What is a percentage? The project "interest in our life", the topic "the history of interest" Interest from the history of occurrence to our times

»; used to indicate the proportion of something in relation to the whole. For example, 17% of 500 kg means 17 pieces of 5 kg each, i.e. 85 kg. It is also true that 200% of 500 kg is 1000 kg, since 1% of 500 kg is equal to 5 kg, and 5 × 200 = 1000.

Origin

In ancient Rome, long before the existence of the decimal number system, calculations were often made using fractions that were multiples of 1/100. For example, Octavian Augustus levied a tax of 1/100 on goods sold at auction, this was known as lat. centesima rerum venalium (a hundredth of the items sold). Such calculations were similar to the calculation of percentages.

During the currency denomination in the Middle Ages, calculations with a denominator of 100 became more common, and from the end of the 15th century to the beginning of the 16th century, this method of calculation began to be widely used, judging by the content of the studied materials containing arithmetic calculations. In many of these materials, this method was used to calculate profit and loss, interest rates, as well as in the rule of three [ unknown term ] . In the 17th century, this form of calculation became the standard for expressing interest rates in hundredths.

In Russia, the concept of interest was first introduced by Peter I. But it is believed that such calculations began to be applied in the Time of Troubles, as a result of the first in the world history of binding minted coins 1 to 100, when the ruble first consisted of 10 hryvnias, and later of 100 kopecks [ ] .

The ratio of percentages and decimals

• 0 % = 0;
• 0,07 % = 0,0007;
• 45,1 % = 0,451;
• 100 % = 1;
• 146 % = 1,46;
• 200 % = 2
• 500 % = 5

Dial rules

In the text, the percent sign is used only for numbers in digital form, from which, when typing, it is separated by a non-breaking space ( income 67%), except when the percent sign is used to abbreviate complex words formed with the help of a numeral and an adjective percentage. For example: 20% sour cream(means twenty percent sour cream), 10% solution, 20% solution [ ] , but fat content of sour cream is 20%, solution with a concentration of 10% etc.

This dialing rule was put into effect in 1982 by the regulatory document GOST 8.417-81 (subsequently replaced by GOST 8.417-2002); previously the norm was not to separate the percent sign with a space from the preceding digit. At present, the percentage sign rule is not generally accepted. Until now, many Russian publishing houses do not follow the recommendations of GOST 8.417-2002 and still adhere to the traditional typing rules, that is, when typing, the percent sign is not separated from the previous number.

Colloquial usage

• "Work for interest" - work for remuneration, calculated depending on profit or turnover.
• "Interestor" - a person who lends money at high interest, usurer.

percentage point

Changes in indicators, which are themselves calculated as a percentage, are usually expressed not as a percentage of the original indicator, but in so-called "percentage points", expressing the difference between the new and old values ​​​​of the indicator. For example, if in a certain country the index of business activity increased from 50% to 51%, then it changed to 51% − 50% 50% = 1 50 = 0 , 02 = 2% (\displaystyle (\frac (51~\%-50~\%)(50~\%))=(\frac (1)(50 ))=0(,)02=2~\%), and in percentage points the change was 51% − 50% = 1% (\displaystyle 51~\%-50~\%=1~\%).

Percent comparison

Sometimes it is convenient to compare two quantities not by the difference between their values, but by percentage. For example, to compare the price of two goods not in rubles, but to evaluate how much the price of one goods is more or less than the price of the other as a percentage. If comparison by difference is quite unambiguous, that is, it is always possible to find how much one value is greater or less than another, then for comparison in percentage, it is necessary to indicate with respect to which value the percentage is calculated. Such an indication, however, is not necessary when one is said to be greater than the other by a percentage greater than 100. In this case, there is only one possibility of calculating the percentage, namely dividing the difference by the smaller of the two numbers and then multiplying the result by 100 .

One of the basic concepts of mathematics is percentage. In order to understand what a percentage is, it is enough to divide the given integer value by one hundred. One hundredth will be one percent (denoted as 1%). As in the exact and economic sciences, as in other areas of life, percentages are used to denote proportions in relation to the whole. In this case, the whole itself is designated as 100%. In some cases, it is used when comparing two values: for example, sometimes the cost of goods is not compared in monetary units, but it is estimated by how much% the price of one product is more or less than the price of another. The term has also become widespread in banking and in most cases is used as a synonym for the phrase "interest rate".

The rule for finding percentages of a number

Calculating percentages of a whole is one of the basic mathematical operations, and it is also often used in everyday life. The rule for finding percentages of a number says that to solve such a problem, it must be multiplied by the amount of% specified in the conditions, after which the result should be divided by 100. You can also divide the number by 100, and multiply the result by the specified amount of%. It is important to remember one more thesis: if the percentage specified by the conditions exceeds 100%, then the resulting numerical value is always greater than the initial (given) value - and vice versa.

The rule for finding a number by its percentage

There is an inverse rule for finding a number by its percentage. In order to get the result for such a mathematical operation (the second of the three basic types of problems for percentage calculations), it is necessary to divide the number specified in the conditions by a given percentage, after which the result is multiplied by 100. In this case, the number of units of the original value in 1 is calculated as the first action %, and the second - in general (that is, 100%). If the amount of % exceeds 100, then the result will always be less than the numerical value specified by the conditions of the problem - and vice versa.

The rule for finding the percentage expression of a number from another

The third basic type of mathematical tasks for percentage calculations are tasks in which it is necessary to use the rule for finding the percentage expression of a number from another (or the ratio of two quantities). It says that to solve it, you need to divide the second number by the first, after which the result should be multiplied by one hundred. Such a ratio shows how much % one numerical value is from another (that is, in fact, we are talking about the ratio between two numerical values, expressed in%).

