Project interest in our lives. Creative mini-project on "interest in our life"

Description of the presentation on individual slides:

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The project "Interest in our life" prepared: Students 6 CL "SOSH№3" Clapov A, Sukmanov A. Head: Dremukhina TA

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Find out where and how percentages are applied in our lives. Expand knowledge about the use of interest calculations in tasks and in different spheres of human life. Purpose:

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Research and with percentage calculations provide data in the form of tasks and charts of the Project problem: to study the history of the interest; Consider tasks for interest from practical life and ambient modern man.

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The relevance of our project interest is one of the most complex topics of mathematics, and very many students find it difficult or do not know how to solve interest tasks. And the understanding of interest and the ability to produce interest calculations are necessary for each person. Application value This topic is very large and affects the financial, economic, demographic and other spheres of our life. The study of the percentage is dictated by life itself. The ability to perform interest calculations and the calculations are necessary to each person, since with percentages we are faced in everyday life.

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The plan of our actions We have learned further the topic of interest. Their history found out that parents know, relatives compiled their interest tasks decided some tasks from the exam prepared a presentation

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A little of history, the word "percentage" has a Latin origin: "Pro Centum" - "from one hundred". Often, instead of the word "percentage" use the phrase "by a hundredth part of the number". Percentage is a hundredth part of the number. 1/100 \u003d 1% percent were especially common in Ancient Rome. The Romans called the interest to the debtor (lender) for each hundred. Since the words "on a hundred" sounded as "percentage", then the hundredth of the one began to be called a percentage

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The symbol  did not appear immediately. At first they wrote the word "hundred" so: in 1685 In Paris, the book "Guide for Commercial Arithmetic", where, by mistake, instead, it was scored. From the Romans, interest crossed to other people's peoples. In Russia, the concept of the percentage introduced Peter I.

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2. Associates in our lives. Interest is one of the mathematical concepts that are often found in everyday life. We have heard for example that in the store a 20% discount in the elections 57% of voters took part in the election, the performance in class 100%, the bank charges 16% per annum, acetic acid 70% material contains 100% cotton, etc. Patzan is 100% - in conversation means Best in everything!

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Three main actions related to interest 1. Finding percent of the number. To find in% from B, it is necessary in · 0.01. 2. Finding a number by its percentages. If it is known that in% of the number x is equal to, then x \u003d in: 0.01. 3. Finding the interest rate of numbers. To find the percentage of numbers, it is necessary to multiply the ratio of these numbers by 100%.

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Percentages apply 1. In medicine 2. In programming 3. In stores 4. In the elections 5. In cooking 6. In statistics 7. In the compositions of fabrics 8. In taxes 9. In solutions 10. In Sberbanks 11. In the analysis of interest, interest is used People of different professions

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After conducting research in our class, we collected some data and processing them we received such results

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From the school accountant, we learned that monthly from the salary of workers, the employer is expelled: - 22% in the pension fund; - Social Insurance Fund - 2.9%; - Foundation Soc. Accident Insurance - 0.2% - Regional Health Fund - 5.9%. Total 30.2% tax deducted from the wages of employee NDFL \u003d 13% For example, a salary is 14500 rubles -13% NDFL \u003d 14500-1885 \u003d 12615rub will receive an employee

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These are the tasks we made up relying on the information received forest areas of Sverobaikalsk, occupy an area of \u200b\u200b1651527 km2. In the summer, our city was all in the smoke for a long time, the forest burned. How many percent of the forest burned down during the fire, if the fire area is 25234kv.km (1.5%)

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History of our city We conducted a survey among the inhabitants of Severobaykalsk "Do you know the emblem of our city" from 123 surveyed 65% of people know the coat of arms, the rest are not. How many people from the respondents do not know the emblem of our city? (79 people know, 44 do not know)

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Interest in trade: Mom wanted to buy a down jacket for 2700 rubles. In the store "Economy". And on November 4, there was a sale. Discount for all goods 20%. For how many rubles Mom will buy a down jacket for sale? (2160 rubles) t 20% discount

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With a mixing of a 5% solution of an acid with a 40% acid solution, 140g of a 30% solution was obtained. How many grams of each solution was to do this?

