How to find out 1 percent of 100. What is percent? Interest formula. Percentages - how to calculate? Find a specified percentage of a given number

To calculate the percentage of one number from another, you need to divide the first number by the second and multiply by 100% For example: what percentage is 5 of the number 25? We calculate: Percentage = 100* 5/25 = 20%

Our world consists of patterns and sequences. They are everywhere: day turns to night, animals migrate in their own order. Animals even have a sense of distance and quantity. The main concept of mathematics is space and quantity, which are built into our brains. In nature, everything is interconnected with this science. Perhaps some people don't think about it. But it is so. Great Representatives different cultures discovered the language of mathematics to describe the Universe. And based on them, a person in modern world uses it in life. For example, the percentage of a number mainly affects the economy, financial and demographic side of our lives. Thus, even this insignificant part of the great science is relevant to every family. In the modern world it is no longer possible to do without certain knowledge in one area or another.

Why does a person need mathematical calculations in life?

This is necessary for uniform development in all respects, for rational use family expenses. The information from this article can be useful to each of us. For some, it will be useful to refresh the knowledge acquired in school, while for some people it is necessary to fill a gap in their education. It's no secret that many of us could not take schooling seriously. When we were children, we believed that some topics were too difficult and would not be useful to us in life at all. We especially need knowledge of how to find the percentage of a number. Mathematics is everywhere: in biology, chemistry, astronomy. She teaches you to think outside the box. Develops mathematical logic and reveals creative abilities. As one said clever man: “Mathematics is special kind art." To imagine all the nuances, you need to include fantasy and abstract thinking. And in order for all this to be interesting, it is necessary high level teaching exact sciences and correct perception. Knowledge of calculations (percentage of a number) simplifies life in material and other respects.

When is interest calculated in life?

This is necessary for comparison and perception (for example, a person consists of 66% water, and a jellyfish is 98%). In economics, a percentage of a number is used (you can calculate profit in business ((3000 - 2000) : 2000) · 100% = 50%). This knowledge will also be useful for analyzing values ​​(for example, in June - 100% salary, in July - 50% higher, 100 + 50 = 150%, (50: 150) multiplied by 100%, it turns out (1: 3) x 100 = 33%, i.e. the salary was 33% less than in July). Calculating the percentage of a number will be easy if you understand the essence of the problem once. If you learn the material about finding a part of a number and vice versa, then there will be no difficulties in calculating percentages. For example, let's find 2/5 of 20. Solution: 20 x 2/5 = 20 x 2: 5 = 8. Now you can understand how to calculate percentages.

Calculation of percentage of number

In order to understand the topic, it is advisable to start with its very basics. One percent is one hundredth of a number: 1/100, or 0.01. Two percent is 2/100, or 0.02. Twenty percent = 20/100 = 1/5 = 0.2. Also 75% = 75/100 = 3/4 = 0.75. Now let’s calculate, say, 25% of 80. Let’s look at an example. 25% = 25/100 = 0.25 = 1/4, and 80 x 0.25 = 20. Another way: 80 x 25/100 = 80 x 1: 4 = 20. As you can see, the decision does not affect the result form of writing a number. Or let's calculate 20% of 150. A simple example: 20% = 0.2. 150 x 0.2 = 30. It was mentioned above that such calculations are necessary when compiling a family budget book. Let's try to calculate our own budget (expenses and income) by considering the proposed example.

Family budget calculations

Parents receive: mom - eight thousand, dad - six thousand. A total of fourteen thousand (100%). You need to find the interest income in the family budget of both parents. Let's apply the rule for finding the percentage of a number. To find the salary percentage, you need to multiply the amount by one hundred and divide by fourteen thousand. (6000 x 100: 14,000 = 42.85%). Next: (8000 x 100: 14,000 = 57.14%). Now consider the family expenses and the percentage of the amount.

Family expenses

• Utilities - 800 rubles (800 x 100: 14,000 = 5.7%).
• Electricity - 490 rubles (490 x 100: 14,000 = 3.5%).
• Payment for a landline phone - 250 rubles (250 x 100: 14,000 = 1.7%).
• Meals - 5,000 rubles (5,000 x 100: 14,000 = 35.71%).
• Clothes - 3900 rubles (3900 x 100: 14,000 = 27.85%).
• Medicines - 510 rubles (510 x 100: 14,000 = 3.64%).
• Detergents - 220 rubles (220 x 100: 14,000 = 1.57%).
• Buying gasoline and other things for a car - 1000 rubles (1000 x 100: 14,000 = 7.1%).
• Payment for school meals - 500 rubles (500 x 100: 14,000 = 3.57%).
• A total of 12,670 rubles (12,670 x 100: 14,000 = 90.5%).

Conclusion: 90.5% of expenses from the number, i.e. from the parents’ salary. Almost 10% remains for any unforeseen event. There are formulas in the world that it is advisable to remember. They will come in handy everywhere. We will devote the next subsection of the article to this topic.

Formulas

Here is an example of existing formulas:

• B = A x P: 100%; A = B x 100%: P;
• P = B: A x 100%; B = A x (1 + P: 100%);
• B = A x (1 - P: 100%);
• A = (B x 100%) : (100% + P).