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In Russia, the concept of interest was first introduced by Peter I. But it is believed that such calculations began to be applied in the Time of Troubles, as a result of the first in the world history of binding minted coins 1 to 100, when the ruble first consisted of 10 hryvnias, and later of 100 kopecks [[C:Wikipedia:Articles without sources (country: Lua error: callParserFunction: function "#property" was not found. )]][[C:Wikipedia:Articles without sources (country: Lua error: callParserFunction: function "#property" was not found. )]] .

The ratio of percentages and decimals

• 0 % = 0;
• 0,07 % = 0,0007;
• 45,1 % = 0,451;
• 100 % = 1;
• 146 % = 1,46;

Dial rules

In the text, the percent sign is used only for numbers in digital form, from which, when typing, it is separated by a non-breaking space ( income 67%), except when the percent sign is used to abbreviate complex words formed with the help of a numeral and an adjective percentage. For example: 20% sour cream(means twenty percent sour cream), 10% solution, 20% solution, but fat content of sour cream is 20%, solution with a concentration of 10% etc.

This dialing rule was put into effect in 1982 by the regulatory document GOST 8.417-81 (subsequently replaced by GOST 8.417-2002); previously the norm was not to separate the percent sign with a space from the preceding digit. At present, the percentage sign rule is not generally accepted. Until now, many Russian publishing houses do not follow the recommendations of GOST 8.417-2002 and still adhere to the traditional typing rules, that is, when typing, the percent sign is not separated from the previous number.

Colloquial usage

percentage point

In an economy where many indicators are calculated as a percentage, the change in these indicators is usually expressed not as a percentage of the original indicator, but as so-called "percentage points", expressing the difference between the new and old values ​​​​of the indicator. For example, if in a certain country the index of business activity increased from 50% to 51%, then it changed to texvc not found; See math/README for setup help.): \frac(51%-50%)(50%)=\frac(1)(50)=0.02=2%, and in percentage points the change was Unable to parse expression (executable file texvc not found; See math/README for setup help.): 51%-50%=1% .

Percent comparison

Sometimes it is convenient to compare two quantities not by the difference between their values, but by percentage. For example, to compare the price of two goods not in rubles, but to evaluate how much the price of one goods is more or less than the price of the other as a percentage. If comparison by difference is quite unambiguous, that is, it is always possible to find how much one value is greater or less than another, then for comparison in percentage, it is necessary to indicate with respect to which value the percentage is calculated. Such an indication, however, is not necessary when one is said to be greater than the other by a percentage greater than 100. In this case, there is only one possibility of calculating the percentage, namely dividing the difference by the smaller of the two numbers and then multiplying the result by 100 .

see also

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Notes

Literature

• / REVIEW OF EDUCATIONAL RESEARCH Winter 1995 vol. 65 no. 4 421-481 doi: 10.3102/00346543065004421 (English)

View this template A plus ( + ) Minus ( − ) Multiplication sign ( · or × ) Division sign ( : or / ) Root sign ( √ ) Equal sign ( = , ≈ , ≡ etc.) Inequality signs ( ≠ , > , < etc.) Infinity sign ( ∞ ) Integral sign ( ∫ ) Factorial ( ! ) Vertical bar ( | ) Degree sign ( ° ) Minute of degree ( ′ ) Degree second ( ″ ) Stroke ( ′ ) Asterisk ( * ) Backslash, backslash ( \ ) Percent ( % ) ppm ( ‰ ) tilde ( ~ ) caret ( ^ ) Circumflex ( ̂ ) plus or minus ( ± ) Obelus ( ÷ ) Decimal separator ( , or . )

View this template Fractions of a number (parts of a whole) Presentation Forms variable value fixed value see also

An excerpt characterizing Percentage

I stood completely shocked, as it was almost always after the next story of the North ...
Was that tiny, newly born boy really the famous Jacques de Molay?! How many different bizarre legends I heard about this mysterious man!.. How many miracles were connected with his life in the stories I once loved!
(Unfortunately, wonderful legends about this mysterious man have not survived to this day... He, like Radomir, was made a weak, cowardly and spineless master who "failed" to save his great Order...)
– Can you tell us a little more about him, Sever? Was he such a powerful prophet and miracle worker as my father once told me? ..
Smiling at my impatience, Sever nodded in the affirmative.
– Yes, I will tell you about him, Isidora... I have known him for many years. And I talked to him many times. I loved this man very much ... And I missed him very much.
I did not ask why he did not help him during the execution? It didn't make sense, since I already knew his answer.
– What are you?! Have you spoken to him? Please, will you tell me about this, Sever?!. I exclaimed.
I know I was like a child in my excitement... But it didn't matter. Sever understood how important his story was for me, and patiently helped me.
“Only I would like to know first what became of his mother and the Cathars. I know that they died, but I would like to see it with my own eyes... Help me, please, Sever.
And again, reality disappeared, returning me to Montsegur, where wonderful brave people lived their last hours - students and followers of Magdalene ...

Cathars.
Esclarmonde lay quietly on the bed. Her eyes were closed, she seemed to be sleeping, exhausted by losses ... But I felt - it was just protection. She just wanted to be alone with her sadness... Her heart suffered endlessly. The body refused to obey... Just a few moments ago, her hands were holding a newborn son... Embracing her husband... Now they are gone into the unknown. And no one could say with certainty whether they would be able to get away from the hatred of the "hunters" who filled the foot of Montsegur. Yes, and the whole valley, as far as the eye covered ... The fortress was the last stronghold of the Cathars, after it there was nothing left. They suffered a complete defeat ... Exhausted by hunger and winter cold, they were helpless against the stone "rain" of catapults that rained down on Montsegur from morning to night.