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Consider an old way to solve this task. The content of the acid solutions is written under each other, to the left of them and approximately in the middle - the acid content in the solution that should turn out after mixing. By connecting the written numbers, we will obtain such a scheme: 30 5 40 Consider the pairs of 30 and 5, 30 and 40. In each pair, it will be subtracted less and the result will write down at the end of the appropriate cake. It turns out such a scheme: 10 30 5 40 25 of it is concluding that 5% of the solution should be taken with 10 parts, and 40% of 25 parts ,. (10 + 25 \u003d 35 pieces of total, 140: 35 \u003d 4G-weight of one part, 4 × 10 \u003d 40g, 4 × 25 \u003d 100g.) I.e. To get 140g. 30% solution You need to take 5% solution 40g., A 40% - CSO - 100g

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On TV I heard that a smoking person reduces his life by 15%, which is 8.4 years. What is the average life expectancy in Russia? (56)

English "href \u003d" / text / category / anglijskij_yazik / "REL \u003d" BOOKMARK "\u003e English

North District of Moscow

(Moscow, ul. Mikhalkovskaya, d. 13 "A",

phone (4, E - Mail: ***** @ *** RU)

Design - research work

on the topic: « His Majesty percentage»

Scientific Director: B, Mathematics Teacher

moscow, 2012/2013

Introduction

The relevance of the topic, the problem, the hypothesis, the purpose and objectives of the project ............ ......... 3

Main part. Stages of research:

I Questioning ........................................................................................ ..4

II Collection and processing and study of information

The history of the appearance of the percent ................................................... ... .............5

Percentages around us (survey classmates) ...................................... ... ... .7

The concept of% in mathematics ...................................................... .. ......... ... ... .9

Key (reference) tasks percent ................................................ ... 10

III Creating a presentation for an interactive lesson and place it on the Internet

Presentation "The main tasks per percentages - we decide together" ............ .. ... ... 12

Experiment .................................................................. ... 12

Conclusion

Conclusions, results of the project ............................................................................. 13

List of references used ....................................................... ... 15

Applications:

Results of the survey ................................................................................. ...... ..16

Slides presentation ........................................................................... 19

Genius consists of 1 percent of inspiration

and 99 percent of sweating.

T. Edison

I. Introduction

The ability to perform percentage calculations is necessary to each person. We can very often hear about discounts, margins, markings, profits, loans, etc. - all this interest.

In almost all areas of human activity there are interest. Without the concept of "percentage", it is impossible to do in financial affairs, or in statistics, nor in medicine or production, even in cooking our mothers face the percentage ratio of products. To charge the employee's salary, you need to know the percentage of tax deductions; To open an account in Sberbank, our parents are interested in the amount of interest accruals on the deposit amount; To know the approximate increase in prices next year, we are interested in the percentage of inflation. Faced with the concept of percent at every step, I realized how important it is to be able to solve interest tasks.

Modern life makes interest tasks relevant, since the sphere of the practical application of interest calculations is expanding. Everywhere - in newspapers, on radio and television, in transport and at work are discussed raising prices, wages, pensions, rising stock value, reducing the purchasing power of the population and t / p. We will add here to announcements of banks that attract the population's money on various conditions, about changing the interest of a bank loan, etc. All this requires the ability to produce interest calculations.

Interest - This is one of the mathematical concepts that are often found in everyday life. You can often read or hear, for example, that "56.3% of voters took part in the elections, or" The rating of the winner of the hit-parade is 74%, "" industrial production decreased by 11.3%, "or" Bank charges 20% Annual, "" Milk contains 1.5% fat, "or" This fabric is 100% consists of cotton. "

It is clear that without the ability to understand this kind of information in modern society just would be difficult to exist.

Interest computations are of interest not only for future financiers, but also for all people. Such tasks have to deal with a savings deposit or loan in the bank, when buying goods by installments, when paying penalties, taxes, insurance, etc. Such tasks demonstrate the practical value of mathematics. This means that it is very important to study the concept of a percentage in mathematics lessons at school.

The tasks of interest are given quite a lot of attention in 6 - 9 grades of high school. However, as I learned, interest in the program in mathematics in high school classes is not included. With this approach, mathematical skills of percentage treatment may be forgotten. In high school classes, the use of interest goes to chemistry lessons, which introduces its surrender to interest through charts. The latter circumstance can confuse students in matters of the greatest use of the progress.

The project introduces middle-class students with basic percentage calculations, and their use in various areas of human life.

My interest in the topic arose in the lessons of mathematics when we solved interest tasks. When solving tasks, you need to distinguish one way to solve from the other. There are support tasks to find a percentage of the number, finding a number by its percentage, finding the percentage of two numbers.

There is a problem when solving tasks percentage in life: how to find a percentage of the number or how to calculate the total amount knowing the percentage? In order to answer these questions, it is necessary to analyze the solution of interest tasks. All interest tasks are solved using reference tasks.

