The percentage calculator is designed to calculate basic mathematical problems related to percentages. In particular, it allows:
- Calculate the percentage of a number.
- Determine what percentage one number is of another.
- Add or subtract a percentage from a number.
- Find a number, knowing its certain percentage.
- Calculate by what percentage one number is greater than another.
The result can be rounded to the required decimal place.
Percentage shows the hundredth part of a unit, which is indicated using the “%” sign. This indicator used to indicate the proportion of something to the whole. They still knew how to calculate the percentage of a number Ancient Rome. Before the decimal system was invented, calculations were made using fractions that were divisible by 1 to 100. Octavian Augustus imposed a tax of one hundredth on goods that were sold at auction, called Centesima Rerum Venalium. Calculation using multipliers was somewhat reminiscent of calculating percentages.
When currency was replaced in the Middle Ages, calculations with the denominator one hundred became more common, and from the late 16th century to the early 17th century, this method of calculation began to be used by everyone, based on materials that contained arithmetic calculations. According to the materials, this method was used when calculating profit and loss, interest rates, and also the rule of three. In the seventeenth century, this form of calculation was the standard for expressing interest rates in hundredths. The concept of interest was introduced in Russia by Peter I. However, it is believed that similar calculations began to be used in Time of Troubles, as a result of the first pegging of minted coins 1 to 100, when the ruble was worth 10 hryvnias, and a little later - 100 kopecks.
Sometimes two quantities are compared not by comparing their values, but by percentage. For example, compare the price of two goods not in monetary terms, but compare as a percentage how much the price of one product exceeds the price of the other. If it is possible to determine how much one indicator is more or less than another, then for comparison in % it is necessary to indicate relative to what value the percentage is calculated. Such an indication is sometimes not necessary when it is said that one indicator is greater than another by a percentage that is greater than 100. In this case, there is one way to find the percentage, divide the difference by the smaller of the two numbers and multiply this number by 100.
How to find the percentage of a number
In order to find the percentage of a number, you need to multiply the given number by the number of percentages and divide the resulting number by one hundred. As a rule, there are three main types of problems for calculating percentages:
- Calculate the percentage of this number. This number you need to multiply by the specified number of percents, and then the result needs to be divided by 100.
- Determine a number from a given other number and its value as a percentage of the desired number. This number must be divided by the percentage and the result multiplied by 100.
- Determine the expression of one number from another as a percentage. The first number must be divided by the second and the result multiplied by 100.
As a rule, in an economy where most indicators are expressed as percentages, the change in such indicators is expressed not as a percentage of the original indicator, but in percentage points, which show the difference between the new and old values of the indicator. For example, if in a country the index business activity increased from 50% to 51%, then its changes are calculated in a similar way: (51%-50%)/50= 1/50=2%, which in percentage points is 1%.
Knowing how to find percentages is necessary for every person. Life constantly gives us tasks to find percentages, and sometimes several times a day. This includes the discount percentage in the store, interest on bank deposits, and much more.
Before you understand how to find percentages, you need to define this mathematical concept. So, one hundredth of any number is called a percentage.
How to find the percentage of a number
Suppose we need to solve the problem: “The store has announced a 5% discount. How many rubles cheaper is a skirt now, the original price of which was 300 rubles?” To solve this problem, we need to calculate how many rubles will be 5% of 300 rubles, i.e. find the percentage of the number.
As we have already said, a percentage is a hundredth part of any number. Then let’s calculate how much 1% of 300 rubles is. To do this, divide 300 by one hundred. It turns out that 1% of 300 is equal to 3.
Now that we know what 1% is equal to, we can easily calculate how many rubles will be 5% of 300 rubles. You just need to do it next action: 3 * 5 = 15 (rubles).
Thus, the skirt became 15 rubles cheaper.
It's even easier to find the percentage of a number using proportion.
300 rubles – 100%
X rubles – 5%
Hence X = (300*5)/100=15 rubles.
How to find a percentage of an amount
Finding the percentage of the amount is very easy. First, add all the terms. Then the resulting amount is divided by one hundred, and the resulting result is multiplied by the number of percent specified by the conditions of the problem.
For example, you need to find 7% of the sum of the numbers 35 and 42.
- 35 + 42 = 77
- 77: 100 = 0,77
- 0,77 *7 = 5,39
How to find percentages using a calculator
The easiest way to understand and remember how to find percentages using a calculator is: specific example. To do this, let's find 9% of 749.
On the calculator, multiply the number from which we find the percentage by the number of percentages and click the “%” icon. Please note that when finding percentages on the calculator, you do not need to press the “=” key.
How it looks in our example: 749 * 9%. If everything is entered correctly, the number “67.41” will appear on the screen, which is the answer to this problem.
Today at modern world It is impossible to do without interest. Even at school, starting from the 5th grade, children learn this concept and solve problems with this value. Interests are found in every area of modern structures. Take banks, for example: the amount of loan overpayment depends on the amount specified in the agreement; the size of the profit is also affected. Therefore, it is vitally important to know what percentage is.