“Tell me, Sever, why didn’t the Perfect Ones defend themselves?” After all, as far as I know, no one was better than them in "movement" (I think they mean telekinesis), "breath" and much more. Why did they give up?!
“There are reasons for this, Isidora. In the very first attacks of the crusaders, the Cathars did not yet give up. But after the complete destruction of the cities of Albi, Beziers, Minerva and Lavour, in which thousands of civilians died, the church came up with a move that simply could not work. Before they attacked, they announced to the Perfects that if they surrendered, not a single person would be harmed. And, of course, the Cathars surrendered... From that day on, the fires of the Perfect Ones began to blaze all over Occitania. People who devoted their whole lives to Knowledge, Light and Goodness were burned like garbage, turning the beautiful Occitania into a desert scorched by bonfires.
Look, Isidora... Look, if you want to see the truth...
I was seized by a real sacred horror! .. For what the North showed me did not fit into the framework of normal human understanding! .. It was Hell, if it ever truly existed somewhere ...
Thousands of knights-murderers dressed in sparkling armor cold-bloodedly slaughtered people rushing about in horror - women, old people, children ... Everyone who fell under the strong blows of the faithful servants of the "forgiving" Catholic Church ... Young men who tried to resist immediately fell dead , hacked with long knightly swords. Heart-rending cries sounded everywhere... the clash of swords was deafening. There was a suffocating smell of smoke, human blood and death. The knights mercilessly cut down everyone: whether it was a newborn baby, which, begging for mercy, was held out by an unfortunate mother ... or there was a weak old man ... All of them were immediately mercilessly hacked to death ... in the name of Christ !!! It was sacrilege. It was so wild that my hair really moved on my head. I was trembling all over, unable to accept or simply comprehend what was happening. I really wanted to believe that this was a dream! That such a reality could not be! But, unfortunately, it was still a reality ...
HOW could they explain the perpetrated atrocity?! HOW could the Roman Church FORGIVE (???) those committing such a terrible crime?!
Even before the start of the Albigensian Crusade, in 1199, Pope Innocent III “graciously” declared: “Anyone who professes a belief in God that does not coincide with church dogma should be burned without the slightest regret.” The crusade against Qatar was called "For the Cause of Peace and Faith"! (Negotium Pacis et Fidei)...

In everyday life, people face interest on a daily basis.

When visiting stores, we see bright announcements about discounts and sales. The benefit of sales for buyers is obvious - it is an opportunity to purchase quality goods at reduced prices. And sellers, in turn, get the opportunity to get rid of excess goods and acquire new loyal customers. Accordingly, the sale is an effective marketing ploy.

In recent years, in the media, one can often hear about the increase in tariffs for utilities. As a rule, all figures are voiced as a percentage. Since July 1, 2015, utility tariffs in Russia have increased by an average of 8.3%. The payment for gas supply increased by 7.5%, for heat supply - by 8.4%, for electricity - by 8.5%, for hot and cold water, as well as for sanitation - by 9.5%. In some regions, due to budgetary support, tariffs increased minimally: in Buryatia by 4.2%, in the Yamalo-Nenets Autonomous Okrug by 2.3%, and in the Chukotka Okrug by 1.9%.

If a person does not pay utility bills on time, a fine is imposed on him, which is called “penalty”. He calculates in accordance with the legislation of the Russian Federation, as a certain percentage of the amount of utilities for each overdue day.

In my work, I tried to show the various areas of application of interest, to establish the relationship between the labor activity of a modern person and the ability to calculate interest using various examples, and also to prove how important it is for every person to understand what interest “says”.

Target: learn to understand and use information presented as a percentage, be able to calculate discounts on goods and services. To establish the relationship between work and life of a modern person with the ability to calculate percentages.

Subject of study: percentages and areas of their application.

Tasks:
1. Generalize, systematize, deepen knowledge on the topic: interest.
2. Show the use of interest in mathematics, economics and other school subjects.
3. Learn different ways to solve percentage problems.
4. Expand the role of interest in a person's life.
5. Show the importance of the ability to calculate interest in various professions: medicine, accounting, cooking, metallurgy, jewelry, banking and in the work of an employee of the state fire supervision when preparing reporting information.

II. The history of interest

The word "percent" comes from the Latin word pro centum, which literally translates as "per hundred", or "from a hundred". Percentages are very convenient to use in practice, since they express parts of whole numbers in the same hundredths. This makes it possible to simplify calculations and easily compare parts with each other and with the whole.

The % sign is believed to come from the Italian word cento (one hundred), which is often abbreviated cto in percentage calculations. From this, by further simplifying the cursive letter t into a slash, the modern symbol for percent was derived.

There is another version of the origin of this sign. It is assumed that this sign occurred as a result of a ridiculous typo made by a compositor. In 1685, a book was published in Paris - a guide to commercial arithmetic, where by mistake the typesetter printed % instead of cto. Gradually gaining a place for itself, this sign began to appear especially often in printed publications at the beginning of the 19th century. The widespread use of the “%” sign in printed publications led to the fact that already in the middle of the 19th century. it has gained universal acceptance as a symbol of the percent. Interest from commercial practice gradually penetrated into various branches of technology and knowledge. The scope of interest quickly expanded, covering various sciences.

The idea of ​​expressing the parts of the whole constantly in the same shares, caused by practical considerations, was born in ancient times among the Babylonians, who used sexagesimal fractions. Already in the cuneiform tables of the Babylonians there are problems for calculating interest. The tables of interest compiled by the Babylonians have come down to us, which made it possible to quickly determine the amount of interest money.

Interests were also known in India. Indian mathematicians calculated percentages by applying the so-called triple rule, that is, using proportion. They were able to perform more complex calculations using percentages.

Cash settlements with interest were especially common in ancient Rome. The Romans called interest the money that the debtor paid to the lender for every hundred. Even the Roman Senate was forced to set the maximum allowable interest charged from the debtor, as some lenders were zealous in obtaining interest money. From the Romans, interest passed to other peoples.

