, that is, you need to divide by 8;
- 20% - 1/5, that is, you need to divide by 5;
- 25% - 1/4, that is, divide by 4;
- 50% - 1/2, that is, it needs to be divided in half;
- 75% is 3/4, that is, you need to divide by 4 and multiply by 3.
True, not all simple fractions are convenient for calculating percentages. For example, 1/3 is close in size to 33%, but not exactly equal: 1/3 is 33.(3)% (that is, a fraction with infinite threes after the decimal point).
How to subtract a percentage from an amount without using a calculator
If you need to subtract an unknown number, which is a certain amount of percent, from an already known amount, you can use the following methods:
- Calculate the unknown number using one of the above methods, and then subtract it from the original one.
- Immediately calculate the remaining amount. To do this, subtract from 100% the number of percentages that need to be subtracted, and convert the resulting result from percentage to number using any of the methods described above.
The second example is more convenient, so let’s illustrate it. Let's say we need to find out how much is left if we subtract 16% from 4779. The calculation will be like this:
- We subtract 16 from 100 (the total number of percent). We get 84.
- We calculate how much 84% of 4779 is. We get 4014.36.
How to calculate (subtract) a percentage from a sum with a calculator in hand
All of the above calculations are easier to do using a calculator. It can be either in the form of a separate device or in the form of a special program on a computer, smartphone or regular mobile phone (even the oldest devices currently in use usually have this function). With their help, the question of how to calculate the percentage of an amount is solved very simply:
- The initial amount is collected.
- The “-” sign is pressed.
- Enter the number of percentages you want to subtract.
- The “%” sign is pressed.
- The “=” sign is pressed.
As a result, the required number is displayed on the screen.
How to subtract a percentage from an amount using an online calculator
Finally, there are now quite a few sites on the Internet that offer an online calculator function. In this case, you don’t even need to know how to calculate the percentage of the amount: all user operations are reduced to entering the required numbers in the windows (or moving the sliders to get them), after which the result is immediately displayed on the screen.
This function is especially convenient for those who calculate not just an abstract percentage, but a specific amount of tax deduction or the amount of state duty. The fact is that in this case the calculations are more complicated: you not only need to find the percentages, but also add a constant part of the amount to them. An online calculator allows you to avoid such additional calculations. The main thing is to choose a site that uses data that complies with the current law.
It may be useful not only for high school students. In everyday life, this skill is necessary in order to calculate the loan payment, calculate and check whether the accountants correctly calculated the amount of taxation for you when you receive your salary. And for many employees of various companies and enterprises, this skill is simply necessary for work.
What is this - percentage? From the school curriculum, everyone remembers that a percentage in the world is considered to be a hundredth part of something. That is, to put it another way, the expression “3 percent” should be understood as 3 hundredths of any number. For the sake of brevity, people have adopted the symbol "%" for the word "percentage".
And from school, we all know how to calculate the percentage of divided by one hundred, finding the value of one percent, and then the resulting quotient is multiplied by a number indicating the number of percents that need to be found.
For example, you need to find out what 28% of 500 is. The line of reasoning should be as follows:
- Find the size of 1% of 500 by division.
- We find the given number by multiplying the resulting quotient from division by 100.
That is, 28% of 500 is 28/100 of 500. Another way to write this action is:
500 X 28/100 = 140.
Since numbers are not always easy to remember, and pen and paper are not always at hand, many people today use calculators.
To calculate, you can use the described method: divide the given number by one hundred and multiply by the required number of percent.
There is a faster calculation option:
- The specified number is entered into the calculator. In our case - 500.
- Next, press the “multiply” key.
- Then we type the number of the required percentages - for our version it is 28.
- Instead of equality, select the % sign on the calculator.
- We get the result - this is 140 in our example.
- In the cell that displays the calculated percentage, enter the equal sign “=”.
- Next, write down a given number from which you need to look for a percentage, or the “address” of the cell where this number has already been entered. In our example we will enter the number 500.
- The third step will be to set the “multiply” or “*” sign.
- Now you should write down the number that reflects the amount of interest you are looking for. For us it's 28.
- The penultimate action will be to enter the “percentage” sign, which looks like “%”.
- To get the result, all you have to do is press the “Enter” button on your keyboard. The result - 140 - will immediately appear on the monitor.
Before starting to work in Excel, you should left-click to set the appropriate format in the table cells or use the “menu” function: “format - cells - number - percentage”.
For example, we are given the numbers 140 and 500. The question is posed this way: what percentage is 140 of 500?
- First, let's find what one percent of 500 is equal to. That is, we follow the old scheme and divide 500 by 100. We get 5.
- Now it remains to find out how many such percentages the given number 140 contains. To do this, 140 must be divided by 5. We get the same 28 percent!
- This calculation can be written in one formula as follows:
140: (500: 100) = 140: 500/100 = 140: 500 X 100 = 28.
That is, the number 140 out of 500 is 28 percent.
And in order to find out what percentage one number is of another, we should divide the smaller number by the larger one and multiply the quotient by 100.
These skills are extremely important for an entrepreneur who is engaged in trading. When setting prices for a product, it usually requires the ability to calculate the percentage of a number, since with the help of this action the necessary “markup” on the product is made. It is most convenient to mark up the entire assortment at the same percentage, for example, 15%.
But calculating net income requires another skill. For example, the daily revenue at the stall was 3,450 rubles. What is the net income from goods sold? Some novice entrepreneurs naively calculate 15% of gross revenue, and make a grave mistake! Having removed the “cheating” obtained in such an incorrect way from circulation, they then sit and puzzle over where the shortage came from.
