3 of the total. Percentage calculator
Example 1
You go to a supermarket and see a promotion on. Its usual price is 458 rubles, now there is a 7% discount. But you have a store card, and a pack of it will cost 417 rubles.
To understand which option is more profitable, you need to convert 7% into rubles.
Divide 458 by 100. To do this, you just need to shift the comma that separates the integer from the fractional part two positions to the left. 1% is equal to 4.58 rubles.
Multiply 4.58 by 7 and you get 32.06 rubles.
Now it remains to subtract 32.06 rubles from the regular price. For the promotion, coffee will cost 425.94 rubles. This means that it is more profitable to buy it with a card.
Example 2
You can see that the game on Steam costs 1,000 rubles, although it was previously sold for 1,500 rubles. You are wondering how much percent the discount was.
Divide 1,500 by 100. By moving the comma two places to the left, you get 15. This is 1% of the old price.
Now divide the new price by 1%. 1,000/15 = 66.6666%.
100% - 66.6666% = 33.3333% This discount was provided by the store.
2. How to calculate the percentage by dividing the number by 10
First you find the size 10%, and then you divide or multiply it to get the percentage you want.
Example
Let's say you put in 530 thousand rubles for 12 months. The interest rate is 5%, capitalization is not provided. You want to know how much money you will take in a year.
First of all, you need to calculate 10% of the amount. Divide it by 10 by moving the comma one character to the left. You will receive 53 thousand.
To find out how much is 5%, divide the result by 2. That's 26.5 thousand.
If the example were about 30%, you would have to multiply 53 by 3. To calculate 25%, you would have to multiply 53 by 2 and add 26.5.
In any case, such large numbers it is quite simple to operate.
3. How to calculate percentages by proportion
Proportioning is one of the most useful skills you have been taught in. With it, you can calculate any percentage. The proportion looks like this:
amount of 100%: 100% = part of the amount: share as a percentage.
Or you can write it like this: a: b = c: d.
Usually, the proportion reads "a refers to b as well as c refers to d". The product of the extreme terms of the proportion is equal to the product of its middle terms. To find out the unknown number from this equality, you need to solve the simplest equation.
Example 1
Let's use a recipe for the calculation example. You want to make it and bought a suitable 90 g bar of chocolate, but you couldn't resist and took a bite or two. Now you only have 70 g of chocolate, and you need to know how much butter to put in instead of 200 g.
First, calculate the percentage of the remaining chocolate.
90 g: 100% = 70 g: X, where X is the mass of the remaining chocolate.
X = 70 × 100/90 = 77.7%.
Now we make up the proportion to find out how much oil we need:
200 g: 100% = X: 77.7%, where X is the required amount of oil.
X = 77.7 × 200/100 = 155.4.
Therefore, you need to put about 155 g of butter in the dough.
Example 2
The proportion is also suitable for calculating the profitability of discounts. For example, you see a blouse for 1,499 rubles with a 13% discount.
First, find out how much the blouse costs in percentage. To do this, subtract 13 from 100 and get 87%.
Make the proportion: 1 499: 100 = X: 87.
X = 87 × 1 499/100.
Pay 1,304.13 rubles and enjoy wearing a blouse.
4. How to calculate percentages using ratios
In some cases, you can use simple fractions. For example, 10% is 1/10 of a number. And to find out how much it will be in numbers, it is enough to divide the whole by 10.
- 20% - 1/5, that is, you need to divide the number by 5;
- 25% - 1/4;
- 50% - 1/2;
- 12,5% - 1/8;
- 75% is 3/4. So, you have to divide the number by 4 and multiply by 3.
Example
You found pants for 2,300 rubles with a 25% discount, but you only have 2,000 rubles in your wallet. To find out if there is enough money for a new thing, carry out a series of simple calculations:
100% - 25% = 75% - the cost of trousers as a percentage of the original price after applying the discount.
2,400 / 4 × 3 = 1,800. That is how much the trousers cost.
5. How to calculate interest using a calculator
If life is not nice to you without a calculator, all calculations can be done with its help. And you can do it even easier.
- To calculate the percentage of the amount, enter the number equal to 100%, the multiplication sign, then the desired percentage and the% sign. For the coffee example, the calculations would look like this: 458 × 7%.
- To find the amount minus interest, enter a number equal to 100%, minus, the percentage and the% sign: 458 - 7%.
- Similarly, you can add, as in the example with a deposit: 530,000 + 5%.
6. How to calculate interest using online services
The site contains various calculators that calculate not only percentages. There are services for lenders, investors, entrepreneurs and all those who do not like to count in their heads.
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The simplest and most intuitive method is proportioning. All further calculations take place on its basis. It looks like this:
- 45 is a known number equal to 100%.