There is an assumption that initially interest arose as a special type of income that owners received for giving fruitful property for use, for example: domestic animals, orchards, etc. Later, sums of money began to be put into circulation, for the use of which they also began to charge a fee.

In the Middle Ages in Europe, in connection with the widespread development of trade, much attention was paid to the ability to calculate interest. First came consumer credit; With the development of trade relations, commercial credit also appeared, one of the incentives of which was already interest. This income was usually expressed in a certain part of the property (things or money capital) taken on loan, and this part subsequently began to be expressed in hundredths of the property put into circulation.

At that time, it was necessary to calculate not only interest, but also interest on interest, that is, compound interest, as they are called in our time. Separate offices and enterprises, in order to facilitate labor in calculating interest, developed their own special tables, which were the trade secret of the company. For the first time he published tables for calculating interest in 1584, Simon Stevin, an engineer from the city of Bruges (Netherlands). Stevin is known for a remarkable variety of scientific discoveries, including a special notation for decimal fractions.

For a long time, interest was understood exclusively as profit and loss for every 100 rubles. They were used only in commercial and monetary transactions. Then the scope of their application expanded, interest is found in economic and financial calculations, statistics, science and technology. Now interest has taken a firm place not only in monetary calculations, but also in science and in everyday practice. Now one has to deal with interest not only in commercial calculations and in economic accounting, but also in technology, and in physics, and in chemistry, and in meteorology, and in other sciences. Over the years, interest has gained popularity among the population, the word "percent" has firmly entered the lexicon of our people.
Today, a percentage is a special kind of decimal fractions, a hundredth of a whole (taken as a unit).

III. Percentages in mathematics

III.1. Percent definition

A percentage is one hundredth of a value or number. Denoted by the symbol "%".

In some questions, sometimes smaller, thousandths are also used, the so-called “promille” (from the Latin pro mille - “from a thousand”), denoted by ‰, by analogy with percent.

Interest is an "international language": in business, in the banking system, in production, in agriculture, in everyday life ...

In the school mathematics course, we get acquainted with percentages in the 5th grade, and we practically do not part with them.

III.2. Percentages and fractions

We come across percentages in the study of fractional numbers. So, to convert percentages to fractions, you need to remove the% sign and divide the number by 100. For example: 2% \u003d 2/100 \u003d 0.02.

To convert a decimal to a percentage, multiply the fraction by 100 and add the % sign. For example: 0.14 = 0.14*100% = 14%.

To convert a fraction to a percentage, you must first convert it to a decimal. For example: 2/5 = 0.4; 0.4*100% = 40%.

So, percentages are closely related to ordinary and decimal fractions. Therefore, it is worth remembering a few simple equalities. In everyday life, you need to know about the numerical relationship of fractions and percentages. So, half - 50%, a quarter - 25%, three quarters - 75%, one fifth - 20%, and three fifths - 60%.

Knowing by heart the ratios from the table below will make it easier to solve many problems.

Interest actions.
Interest can be added and subtracted only with the interest itself. Percentages are added and subtracted to each other like ordinary numbers.

For example:
1% + 37% − 25% = 38% − 25% = 13%
70% − (42% + 3%) = 70% − 45% = 25%

In everyday life, it is useful to know the different forms of expressing the same change in quantities, formulated without percentages and with the help of percentages.

For example, to increase by 2 times means to increase by 100%. Let's see why this is so.

Let x be 100%.

Then, multiplying x by 2, we get 2x

Let's compare the results.

It turned out that the total number of percent is 200%. To increase by 2 times means to increase by 100% and vice versa.

Arguing in the same way, it can be proved that an increase of 50% means an increase of 1.5 times.

The decrease in number can also be expressed as a percentage.
Let x be 100%.
It is known that x has decreased by 80%. Find how many times x has decreased.
First, let's find how many percent of x is left.
100% − 80% = 20%
20% left of x. Let's denote the remainder of x as y.

Let's make a proportion.
By the numerical coefficient, we determine how many times x has decreased.

x / y = 100% / 20%

Thus, we have established that to reduce by 80% means to reduce by 5 times.

Once you understand the connection between percentages and "times", you can easily understand what is so often said in the news and in newspapers, citing various static data. Some of the most frequently used phrases, it is advisable to simply remember in order to always understand exactly what is being said. A list of such phrases is presented below.

The meaning of the phrases “increase and decrease by ... percent”

To increase by 50% means to increase by 1.5 times.
by 100% → 2 times
by 150% → 2.5 times
by 200% → 3 times
by 300% → 4 times
To reduce by 80% means to reduce by 5 times.
by 75% → 4 times
by 50% → 2 times
by 25% → ≈ 1.33 times
by 20% → 1.25 times

III.3. Interest tasks

There are four types of interest tasks:

1. Finding a percentage of a number.

To find the percentage of a number, multiply the number by the percentage.

Task: The enterprise produced 500 pumps in a quarter, of which 60% were of the highest quality category. How many pumps of the highest quality category have the enterprise produced?

Solution: Find 60% of 500 (total number of pumps)
60 % = 0,6
500 * 0.6 = 300 pumps of the highest quality category.
Answer: 300 pumps of the highest quality category.

2. Finding a number by its part.

To find a number by its percentage, you need to divide its known part by how many percent it is of the number. Since the tasks “percentage by number” and “number by its percentage” are very similar and it is often not immediately clear what type of problem we have in front of us, we need to carefully read the text. If the words “which”, “what constitutes” and “which constitutes” occur, most likely this is the “number by its percentage” problem.

Task: The student read 138 pages, which is 23% of all pages in the book. How many pages are in the book?