Interest concept
According to one legend, the percentage appeared due to a stupid typo. The typesetter was supposed to set the number 100, but he got it wrong and set it like this: 010. This caused the first zero to rise slightly and the second to fall. The one turned into a backslash. Such manipulations resulted in the appearance of the percent sign. Of course, there are other legends about the origin of this quantity.
Hindus knew about interest back in the 5th century. In Europe, with which our concept is closely interconnected, they appeared a millennium later. For the first time in the Old World, the idea of what interest is was introduced by a scientist from Belgium, Simon Stevin. In 1584, a table of quantities was first published by the same scientist.
The word "percentage" originates in Latin as pro centum. If you translate the phrase, you get “from a hundred.” So, by percentage we mean one hundredth of any value or number. This value is indicated by the % sign.
Thanks to percentages, it became possible to compare parts of one whole without much difficulty. The appearance of shares greatly simplified calculations, which is why they became so common.
Converting fractions to percentages
To translate decimal as a percentage, you may need the so-called percentage formula: the fraction is multiplied by 100, and % is added to the result.
If you need to convert to percentage common fraction, first you need to make it decimal, and then use the above formula.
Converting percentages to fractions
As such, the percentage formula is quite arbitrary. But you need to know how to convert this value into a fractional expression. To convert fractions (percents) to decimals, you need to remove the % sign and divide the indicator by 100.
Formula for calculating percentage of a number
1) 40 x 30 = 1200.
2) 1200: 100 = 12 (students).
Answer: test work 12 students wrote “5”.
You can use a ready-made table that shows some fractions and the percentages that correspond to them.
It turns out that the formula for percent of a number looks like as follows: C = (A∙B) / 100, where A is the original number (in the specific example equal to 40); B - number of percents (in this problem B = 30%); C is the desired result.
Formula for calculating a number from a percentage
The following problem will demonstrate what a percentage is and how to find a number using a percentage.
The garment factory produced 1,200 dresses, of which 32% were dresses of a new style. How many dresses of the new style did the garment factory produce?
1. 1200: 100 = 12 (dresses) - 1% of all products released.
2. 12 x 32 = 384 (dresses).
Answer: the factory produced 384 dresses of the new style.
If you need to find a number by its percentage, you can use the following formula: C = (A∙100) / B, where A - total quantity objects (in this case A=1200); B - number of percent (in specific task B=32%); C is the desired value.
Increase or decrease a number by a specified percentage
Students must learn what percentages are, how to count them, and solve a variety of problems. To do this, you need to understand how a number increases or decreases by N%.
Often tasks are given, and in life you need to find out what a number will be equal to when increased by a given percentage. For example, given the number X. You need to find out what the value of X will be equal to if it is increased, say, by 40%. First you need to transfer 40% to fractional number(40/100). So, the result of increasing the number X will be: X + 40% ∙ X = (1+40 / 100) ∙ X = 1.4 ∙ X. If you substitute any number instead of X, take, for example, 100, then the whole expression will be equal : 1.4 ∙ X = 1.4 ∙ 100 = 140.
Approximately the same principle is used when reducing a number by a given percentage. It is necessary to carry out calculations: X - X ∙ 40% = X ∙ (1-40 / 100) = 0.6 ∙ X. If the value is 100, then 0.6 ∙ X = 0.6. 100 = 60.
There are tasks where you need to find out by what percentage a number has increased.
For example, given the task: The driver was driving along one section of the track at a speed of 80 km/h. On another section, the train speed increased to 100 km/h. By what percentage did the speed of the train increase?
Let's say 80 km/h - 100%. Then we make calculations: (100% ∙ 100 km/h) / 80 km/h = 1000: 8 = 125%. It turns out that 100 km/h is 125%. To find out how much the speed has increased, you need to calculate: 125% - 100% = 25%.
Answer: the speed of the train on the second section increased by 25%.
Proportion
There are often cases when it is necessary to solve problems involving percentages using proportions. In fact, this method of finding the result greatly simplifies the task for students, teachers and others.
So what is proportion? This term refers to the equality of two ratios, which can be expressed as follows: A / B = C / D.
In mathematics textbooks there is such a rule: the product of the extreme terms is equal to the product of the middle terms. This is expressed by the following formula: A x D = B x C.
Thanks to this formulation, any number can be calculated if the other three terms of the proportion are known. For example, A is an unknown number. To find it you need
When solving problems using the proportion method, you need to understand from which number to take percentages. There are cases when shares need to be taken from different values. Compare:
1. After the end of the sale in the store, the cost of the T-shirt increased by 25% and amounted to 200 rubles. What was the price during the sale?
In this case, the required value is 200 rubles, which corresponds to 125% of the original (sale) price of the T-shirt. Then, to find out its cost during the sale, you need (200 x 100): 125. The result is 160 rubles.
2. On the planet Vicencia there are 200,000 inhabitants: people and representatives of the humanoid race Naavi. The Na'avi make up 80% of the entire population of Vicencia. Of the people, 40% are engaged in servicing the mine, the rest are extracting tettanium. How many people mine tetanium?