Problem:Not knowledge of the basic rules for solving interest tasks leads to difficulties in solving such tasks in everyday life.

Hypothesis Solutions of the problem: A clear assimilation of interest support tasks in school affects the speed and correctness of decision-making in everyday life.

My project I want to prove that many interest tasks are solved using reference tasks. I want to learn yourself and help other competent and quickly carry out elementary interest calculations.

Objective of the project: Explain the solution to key interests with the help of creating a presentation on "interest" for the lesson of mathematics.

Subject Studies are reference tasks when solving interest tasks.

To achieve the goal, the following were set tasks:

1) to summarize the literature on the topic "Interest" and give the most complete picture of this concept;

2) show the breadth of interest; 3) to study the history of percentage;

4) to analyze the classification of interest tasks by ways to solve support tasks;

5) Create a presentation for a lesson on solving three standard tasks percentage "Finding percent of the number", "Finding a number by its percentage", "How many percent one value is from another";

6) consider the tasks, the plots of which are taken from reality, the environment of a modern person.

When executing research used methods:

Comparative analysis of literature

Building diagrams and graphs using a computer program

Generalization of the results obtained.

II. MAIN PART

Questioning

To identify the opinion of my classmates about the prevalence of interest in our life and to show the use of this mathematical concept in their own interests, I conducted a survey among 26 students:

History of the appearance of%

"The idea of \u200b\u200bexpressing parts of a whole constantly in the same stakes caused by practical considerations was born back in antiquity in Babylonians who used six-month fractions. Already in clinical tablets, Babylonians contains tasks for calculating interest. We have reached the charts compiled by Babylonians, which allowed them to quickly determine the amount of interest money. Interest and in India were known. Indian mathematicians calculated interest, applying the so-called triple rule, i.e. using the proportion. They could produce more complex calculations using interest.

Monetary calculations with interest were especially common in ancient Rome. The Romans called the interest of money, which paid the debtor to the lender for each hundred. Even the Roman Senate was forced to establish the maximum permissible percentage charged from the debtor, as some lenders were learned in obtaining interest money. From the Romans, interest crossed to other peoples.

The percentages were known to the Indians in the V c. This is natural, since in India, for a long time, the score was conducted in a decimal number system.

In the middle of the century in Europe, in connection with the wide development of trade, especially much attention paid for the ability to calculate interest. At that time, it was necessary to count not only interest, but also interest from interest, i.e., complex interest, as they call them in our time. Separate offices and enterprises to facilitate labor in percent calculations developed their special tables, which constituted the commercial secret of the company. For the first time published tables for calculating interest in 1584 Simon Stevein - an engineer from the city of Brugge (Netherlands). Stevein is known for a wonderful variety of scientific discoveries, including a special record decimal fractions».

For a long time, percentages were understood only by profit or loss for every 100 rubles. They were used only in trade and cash transactions. Then the area of \u200b\u200btheir application has expanded, interest is found in economic and financial calculations, statistics, science and technology. Nowadays the percentage is a private type of decimal fractions, a hundredth fraction of a whole (adopted per unit).

Apparently, the concept of "percent" appeared in Europe along with usury. "The word" percent"Comes from Latin words pro Centum.that literally means "up to one hundred". The% sign occurs, as believed from the Italian word CENTO (STR), which in percentage calculations often written abbreviated CTO. From here, by further simplification in the curtain of the letter T turned into an inclined line (/), originated modern symbol For percent designation. There is even a story of the emergence of modern designation%: "In 1685, the book" Guide for Commercial Arithmetic "Mathie de la port was published in Paris. In one place, we were talking about interest, which then denoted "CTO" (abbreviated from Cento). However, the typewriter accepted this "CTO" for the fraction and printed "%". So because of the typos, this sign entered into use. "

Many mathematics began to use a sign % To designate interest, and gradually he received universal recognition.

Percentage around us

Currently relevant more in-depth study Themes "Interest" in different situations. The reason for such a need is the significance, since the tasks on this topic are often found on various exams, and also apply not only in the lessons of mathematics, chemistry, economics. Interest is firmly included in our daily life: loans, bank interest, chemical compositions.