Solution: So, we don't know how many pages there are in the book. But we know that the part that the student read (138 pages) is 23% of the total number of pages in the book. Since 138 pages is only a fraction, the number of pages itself will naturally be greater than 138. This will help us in our verification.

138 / 23% = 138 / 0.23 = 600

Check: 600 > 138 (meaning 138 is part of 600).
Answer: 600 (pages) - the total number of pages in the book.

3. Finding the percentage of two numbers

1) Find the ratio of two numbers
2) Multiply this ratio by 100 and assign the % sign

50 shots were fired from the rifle, while 45 bullets hit the target. What percentage of hits is less than misses? How many more misses than hits?
1) 50-45=5(misses)
2) 45-5=40(v.)-difference
3) 40:5*100=8%

Answer: 800%

4. How many percent one value is from another.

To find how many percent one number is of another, you need to divide the part from which you are asking by the total number and multiply by 100%.

Task: Out of 200 watermelons, 16 were unripe. What percentage of all watermelons were unripe watermelons?

Solution: What are they asking? About unripe watermelons. So, 16 is divided by the total number of watermelons and multiplied by 100%.

16 / 200 * 100% = 8%

Answer: 8% - are unripe watermelons from all watermelons.

IV. Interest in school subjects

IV.1. Interest in the economy

Every year, economists around the world study how the growth of the economy of each state has changed (the purchasing power of citizens):

The table shows that in the USA and China there is an increase in “economic growth” by 22 and 93%, and in Japan and Russia, a decrease in “economic growth” by 24 and 15%.

The growth of the Russian economy depends on the price of oil, and in the last year oil prices have fallen by 46%: in 2014, oil cost $96 per barrel, and in 2015 about $51. According to experts' forecasts, in 2016, oil prices will decline, which will lead to a decrease in the purchasing power and living standards of Russian citizens.

IV.2. Percentages in geography

In geography lessons, the teacher often uses percentages, for example:

Everyone knows that air is a mixture of gases. Air consists of: 78.1% nitrogen, 20.9% oxygen and 0.9% argon (this ratio of their content is maintained up to an altitude of about 100 km). These gases account for 99.96% of the mass of the atmosphere.

Fresh water is the water of the Earth, in which salts are contained in minimal quantities, the salinity of which does not exceed 0.1%, even in the form of steam or ice. Ice masses (for example, icebergs) in the polar regions and glaciers contain the largest part of the Earth's fresh water. In addition, fresh water exists in rivers, streams, underground waters, fresh lakes, and also in clouds. According to various estimates, the share of fresh water in the total amount of water on Earth is 2.5-3%. About 85-90% of fresh water is contained in the form of ice.

IV.3. Interest in biology

Many topics studied in biology lessons contain percentages.

Each person has individual parameters that determine his physical development: height, weight, lung capacity, etc., and the values ​​of these parameters can vary greatly for a certain group of people, while remaining within the normal range. The percentage allows you to indicate the average value of the parameter of physical development (the value is normal).

There are 400-600 muscles in the human body. In a newborn, muscle mass is 20-22% of the total body weight, muscle mass in men is 40-45%, in women (aged 22-25 years) - 30% of body weight; in old age, there is a gradual decrease in muscle mass up to 25-30%.

The heart is a small hollow muscular organ. In humans, it is the size of a fist and weighs only 300 g, which is approximately 0.4-0.5% of the weight of the entire body. 85% of the energy of the heart is spent on moving blood through arterioles and capillaries, and only 15% is spent on moving through large and medium arteries and veins.

IV.4. Interest in chemistry

Solutions consist of a solvent and a solute(s). If one of the substances that make up the solution is a liquid, and the others are gases or solids, then the solvent is usually considered a liquid. In other cases, the solvent is considered to be the component that is larger.

The gaseous solution is, for example, air and other mixtures of gases.

Sea water is the most common liquid solution of various salts and gases in water.

Many metal alloys belong to solid solutions.

Whatever the state of aggregation of the solvent, its name necessarily indicates “how many percent of the substance is dissolved in a certain volume of the solvent”. The more a substance is dissolved, the more concentrated the solution. Often, in order to dissolve a larger amount of a substance, it is heated to a certain temperature.

Hydrochloric acid - HCl, a solution of hydrogen chloride in water; strong acid. Colorless (technical hydrochloric acid is yellowish due to impurities of Fe, Cl 2, etc.), “fuming” in air, caustic liquid. The maximum concentration of hydrogen chloride at 20 °C is 38%.

In chemistry, seven varieties of hydrochloric acid are used: 10%, 20%, 30%, 32%, 34%, 36% and 38%.

Everyone knows that human gastric juice has an acidic environment, this is possible due to the presence of 0.3 - 0.5% hydrochloric acid in gastric juice.

IV.5. Interest in history

During the Great Patriotic War, 600,000 Gorky fought on the fronts. For the courage shown in battle, 300 of our countrymen were awarded the highest award of the Motherland - the title of Hero of the Soviet Union. More than 50% (300,000) of Gorky residents were awarded military orders and medals.

26% of all fighters were produced for the front in Gorky, and this is 16324 aircraft. During the war years, the city of Gorky produced 28227 tanks for the front, of which 61% were GAZ.

In the first days of the war, mass mobilization took place and skilled workers became soldiers. They were replaced by women and teenagers without qualifications and work experience. During the first year of the war, 11,478 people came to the factory shops, which amounted to approximately 30% of the total number of labor collectives.

With the beginning of the Second World War, the production of cars was curtailed at GAZ, only trucks were left on the assembly line. These were, first of all, the legendary "one and a half" - GAZ MM. "Machine-soldier" - she saved Leningrad in those terrible years...
During the war years, GAZ produced 167,220 vehicles, of which 71% (117,325 units) were lorries.