- ? - a number that is 15% of 45.
Further, there is a simplification of the fraction to an equation with one unknown. According to mathematical laws, cross-sectional data in proportions are equal to each other, that is: 45 * 15% =? * 100%. To find "?", We use simple rule and we get the following.
The calculation of the proportion formula always occurs according to the principle of multiplying the known data, standing on the diagonal and dividing them by the third number.
You can compose a formula with any unknown in. In order not to be confused, percent or a number is obtained as a result, recall the rule of reduction in a fraction - if the percent sign (%) or monetary designation(rub) is present both above and below, it is reduced. Example:
The result of the calculation is the amount of money.
How to find the percentage of a number. Variants
Let us consider in order the situations of finding interest.
How to find 100%. It is necessary to calculate the number, 15% of which is equal to 45. We make the proportion:
Calculated by the formula: (45 * 100) / 15 = 300
If it is not known how much is 100%. Sometimes the calculation is carried out with respect to the same initial data, but their exact meaning is not known. For example: yesterday 15% of the total number of cookies worth 450 rubles, and today 25%.
How much did you sell today? Since the amount for 100% is a common value for both 15% and 25%, it is possible to perform calculations without looking for the full cost.
Calculated by the formula: (25 * 450) / 15 = 750
You can complicate the task if you are not sure of the calculations, or there is a need to check the result. To do this, first, be 100%, based on full data (15% costs 450 rubles), and then 25% is counted from 100%.
How much less than another number as a percentage
For example: the usual cost of a powder is 500 rubles. For the action, the price was reduced to 480 rubles. How much is the share price less than the original percentage? First, the percentage of the promotional price from the base price is found, and then their difference is found. We make the proportion:
We calculate by the formula: (480 * 100) / 500 = 96. 100% -96% = 4%. The share price is 4% less than the original one.
How much the number is greater than the other as a percentage. Example: the keyboard cost 300 rubles, and after the increase in the dollar rate, the price increased to 390 rubles. How much has the price of the keyboard changed in percentage? In the beginning there is a common interest rate the new price, relative to the original, then their difference is calculated. We make the proportion:
We calculate by the formula: (390 * 100) / 300 = 130. 130% -100% = 30%. The price has increased by 30%.
The unknown number is higher than the known one by a certain percentage. Example: a product in a store is 15% more expensive than a product in stock. The price of sugar in the warehouse is 50 rubles and is equal to 100%. Shop price - 100% + 15% = 115%. Calculated by the formula: (115 * 50) / 100 = 57.5
The unknown number is less than the known number by the specified percentage. Example: wholesale is 5% cheaper. Retail price - 60 rubles and equal to 100 percent, for wholesale - 100% -5% = 95%. We make the proportion:
Calculated by the formula: (60 * 95) / 100 = 57
Percentage between two numbers. A situation when a number is known that is 100% and a number that is a certain fraction of the original. Example: a batch of 60 boxes was expected, but 53 were delivered. What percentage of the plan was fulfilled. We make the proportion:
Calculated by the formula: (53 * 100) / 60 = 88.3
The most difficult "task" is not to get confused in the proportion.
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The question "how to calculate percentages" begins to prevail among schoolchildren in grade 5. It is then that such a topic appears in mathematics. It seems that fifth-graders are not offered difficult problems. Then why do many 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 problems on this topic. If a person can determine one percent, then he can do thirteen, eighty-nine and one hundred thirty-five. At least four hundred and twenty ...
And this is one hundredth of the total, about which in question in the task. Moreover, it can be set explicitly, but it happens that it is only indirectly referred to.
What situations exist?
Find out the percentage of the number
That is, a certain value is known and it is required 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? It is necessary to make a proportion, in the first line the known data will be written, in the second - the required data. Now you need to multiply the known value by the desired percentage and divide by 100%.
If you write it shorter, you get the following proportion:
known number - 100%,
the required number is x%.
From this entry, you can compose the formula:
desired = (known * x%) / 100%.
The result is obtained by multiplying crosswise two known quantities and dividing by the one that was left without a pair.
If in the problem the total number is the sum of several, then the question arises of how to calculate the percentage of the amount. There are two ways to do this:
Find out the number by a known percentage
In this situation, the part of the number and the corresponding% are known. To find out how to calculate percentages correctly, you will need to use the proportion already recorded. Only the first line will contain the required number, and the second will contain the known one:
desired = (known * 100%) / x%.
Find out the percentage of one number from another
You are given two values, and you need to calculate how many percent will be more or less. Typically, such tasks contain information about the overfulfilled plan or, conversely, about a decrease in the quantity compared to an earlier value.
Again, proportion is required. It is customary to take the value with which it is compared for 100%.
the first value is 100%,
the second value is x%,
x = (second value * 100%) / first value.