For a complete study of the use of interest in our life, I spent a survey among my classmates, where they met this concept. The survey results surprised even the guys themselves. Together we remembered so many areas of application of the percentage, which it became another confirmation of the relevance of the topic of my project. Here is a list of given examples:

Interest apply:

When calculating discounts in the store, draw up a contract in the bank, determining the visual acuity, the ratio of the threads in the composition of the tissue, determining the fat content in products, the definition of program downloads in a computer or charging of batteries, the value of the ratio of votes in elections or voting, when distributing the profit of the company, count execution tests EGE, tax calculation from s / board, with harvest and determining his losses from the elements, the ratio of water in the body of a person, or water and sushi on earth, in the ratio of impurities and gold in the decorations enrolled in universities from the general clean of the applicants, information for the motorist On the remainder of gasoline in the tank, with the ranking of the participants of the hit parade, the determination of the threshold of the epidemic.

So, we can say that interest is applied in the following areas: trade, programming, economics, production technology, statistics, medicine, public life, household life, different areas of science, art.

Interest are an integral part of banking, trade, tax, pharmaceutical, etc. operations. They entered our life not only with baking culinary products and with the preparation of delicacies, they literally attack us at the time of market relations in the economy, at the time of bankruptcies, inflation, crises.

The savings depositor in the bank learns to live percentage, competently posting money on a profitable business. Properly use mortgage loan in the bank will also help interest. Competently carry out interest calculations - it means to benefit in bank transactions, have cost-effective business and commercial offers.

Interest - This is one of the mathematical concepts that are very often found in everyday life.

After the survey, it became finally clear that without the ability to understand this kind of information in modern society just would be difficult to exist.

The concept of interest in mathematics

Some fractions are more often found in everyday life, and therefore they received their names: half (1/2), a third (1/3), quarter (1/4) and percentage (1/100).

In practice, fractional numbers very often have to be compared, and it is convenient to do it when they are expressed in the same fractions - only thirdly, only in the fourths, only in the tenths ... the most comfortable were hundredths, which are called interest (from Latin words Pro Centum - "For a hundred"). From here I. definition: the percentage is called a fraction 1/100 (0,01).

People have noticed long ago that hundredths of values \u200b\u200bare comfortable in practical activity. A hundredth part of the meter is a centimeter, a hundredth part of the ruble - a penny, a hundredth part of the centner - a kilogram. Therefore, a special name was invented - percentage. So one penny is one percent of one ruble, and one centimeter is one percent of one meter.

One percentage is one hundredth of the number.

So, 1kop. - 1% ruble

1cm - 1% meter

1A - 1% hectare

Since 1% is equal to a hundred parts of the value, then the whole value is 100%.

"Interest is the numbers that are another expression of decimal fractions. Any number can be expressed by a decimal fraction, which means, and in percent.

Judgment: The unit contains a hundred hundredths, that is, 1 \u003d 100%. Each number can be represented as a piece of unit to this number, and therefore express it as a percentage:

2 \u003d 1 x 2 \u003d 100% x 2 \u003d 200%

In order to solve interest tasks, it is necessary to know the definition of a percentage and be able to perform actions with interest: translating% in fraction, and vice versa - fraction in%.

0,58 = =(0,58 × 100)% = 58 %

It is convenient to first express the number in the form of a decimal fraction, and then transfer the comma for two signs to the right and put%.

Examples: 4 \u003d 4.00 \u003d 400%; 5/10 \u003d 0.5 \u003d 50%; ¾ \u003d 0.75 \u003d 75%

For reverse transition, the opposite is performed. In this way, to translate interest in a decimal fraction, you need to divide the number of percent per 100. For example: 39% = 39: 100 = 0,39.

T. to. 1% is one hundredth of the number, i.e. 0.01,

then 0.03 \u003d 3%; 0.85 \u003d, 1.5 \u003d \u003d 150%.

To express interest with a decimal fraction, you need a number that stands in front of a% sign, divided by 100 or something else, multiply by 0.01

2,5%=0,025 0,1%=0,%=3,5

Interest is used to compare homogeneous positive quantities, and only for this.

One percentage is one hundredth of the number: 1% \u003d "[12, 3]

Many percentage tasks are reduced to solving template tasks, some of which I will consider in the following paragraphs.

Key interest tasks

In the simplest tasks percent BUTaccepted by 100% , and its part b. equal p. %.

I.______100% = BUT____________ I. I. r% = b. I.

Finding percent of this number

These tasks refers to the situation when the total number A and some percentage p are given. It is required to find the number that this percentage expresses. Here keyword "from". The question may sound, for example, like this: to find R% of or or so, to find p% of the total number of A.

So: what is the number of pm% of e?

Such tasks are solved through the favor of one percent of the total

Such: b. = BUT× = (A. : 100) · p.