Before advancing on Leningrad, Hitler declared: “Leningrad will raise its hands: it will inevitably fall, sooner or later. No one will be freed from there, no one will break through our lines. Leningrad is destined to starve to death.” But this prophecy of Hitler did not come true. In Leningrad, bakeries continued to operate, bakers continued to bake bread.

What did blockade bread consist of?

From the beginning of 1941, bread was baked from the mixture and had the following composition:

There were other impurities and additives that reduced the nutritional value of bread, with them the bread was lush, and tasted like wormwood.

V. The use of interest in various professions

In their work, many people use the ability to calculate percentages of a number, and find a number by its part daily. They have been using percentage problem solving skills acquired in 5th grade for decades. I would like to dwell on some professions in my work.

V.1. Interest in medicine and pharmaceuticals

Every day, medical workers are faced with the ability to calculate percentages, for example, with intramuscular injections, a 1% solution of lidocaine is used to dilute the drug. The domestic industry produces only a 2% solution of lidocaine, respectively, before giving the patient an injection, the nurse dilutes the lidocaine with water for injection in the required proportion. If this is not done, the patient will get burned.

One of the main tasks of pharmacology is the development of drugs that help in the fight against a particular disease.

Pharmacists, empirically, using theoretical knowledge, make up solutions of medicinal substances in such proportions as to help the human body, and at the same time do no harm.

When buying any medicine, the patient, before using it, carefully studies the instructions for it, which lists in detail the composition of the drug, indicating the percentage of all its constituent substances.

V.2. Interest in cooking

Vinegar is one of the most ancient spices, which is used in the preparation of many culinary recipes, as well as for preserving food for the winter. That's just a variety of dishes requires a different percentage of vinegar. Some recipes call for 70% vinegar, while others require 6% or 9% vinegar.

And since it is not always possible to find vinegar of the desired percentage at hand, you have to independently calculate the amount of water that needs to be added to acetic acid in order to get vinegar with the required percentage of acid.

V.3. Interest in accounting

The accountant of any enterprise monthly calculates the profit received by the enterprise, calculates wages for all employees of the enterprise, makes contributions to the tax office, pension fund, social insurance fund and others. All deductions are calculated individually for each employee, but the accountant uses the same interest rate for all, for example, payroll tax (personal income tax) in Russia is 13%, pension contributions are 22%, medical care contributions are 5.1% , to the social insurance fund - 2.9%.

As a result, the total amount of deductions from the employee's salary is (13 + 22 + 5.1 + 2.9)% / (100 + 22 + 5.1 + 2.9) = 33.1%. On hand, that is, net or even say net salary, the employee receives about 66.9% of the total cost of the enterprise for wages and insurance premiums to the funds for this employee. If the employee's annual wage fund exceeds the taxable base for insurance contributions to the funds (in 2014, this base is 624,000 rubles), a regression occurs (a decrease in the effective rate), since from the amount exceeding the base, the enterprise pays to the funds not 30% instead of 10%. Accordingly, the effective tax rate in Russia is regressive (the higher the salary, the lower the tax), in contrast to many developed economies where taxation is progressive (the higher the salary, the higher the taxes).

V.4. Interest in metallurgy

The ability to calculate percentages is very important in the preparation of alloys, for example, to obtain a steel alloy, at least 45% iron and no more than 2.14% carbon are taken, as well as alloying elements (the purpose of the resulting steel alloy depends on the percentage of which depends).

Stainless steel - alloy steel, resistant to corrosion in the atmosphere and aggressive environments.

The main alloying element of stainless steel is chromium Cr (12-20%); in addition to chromium, stainless steel contains elements that accompany iron in its alloys (C, Si, Mn, S, P), as well as elements introduced into steel to give it the necessary physical and mechanical properties and corrosion resistance (Ni, Mn, Ti, Nb, Co, Mo).

The resistance of stainless steel to corrosion directly depends on the chromium content: at its content of 13% and above, the alloys are stainless under normal conditions and in slightly aggressive environments, more than 17% - corrosion-resistant and in more aggressive oxidizing and other environments, in particular, in nitric acid with a strength up to 50 %.

V.5. Interest in jewelry

Gold has always been not just an ornament, but a symbol of power, status, wealth and luxury.

An alloy of 585 gold consists of 58.5 percent pure gold and ligature (two other metals): not more than 34 percent copper and silver. Due to the rather large amount of gold, the appearance of the product from 585 samples does not fade during operation. Copper in the alloy gives products from 585 samples special strength and hardness.

There are many other samples of gold in the world.

Different shades of 585 samples are created by a jewelry manufacturer by adding ligature metals in certain quantities. For example, you can remember when making white gold, 58.5% pure gold and ligature metals - nickel or palladium - are added to the alloy. The predominance of nickel gives the product a slightly yellowish tint. Ordinary 585 samples traditionally have a slight pink tint. The colors of 585 gold alloy vary from green to light yellow.

The most prestigious, according to international standards, are items made of 750 gold. The color of 750 gold alloy products, including, in addition to pure gold - 75%, is affected by ligature metals:
Red gold: silver - 4%, copper - 21%
Yellow gold: silver - 15%, copper - 10%
Green gold: silver - 25%
White gold: silver - 7%, palladium - 14%, nickel - 4%.

Silver - in its purest form, “pure silver” (contains no more than 0.1% impurities in its composition) is an easy to process, but too soft metal. To give silver strength, copper has been added to it since ancient times. Today, copper is sometimes replaced by other chemical elements. 925 sterling silver contains no more than 7.5% impurities. In addition to copper, it can include platinum, germanium, zinc and even silicon. This is done in order to influence the color of the alloy, as well as its physical properties, the most important of which is the ability to resist oxidation. Due to its affordability and beautiful appearance, 925 sterling silver remains one of the main precious metals used to make highly artistic jewelry.