First of all, you need to find in numerical form the number of people and the number of Naavi. So, 80% of 200,000 would equal 160,000. This is how many representatives of the humanoid race live on Vicencia. The number of people, accordingly, is 40,000. Of these, 40%, that is, 16,000, service the mine. This means that 24,000 people are engaged in tettanium mining.
Repeated change of a number by a certain percentage
When it is already clear what percentage is, you need to study the concept of absolute and relative change. An absolute conversion means increasing a number by a specific number. So, X increased by 100. No matter what we substitute for X, this number will still increase by 100: 15 + 100; 99.9 + 100; a + 100, etc.
A relative change is understood as an increase in a value by a certain number of percent. Let's say X increased by 20%. This means that X will be equal to: X+X∙20%. Relative change is implied whenever we talk about an increase by half or a third, a decrease by a quarter, an increase by 15%, etc.
There is another one important point: if the value of X is increased by 20%, and then by another 20%, then the resulting total increase will be 44%, but not 40%. This can be seen from the following calculations:
1. X + 20% ∙ X = 1.2 ∙ X
2. 1.2 ∙ X + 20% ∙ 1.2 ∙ X = 1.2 ∙ X + 0.24 ∙ X = 1.44 ∙ X
This shows that X increased by 44%.
Examples of problems involving percentages
1. What percentage of the number 36 is the number 9?
According to the formula for finding the percentage of a number, you need to multiply 9 by 100 and divide by 36.
Answer: The number 9 is 25% of 36.
2. Calculate the number C, which is 10% of 40.
According to the formula for finding a number by its percentage, you need to multiply 40 by 10 and divide the result by 100.
Answer: The number 4 is 10% of 40.
3. The first partner invested 4,500 rubles in the business, the second - 3,500 rubles, the third - 2,000 rubles. They made a profit of 2400 rubles. They divided the profits equally. How much in rubles did the first partner lose, compared to how much he would have received if they had divided the income according to the percentage of the funds invested?
So, together they invested 10,000 rubles. The income for each was an equal share of 800 rubles. To find out how much the first partner should have received and how much he, accordingly, lost, you need to find out the percentage of invested funds. Then you need to find out how much profit this contribution makes in rubles. And the last thing is to subtract 800 rubles from the result obtained.
Answer: the first partner lost 280 rubles when dividing the profits.
A bit of economics
Today, a fairly popular question is applying for a loan for certain period. But how to choose a profitable loan so as not to overpay? First, you need to look at the interest rate. It is desirable that this figure be as low as possible. It should then be applied against the loan.
As a rule, the amount of overpayment is affected by the amount of debt, interest rate and method of repayment. There are annuity and In the first case, the loan is repaid in equal installments every month. Immediately, the amount that covers the principal loan grows, and the cost of interest gradually decreases. In the second case, the borrower pays constant amounts to repay the loan, to which interest is added on the balance of the principal debt. Monthly total amount payments will decrease.
Now you need to consider both methods. So, with the annuity option, the amount of overpayment will be higher, and with the differential option, the amount of the first payments will be higher. Naturally, the loan terms are the same for both cases.
Conclusion
So, percentages. How to count them? Simple enough. However, sometimes they can cause difficulties. This topic begins to be studied in school, but it catches up with everyone in the field of loans, deposits, taxes, etc. Therefore, it is advisable to delve into the essence of this issue. If you still can’t make the calculations, there are a lot of online calculators that will help you cope with the task.
A percentage is one hundredth of something. From the definition it follows that anything whole is taken as 100 percent. The percentage is indicated by the "%" symbol.
How to solve problems in which you need to calculate percentages of a number? The percentage of a number can be calculated either by a formula or on a calculator.
- Example task: The price of a basket of apples is 160 rubles. The price of a basket of plums is 20% more expensive. How many rubles is more expensive than a basket of plums?
- Solution: In this task, we are required to do nothing more than find out how many rubles are 20% percent of the number 160.
Formula for calculating percentage:
1 way
Since 160 rubles is 100%, we first find out what 1% will be equal to. And then multiply this number by the 20% we need.
- 160 / 100 * 20 = 1,6 * 20 = 32
Answer: a basket of plums is 32 rubles more expensive.
2 way
The second method is a modified version of the first method. Let's multiply the number that is 100% by a decimal fraction. This fraction is obtained by dividing the number of percentages that need to be found by 100. In our case:
- 20% / 100 = 0,2
We multiply 160 by 0.2 and get the same answer 32.
3 way
Method 3 - proportion.
Let's make a proportion of the form:
- x = 20%
- 160 = 100%
We multiply the parts of the proportion cross by cross and get the equation:
- x = (160 * 20) / 100
- x = 32
Calculating percentage of a number on a calculator
In order to calculate 20% of the number 160 on a calculator, you need:
- First, dial the number 160 on the screen - that is, our 100%
- Then press the multiply button "*"
- We will multiply by the number of percents that need to be found, that is, by 20. Press 20
- Now press the % key
- The answer should appear on the screen: 32
Read more about interest calculation algorithms in the article