Find out the percentage when nothing is known about the total
In such problems, it is reported that some number is a known percentage and another is unknown. This is what you need to calculate. How to calculate interest in this case? Again using proportion:
the first number is a known%,
second number - x%,
x = (second * known%) / first.
Tasks with more difficult questions
Find out how much the numbers differ
There are two possibilities 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 the percentage comes down to figuring out what to choose for 100%. The one that's bigger. And then the proportion will look like this:
higher number - 100%,
smaller number - x%,
x = (less * 100%) / more.
But that's not the answer. For it, you need to subtract the found value of x from 100%.
The second option is when the lower number is compared with the one that is larger. In it, the lower value is taken as 100%. The proportion looks like this:
smaller number - 100%,
larger number - x%,
x = (more * 100%) / less.
To calculate the final value, you need to find out how much x% will be - 100%.
Find out the result from increasing the number by a known percentage
In such tasks, you need to find the answer that will turn out after increasing the known percentage of it by some value. In this case, the proportion will look like this:
known number - 100%,
the required number - 100 + x%,
desired = (known * (100 + x%)) / 100%.
Find out the result from reducing the number by a known percentage
known number - 100%,
the required number - 100 - x%,
desired = (known * (100 - x%)) / 100%.
Calculator as an assistant in calculating interest
It can be used in two ways. The first is when all the steps described above are performed step by step on the device screen. Everything is simple here. You just need to not get confused with the procedure. In general, a calculator will simply replace a person at the moment of practical calculation.
In the second method, he will do everything himself. For example, you can select the engineering type of the calculator on a computer and enter the entire formula with brackets and the 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 dial a known value on the calculator. Then press the multiplication sign. Then the number of percent and the "%" button. The answer will immediately appear on the screen.
They will allow you not to get confused. Moreover, it will be able to answer any question about how to calculate the percentage of the amount or difference, you no longer have to think about it - everything will be solved automatically.
- Always go to specific values. Percentage is something impersonal. But the kilograms, students and boxes are quite tangible and understandable. And you need to strive for them.
- Read the condition very carefully. Because there are situations when interest is taken several times and on different values.
- Check the answer. Is it really finite? Or maybe it's just an intermediate value.
Perhaps math was not your favorite subject in school, and the numbers were frightening and boring. But in adulthood there is no escape from them. Without calculations, it is impossible to fill out a receipt for paying for electricity, not to draw up a business project, not to help a child with homework. Often in these and other cases it is required to calculate the percentage of the amount. How to do this if you have vague memories of what percentage is from school days? Let's strain our memory and figure it out.
Method one: a percentage of the amount by determining the value of one percent
Percentage is one hundredth of the number and is denoted by the% sign. If you divide the amount by 100, then just one percent of it will turn out. And then everything is simple. The resulting number is multiplied by the required percentage. In this way, it is easy to calculate the profit on a bank deposit.
For example, you put in an amount of 30,000 at 9% per annum. What will be the profit? The sum of 30,000 is divided by 100. We get the value of one percent - 300. We multiply 300 by 9 and we get 2700 rubles - an increase to the original amount. If the contribution is for two or three years, then this figure is doubled or tripled. There are deposits on which interest is paid on a monthly basis. Then you need to divide 2700 by 12 months. 225 rubles will be a monthly profit. If the interest is capitalized (added to the total account), then every month the amount of the deposit will increase. This means that the percentage will not be calculated from down payment, but from the new indicator. Therefore, at the end of the year, you will receive a profit not of 2700 rubles, but more. How many? Try to count.
Method two: convert percentages to decimal
Remember, percent is one hundredth of a number. In decimal form, it is 0.01 (zero point one cell). Therefore, 17% is 0.17 (zero point, seventeen hundredths), 45% - 0.45 (zero point, forty-five hundredths), etc. The resulting decimal fraction is multiplied by the amount, the percentage of which is counted. And we find the desired answer.
For example, let's calculate the amount income tax from a salary of 35,000 rubles. The tax is 13%. In decimal form, this will be 0.13 (zero point, thirteen hundredths). Multiply 35,000 by 0.13. It will turn out to 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, without tax, is called "wages on hand" or "clean". In contrast, the amount together with the tax "dirty wages". It is the “dirty salary” that is indicated in the company's vacancy announcements and in the employment contract. Less is given to hands. How many? Now you can easily calculate.
Method three: count on a calculator
If you are in doubt about your mathematical abilities, then use a calculator. With its help, it is considered faster and more accurate, especially when it comes to large amounts. It's easier to work with a calculator that has a button with a percent% sign. We multiply the amount by the number of percentages and press the% button. The required answer will be displayed on the screen.