Silver samples from 720 to 830 are distinguished by a fairly high copper content. This explains the serious shortcomings of these samples, which include a yellowish color and a tendency to oxidize. For this reason, low-grade silver is used only in industry. For the manufacture of jewelry, 875 silver is used, and even then on a limited scale (due to the shortcomings mentioned above). The same can be said about the 960 fineness, but for a different reason: due to the high content of silver, the products are refined, but not strong enough, which virtually excludes their everyday use.

V.6. Interest in banking

Even in ancient times, the concept of usury was widespread - the issuance of money at interest. The difference between the amount that was returned to the usurer and that which was originally taken from him was called interest. So in ancient Babylon it was 20 percent or more. It is known that in the XIV-XV centuries, banks were widely spread in Europe - institutions that lent money. Of course, the banks did not give money disinterestedly: they took a fee for the use of the provided money, just like the usurers of antiquity. This fee was usually expressed as a percentage of the amount of money lent. Those who borrow money from a bank are called borrowers, and a loan, i.e. The amount of money borrowed from a bank is called a loan.

In addition, the bank also provided the opposite service to a loan: it took money from the population for storage (deposits), for which it paid a certain percentage to the depositor. Funds deposited in the bank, after a certain time, bring some income equal to the amount of interest accrued over this period.

So, on the one hand, banks accept deposits and pay interest on these deposits to depositors, on the other hand, they give loans to borrowers and receive interest for using this money. Thus, the bank is a financial intermediary between depositors and borrowers.

A loan is a relationship between two participants in a transaction, which involves the provision of cash or in-kind funds by one participant in the transaction (creditor) for temporary use to another (borrower), subject to the conclusion of an agreement on the principles of urgency (for a certain period), security (secured by something ) and payment (at a certain percentage). There are a large number of different types of loans, almost every day new loan products with different conditions appear on the loan market. According to the principle of urgency, types of loans are divided into: short-term (from several months to a year), medium-term (from one to three years) and long-term (from three years or more). The interest rate for its use depends on the period for which the loan is issued.

There are also several main types of loans, which differ in debt repayment schemes. The most common are loans with monthly debt repayment by differentiated (decreasing) or annuity (equal) payments.

There are also loans with a one-time debt repayment, when the principal and interest are repaid at the end of the loan term. Some banks issue loans with individual debt repayment schemes, which are specified in the loan agreement.

But most often loans differ in purpose. The purposes for which a loan is taken can be different. For example: buying a car, real estate, household appliances, a loan for vacation or education, etc.

There are also loans that are not taken for any particular purpose. These loans include a loan for urgent needs (consumer loan).

Loans can be issued in various forms: in rubles or in foreign currency, in the form of goods (commodity credit) or in cash, in the form of a credit card.

The terms of the loan directly depend on the form in which the loan is issued: interest rate, term, down payment, security. Therefore, when choosing a loan, it is very important to study all the advantages and disadvantages of the types of loans you are interested in. This is necessary in order to choose the most convenient and profitable loan for yourself, without unnecessary fears and overpayments.

Today there are quite a lot of loans for the population.

Types of bank loans:
1. Loans for consumer needs. Such loans are usually issued for the purchase of various goods and services. This can be the purchase of household appliances, furniture, various electronics, as well as loans for treatment, education, apartment renovation, and recreation.
2. Car loans. They are a type of consumer loan issued for the purchase of a car. Such a loan is much easier to obtain for the purchase of a new car.
3. Mortgage loans. These are long-term loans issued for the purchase of housing. Mortgage lending will be characterized by large amounts of loans, a rather serious approach to studying the solvency of borrowers. The acquired property is automatically transferred to the mortgage on the loan.
4. Leasing. A type of lending that does not involve the transfer of property ownership. A kind of financial lease. A few years ago, only legal entities could use leasing, but today it is available to everyone. Leasing is especially good as an alternative to car loans.

V.7. Interest in the work of an employee of the state fire supervision

In 2010, 179,098 fires occurred on the territory of the Russian Federation, in which 12,983 people died and 13,067 people received various injuries. In 2014, these figures were: 153,002 fires, as a result of which 10,253 people died, 11,089 people were injured.

Task: To express in percentage the dynamics of the situation with fires for the period 2010-2014.

To do this, you must perform the following steps:

1. Calculate the difference between the indicators of 2010 and 2014:

The result obtained shows how many fires (dead and injured people) in 2010 were more than in 2014, or vice versa, how many fewer in 2014 than 4 years ago.

2. Now let's show this difference as a percentage:

Conclusion: In 2014, compared to 2010, the number of fires decreased by 14.6%, the death toll from fires decreased by 16.5%, the number of people injured - by 15.1%.

Conclusion: In 2010, there were 17% more fires than in 2014, more people died in fires by 19.8%, the number of people injured was 17.8% more.

VI. Conclusion

So, the role of interest in a person's life is great. They have a wide practical application in industry, medicine, science and many other industries. With the help of percentages, you can more clearly convey the necessary information to any person. Percentages help us learn a lot, we just need to be able to understand what they “talk about”.

VII. Bibliography.

1. Vilenkin N. Ya. Maths. Textbook for the 5th grade of high school. - M .: Education, 2005.
2. Dorofeev G.V., Kuznetsova L.V., Minaeva S.S., Suvorova S.B. The study of interest in basic school // Mathematics at school, 2002, No. 1.
3. Vilenkin N.Ya. Maths. Textbook for the 6th grade of high school. - M .: Education, 2005.
4. Belousov R.S. and others. I know the world. Economy. Encyclopedia. Moscow LLC publishing house AST, 2001 - 489s.
5. Lipsits I.V. Economics M.: Vita - Press, 1996 - 352p.
6. Internet resources: en.wikipedia.org
7. Barabanov O.O. Tasks for percentages as a problem of the norm of word usage // Mathematics at school, 2003, No. 5.
8. Simonov A.S. Interest and bank calculations // Mathematics at school, 1998, No. 4.
9. Simonov A.S. Compound interest // Mathematics at school, 1998, No. 5.
10. Dorofeev G.V., Sedova E.A. Percentage calculations. - Moscow: Bustard, 2003.
11. Goncharova L.V. Subject weeks at school. Maths. Volgograd: publishing house "Teacher", 2003.