The list also continues with the formulas:

• A = (B x 100%) : (100% - P);
• B = A x (1 + P: 100%) x n.

Designations: B - future value; A - current value; P - interest rate for a certain period; n is the number of all computational periods.

Let's give an example. Problem No. 1: you need to find B, which is 6% of 36. Solution: B = 36 x 6: 100 = 2.16. Answer: B = 2.16.

Problem No. 2. What percentage is the number 37 of 21? Solution: 37: 21 x 100 = 176%. Answer: 176%.

Problem No. 3. Find a number 17% less than 30. Solution: 30 x (1 - 17: 100%) = 30 x 0.83 = 24.9. Answer: the number 24.9 is 17% less than 30.

On clear example We see that there is nothing difficult in solving problems with percentages. The main thing is to develop an interest in this topic in advance. And even if you lack knowledge, you can fill it up by reading this article to the end.

Factors that develop interest in learning

It is noticeable that if you spend a little time solving percentage problems, then anyone will become interested, and mathematics will become an integral part of life. But you need to start learning from kindergarten. And even better from birth. The child perceives science more easily during these years. There is an opinion that if you miss education until the age of three, then later it will be more difficult to instill in your child a love for school and lessons. There are factors that shape a person’s interest in mathematics: the kind attitude of the teacher, the attention of parents, praise and the correct active teaching method (try to captivate the child and turn the task into an exciting adventure). After all, even the most difficult task can become exciting. A teacher must be, first of all, a psychologist and find an approach to each student, prepare individual sessions. This can develop confidence and feeling self-esteem in children.

A conscientious teacher develops various competitions, skits, and mathematical KVN so that children fall in love with his science and other subjects at school and preschool. This sparks enthusiasm in children. Learning through fairy tales will appeal to everyone. Some teachers give home assignments, for example, to write a fairy-tale essay on the topic “Journey to the Land of Mathematics.” And children use their imagination and write exciting stories. In this case, the kids will really love school! And then, as children grow up, they will find the use of mathematics in any area of ​​life. Yes, all of humanity should expand its knowledge in the field of percentage calculations, despite the fact that this topic is one of the most difficult. What grades teach percentage problems? This topic is discussed in detail only in the fifth and sixth grades. Later, a small part of the time is devoted to this. Therefore, anyone who encounters percentage calculations will have to remember middle school mathematics. As it turns out, this is not difficult to do. Who came up with this?

History of interest problems

The Latin expression pro centum is defined as “per hundred”, “from a hundred”. But it comes from an Italian word that is written as “one hundred.” However, there is still an assumption that the “%” (percentage) sign appeared due to an oversight by the book’s writer. Instead of “one hundred,” he typed %. One engineer from the Netherlands, as a pioneer, released the percentage calculation table to the world in 1584. At first this science was used in trade areas, then gradually percentages began to be used in technical work, science, economic affairs, statistics. We can conclude that mathematics and the use of percentage calculations will be very useful in life.

In this short video lesson we will learn how to solve problems involving percentages using a special formula called the simple interest formula. Let's formalize this formula as a theorem.

The simple interest theorem. Let's assume that there is a certain initial value x, which then changes by k%, and a new value y is obtained. Then all three numbers are related by the formula:

A plus or minus is placed in front of the coefficient k depending on the conditions of the problem. If, according to the condition, the value x increases, then there is a plus in front of k. If the value decreases, then the coefficient k is preceded by a minus.

Despite the apparent intricacy of this formula, many problems can be solved very quickly and beautifully with its help. Let's try.

Task. The price of the product was increased by 10% and amounted to 2970 rubles. How many rubles did the product cost before the price increase?

To solve this problem using the simple interest formula, we need three numbers: the original value x, the percentage k, and the final value y. From all three numbers, we know the percentage k = 10 and the final value y = 2970. Please note: 2970 is exactly the final price, i.e. y. Because according to the conditions of the problem, the initial price of the product is unknown (it is precisely what needs to be found). But then it was increased, and only then it amounted to 2970 rubles.

So, we need to find x, i.e. original value. Well, we substitute our numbers into the formula and we get:

We add the numbers in the numerator and get:

We reduce one zero each in the numerator and denominator, and then multiply both sides of the equation by 10. We get:

11x = 29,700

To find x from this simplest linear equation, you need to divide both sides by 11:

x = 29,700: 11 = 2700

As you can see, it's quite big numbers, so you can’t carry out such calculations in your head. If you encounter such a problem on the Unified State Exam, you will have to divide it into a corner. In this case, everything was divided without a remainder, and we received the value x:

x = 2700

This is how much the product cost before the price increase. And it was this number that we needed to find according to the conditions of the problem. So that’s it: the problem is solved. Moreover, it was solved not “outright”, but using the simple interest formula - quickly, beautifully and clearly.

Of course, this problem could have been solved differently. For example, through proportions. Or the exotic coefficient method. But it will be much better and more reliable if you have several techniques in your arsenal for solving any percentage problem. So be sure to practice using this formula.

And that's all for me. Pavel Berdov was with you. See you again! :)