For example, you want to calculate what your childcare allowance will be for up to 1.5 years old. It is 40% of the average earnings for the last two closed calendar years. Let's say average salary it turned out 30,000 rubles. On the calculator, multiply 30,000 by 40 and press the% button. The = key does not need to be touched. The screen will display the answer 12,000. This will be the amount of the benefit.
As you can see, everything is very simple. Moreover, the "Calculator" application is now in every cell phone... If the device does not have a special button%, then use one of the two methods described above. And multiply and divide on a calculator, which will facilitate and speed up your calculations.
Don't forget: there are online calculators to make your calculations easier. They work in the same way as usual, but always at hand when you work on your computer.
Method four: make up the proportion
You can calculate the percentage of the amount using proportions. This is another scary word from the school math course. Proportion - equality between two ratios of four quantities. For clarity, it is better to immediately understand specific example... You want to buy boots for 8,000 rubles. The price tag states that they are on sale with a 25% discount. How much is it in rubles? Of the 4 values, we know 3. There is a sum of 8,000, which equates to 100%, and 25%, which is required to be calculated. In mathematics, the unknown quantity is usually called X. It turns out the proportion:
For the convenience of calculations, 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 - a discount on boots. Subtract this amount from the old price. 8,000 - 2,000 = 6,000 rubles ( new price with discount). Here is such a nice proportion.
This method can also be used to determine the value of 100%, if you know the numerical indicator - for example, 70%. At the general corporate meeting, the chief announced that 46,900 units of the product had been sold during the year, while the plan was only 70% fulfilled. How much did you need to sell to fulfill the plan completely? We make the proportion:
We convert percentages to decimal fractions, it turns out:
We solve the proportion: X = 46,900 * 1: 0.7X = 67,000. These are the results of work expected by the authorities.
As you may have guessed, the proportion method can be used to calculate how much of a percentage is a numerical indicator of the amount. For example, on a test, you answered 132 out of 150 questions correctly. What percentage of the assignment was completed?
There is no need to translate 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 so scary. A little patience and attention, and now you have mastered the calculation of percentages.
How to calculate the percentage of the amount, you need to know in many cases (when calculating state fees, loans, etc.). We will show you how to calculate the percentage of the amount using a calculator, proportions and known ratios.
How to find out the percentage of the amount in general?
After that, there are two options:
- If you need to find out how much interest is another amount from the original, you just need to divide it by the amount of 1% obtained earlier.
- If you need the size of the amount, which is, say, 27.5% of the original, you need to multiply the size of 1% by the required number of percent.
How to calculate the percentage of the amount using the proportion?
But you can do it differently. To do this, you will have to use knowledge about the method of proportions, which is passed within the framework of the school mathematics course. It will look like this.
Suppose we have A - the principal amount equal to 100%, and B - the amount, the ratio of which 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 get the following formula:
X = 100 * B / A
If you need to find out how much the amount B will be with the already known number of percent of the amount A, the formula will look different:
B = 100 * X / A
Now it remains to substitute the known numbers into the formula - and you can make the calculation.
How to calculate the percentage of the amount using known ratios?
Finally, you can use more in a simple way... To do this, it is enough to 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 appropriate number - and the result will mean the amount of interest.
In addition, sometimes you can use simple fractions. For example, 10% is 0.1, that is, 1/10, therefore, to find out how much 10% will be, it's 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, you need to divide in half;
- 75% - 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 triples after the decimal point).
How to subtract a percentage of the amount without using a calculator
If it is required to subtract an unknown number from an already known amount, which is a certain amount of percent, you can use the following methods:
- Calculate an unknown number using one of the above methods, and then subtract it from the original.
- Calculate the remaining amount immediately. To do this, we subtract from 100% the number of percent that needs to be subtracted, and the result obtained is converted from percent to number in any of the ways described above.
The second example is more convenient, so let's illustrate it. Let's say you need to find out how much will remain if you subtract 16% from 4779. The calculation will be like this:
- We subtract from 100 ( total amount percent) 16. We get 84.
- We consider how much will be 84% of 4779. 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 ordinary mobile phone (even the oldest devices in use today usually have this function). With their help, the question of how to calculate the percentage of the amount is solved very simply:
- The initial amount is dialed.
- The "-" sign is pressed.
- The number of percent to be subtracted is entered.
- 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 enough sites on the web that offer an online calculator function. In this case, knowledge of how to calculate the percentage of the amount is not even required: all user operations are reduced to entering the necessary numbers into the boxes (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 size tax deduction or the amount of state duty. The fact is that in this case the calculations are more complicated: it is required not only to find the percentages, but also to add a constant part of the amount to them. The online calculator avoids such additional calculations. The main thing is to choose a site that uses data that complies with applicable law.