And everything is very simple. After markup, the product began to contain not 100% of the cost, but 100% + 15% = 115%. Therefore, to find the amount of added value received, 15% is calculated as follows:
- They find 1% of the revenue by dividing it not by 100, but by 115. That is, in our case
- And now you can look for added value, which you can bravely extract from circulation.
These numbers are taken out of thin air, so you shouldn’t take these data seriously. But the calculation methods themselves deserve attention; there are no errors in them.
Perhaps math wasn't your favorite subject in school, and numbers were scary and boring. But in adult life there is no escape from them. Without calculations, you can’t fill out a receipt for paying for electricity, you can’t draw up a business project, you can’t help your child with his homework. Often in these and other cases it is necessary to calculate the percentage of the amount. How to do this if you have vague memories of what percentage is from your school days? Let's strain our memory and figure it out.
Method one: percentage of the amount by determining the value of one percent
A percentage is one hundredth of a number and is denoted by the % sign. If you divide the amount by 100, you get just one percent. And then everything is simple. We multiply the resulting number by the required percentage. In this way it is easy to calculate the profit on a bank deposit.
For example, you deposited an amount of 30,000 at 9% per annum. What will be the profit? We divide the amount of 30,000 by 100. We get the value of one percent - 300. Multiply 300 by 9 and get 2,700 rubles - an increase to the original amount. If the contribution is for two or three years, then this figure doubles or triples. There are deposits for which interest payments are made monthly. Then you need to divide 2700 by 12 months. 225 rubles will be a monthly profit. If interest is capitalized (added to the total account), then the deposit amount will increase every month. This means that the percentage will be calculated not from the down payment, but from the new indicator. Therefore, at the end of the year you will receive a profit of not 2,700 rubles, but more. How many? Try to count.
Method two: convert percentages to decimals
As you remember, a percentage is a hundredth of a number. As a decimal it is 0.01 (zero point one hundredth). Therefore, 17% is 0.17 (zero point, seventeen hundredths), 45% is 0.45 (zero point, forty-five hundredths), etc. We multiply the resulting decimal fraction by the amount of which we calculate the percentage. And we find the answer we are looking for.
For example, let's calculate the amount of income tax from a salary of 35,000 rubles. The tax is 13%. As a decimal it would be 0.13 (zero point one, thirteen hundredths). Let's multiply the amount of 35,000 by 0.13. The result will be 4,550. This means that after deducting income tax, you will receive a salary of 35,000 - 4,550 = 30,050. Sometimes this amount, already without tax, is called “salary in hand” or “net.” In contrast, the amount together with tax is “dirty wages”. It is the “dirty salary” that is indicated in company vacancy announcements and in the employment contract. Less is given to your hands. How many? Now you can easily count.
Method three: count on a calculator
If you doubt your mathematical abilities, use a calculator. With its help, it is calculated faster and more accurately, especially when it comes to large amounts. It is easier to work with a calculator that has a button with a percentage sign. Multiply the amount by the percentage and press the % button. The required answer will be displayed on the screen.
For example, you want to calculate what your child care benefit will be for up to 1.5 years. It is 40% of average earnings for the last two closed calendar years. Let’s say the average salary is 30,000 rubles. On the calculator, multiply 30,000 by 40 and press the % button. Key = no need to touch. The answer 12,000 will be displayed on the screen. This will be the amount of the benefit.
As you can see, everything is very simple. Moreover, the “Calculator” application is now available on every cell phone. If the device does not have a special % button, then use one of the two methods described above. And perform multiplication and division on a calculator, which will facilitate and speed up your calculations.
Don't forget: there are online calculators to make calculations easier. They operate in the same way as regular ones, but are always at hand when you work on the computer.
Method four: making a proportion
You can calculate the percentage of the amount using a proportion. This is another scary word from a school mathematics course. Proportion is equality between two ratios of four quantities. For clarity, it is better to immediately understand it with a specific example. You want to buy boots for 8,000 rubles. The price tag indicates that they are sold at a 25% discount. How much is this in rubles? Of the 4 values, we know 3. There is a sum of 8,000, which is equal to 100%, and 25% that needs to be calculated. In mathematics, an unknown quantity is usually called X. The proportion we get is:
For ease of calculation, we convert percentages to decimal fractions. We get:
The proportion is solved as follows: X = 8,000 * 0.25: 1X = 2,000
2,000 rubles – discount on boots. We subtract this amount from the old price. 8,000 – 2,000= 6,000 rubles (new discounted price). This is such a nice proportion.
This method can also be used to determine the value of 100%, if you know the numerical indicator - say, 70%. At a company-wide meeting, the boss announced that 46,900 units of goods had been sold during the year, while the plan was only 70% fulfilled. How much did you need to sell to fully fulfill the plan? Let's make a proportion:
Converting percentages to decimal fractions, it turns out:
Let’s solve the proportion: X = 46,900 * 1: 0.7X = 67,000. These were the results the bosses expected.
As you may have guessed, the proportion method can be used to calculate what percentage a numerical indicator is of the amount. For example, while taking a test, you answered 132 out of 150 questions correctly. What percent of the task was completed?
There is no need to convert this proportion into decimal fractions; you can solve it right away.
X = 100 * 132: 150. As a result, X = 88%
As you can see, it's not all that scary. A little patience and attention, and now you have mastered the calculation of percentages.