I've done the work:
Bolshakov Anton
Pupil 6 "A" class

Scientific adviser:
Makarova Galina Sergeevna
Mathematic teacher

Municipal budgetary educational institution
“School No. 128”
Nizhny Novgorod
2016

The history of the origin of interest began in antiquity.

And the first idea to express in this way parts of the whole in the same shares, came up with the ancient Babylonians. The fact is that this system used sexagesimal fractions, so they simply needed such an innovation. The cuneiform tables of the Babylonians have survived to this day, with the help of which you can easily and quickly determine what the amount of interest money is.

The peoples of India have their own history of the appearance of interest.

Interest was known in India as early as the 5th century. Indian mathematicians calculated percentages in their own way. And this is obvious, since it was in India that for a long time the account was kept in the decimal number system. They used the triple rule (the use of proportion). In addition, in India, more complex operations with interest were carried out than just counting the change.

The history of the appearance of interest in ancient Rome.

Officially, the history of the appearance of interest begins from the time when the Senate had to set the maximum allowable interest charged from debtors, so that lenders "do not overdo it" in "knocking out debts." The Romans called interest the money that the debtor paid to the lender for every hundred. The Romans took interest from the debtor (i.e., money in addition to what they lent). At the same time, they said: "For every 100 sesterces of debt, pay 16 sesterces of interest." By the way, it was from Rome that interest began its "march" around the world.

In the Middle Ages trade was very widespread, in connection with which much attention was paid to the correctness and ability to calculate interest. Then interest, whose history began much earlier, began its evolution.
Merchants had to calculate not just interest, but interest on interest, compound interest, etc. Some companies even compiled their own tables and charts for calculating interest. These tables, by the way, were considered a trade secret and were carefully guarded.But already in 1584, tables with the calculation of interest ceased to be a secret. The fact is that Simon Stevin, an engineer from the Netherlands, published a table of percentages.

Use of the term "percentage"in Russiabegins at the end of the 18th century. For a long time, interest was understood exclusively as profit or loss for every 100 rubles. Interest was accepted only in commercial and monetary transactions. Then the scope of their application expanded.

History of the % sign

There are two versions of the origin of the sign%. One of the versions, more like fiction, is the mistake of a typesetter who, while typing in 1685 in Paris a book called "Manual of Commercial Arithmetic" by Mathieu de la Porte, mistakenly put the sign% instead of the word "cto".

According to the second, more plausible version, the% sign is a simplification of the letter t in the word "cto" (which previously denoted percentages). In cursive, the letter t became a bar (/), and then the modern sign cto - c/o - %. We will no longer know which version is correct, but the % sign is used in the modern world, and very actively.

Scope of interest.

In the markets, in banks, in shops without interest, there’s nothing like it.
Even on the streets, on posters, everything is in percentages, and not in rubles.
Interest is very convenient for us, we don’t have to strain our brains.
You can even count them without a calculator.
They help us with our work and count everything.
Interest is what you need, everything is quick and easy with them!

Percentage is a mathematical concept that is very common in everyday life. The scope of interest is wide: in economic and financial calculations, statistics, science and technology.
Often we read or hear, for example, that 60% of voters took part in the elections, academic performance in the class is 95%, the rating of the hit parade winners is 85%, the bank charges 12% per annum, milk contains 1.5% fat, the material contains 100 % cotton, etc.
It is clear that without understanding this kind of information in modern society it would simply be difficult to exist. Let's look at the scope of the concept of "percentage" and the tasks that can be found in a particular area.

• deposit interest- this is the payment of banks for the storage of cash, securities and other valuables in accounts, depositories, vaults. For example, consider the following problem: A depositor decided to deposit 35,000 rubles in a bank. How much money will he receive in six months if the annual interest is 7.5%? Because 7.5% is the depositor's income for one year, then for six months his income will be 3.75%.Thus, to 35000 we must add 3.75% of 35000 and then we will find out how much money the depositor will receive (35000 + 0.0375 * 35000 = 35000 + 1312.5 = 36312.5 rubles).
• financial definition of interest- a payment that one person (the borrower) transfers to another (creditor) for the fact that the latter provides the first for temporary use of funds. For example, consider the problem: Petya Ivanov came to the bank and took out a loan of 10,000 rubles at 5% interest (in this problem, Petya Ivanov is the borrower, and the bank is the lender that provided Petya with 10,000 rubles). Question: How much money should Petya return to the bank? 5% is a fee that Petya must transfer to the bank for the use of funds, but not only 5% must be returned, but also the amount that the bank provided. Thus, to 10,000 we must add 5% of 10,000 and give the received amount to the bank (10,000 + 0.05 * 10,000 = 10,000 + 500 = 10,500).
• business vocabulary: work for interest - means to work for remuneration, calculated depending on profit or turnover. For example, consider the problem: Maria, who came to get a job in a store, was told that she would receive 30% of the proceeds. Question: How much money will Maria get in a day if she sells goods worth 120,000 rubles? To answer this question, you need to find 30% of the number 120000 (0.3 * 120000 = 36000).

Interest works wonders. Knowing them, the poor can become rich. The buyer, who was deceived yesterday in a trade transaction, rightly demands a percentage of the trade discount today. The saver learns to live on interest by wisely investing money in a profitable business.