2 way: b. \u003d A · 0,01r

Example: 20% of 80 is:

80: 100 · 20 \u003d 0.8 · 20 \u003d 16

80 · 0.1 · 20 \u003d 80 · 0.2 \u003d · 16 Reply: 16

A task:In December, elections of the head of administration took place, in which 5,000 people took part. 30% of them gave votes for now the operating chapter. How many people voted for this candidate?

Decision: By condition, 5,000 people took part in the elections.

1 method: 5000: 100 · 30 \u003d 50 · 30 \u003d 1500

2 Method: 30% is 0.3 5000 × 0.3 \u003d 1500 people.

Answer: 1500 people.

A task: In soy seeds contain 20% oil. How many oil is contained in 700 kg of soy?

Decision. It is required to find the specified part of 20% of the known value of 700 kg.

1 method: 700: 100 · 20 \u003d 140

2 Method: 20% \u003d 0.2 700 · 0.2 \u003d 140 (kg).

Answer: 140 kg.

Finding a total of its percentages

How to find a total of if known R% and the amount of this percent a? or the found of the total number at a well-known part of the number and its value in percent.

If it is known that r% of the total number isb.T.

Such tasks are solved through the favor of one percent of the known number.

1 way : A \u003d b: \u003d B. : P · 100

2 way: a = b. : 0,01 p.

Example. 12% of the number x. Make up 30.

x \u003d 30: 12 × 100 \u003d 2.5 × 100 \u003d 250

x \u003d 30: 0.12 x \u003d 250 answer: 250

A task. From cotton it turns out 24% fiber. How much do you need to take cotton to get 480 kg of fiber?

1 Method: 480: 24 × 100 \u003d 20 × 100 \u003d 2000 kg

2 Method: 480: 0.24 \u003d 48 000: 24 \u003d 2000 (kg)

Answer: You need to take 2t cotton.

A task. From cotton it turns out 24% fiber. How much do you need to take cotton to get 6000 kg (6t) fibers?

1 method: 6000: 24 × 100 \u003d 250 × 100 \u003d 25000 kg

2 way: 6000: 0.24 \u003d 25000 (kg)

Answer: You need to take 25t cotton.

Finding the percentage of two numbers.

Finding the percentage of two numbers.

To find out how much percent one number is from the second, it is necessary to divide the first number to the second and the result multiply 100%.

Question: How many percentb. Makes out BUT ?

Task: We need to plow the field of the field in 500 hectares. 150 hectares plowed on the first day. How many percent is a plowed plot from the entire site?

To answer the question of the task, it is necessary to find the attitude (private) plowed part of the site to the entire area of \u200b\u200bthe site and express its relationship as a percentage: T. E. To divide the plowed area on the total area of \u200b\u200bthe site and multiply 100%.

150: 500 × 100% \u003d 0.3 × 100% \u003d 30%

Task 2. A worker made for shifting 45 parts instead of 36 according to plan. How much percent worker exceeded the plan?

Solution: To answer the question of the task, it is necessary to find the ratio (private) number 45 to 36 and express it as a percentage: 45: 36 × 100% \u003d 1.25 × 100% \u003d 125%.

Answer: Worker exceeded a 25% plan

Creating a presentation "The main tasks per percentages - we decide together!"

For several years now, I am pleased to make a presentation on the most different topics. This is lighting interesting facts For classroom hours, and preparing homework for lessons, and a special place is occupied by presentations for my projects. They are preparing for a long time, carefully and take more time on their presentation. To implement this project, I decided to create a presentation "The main tasks per percentages - decide together."

In this presentation there are slides devoted to the history of the occurrence of the percentage, the concept of "percentage", the analysis of the main tasks. For better consolidation of the topic covered at the end of the presentation, a test for basic tasks.

T. K. The presentation took place in an interactive form, then it was very useful for me. I could answer many questions, and many we understood in the class with Olga Vladimirovna, the head of my project.

In the lesson it became clear that the formulas written by me are not always clear if their mathematical expression is not explained. In addition, I wanted to supplement the presentation of a memo with basic formulas to solve the reference tasks percentage, since the guys were difficult to remember all formulas.

Experiment

As a result of an interactive lesson on the basis of the presentation, the 4th stage of the study was the conduct of an experiment. It consisted in comparing the results of two tests: before presentation and after. The experiment was a success! Prior to the presentation, the proposed interest tasks were able to solve only a few people, and after the percentage decided amounted to almost 90%.

Now, I hope my classmates will not ask Mom, how cheaper has become the thing, taking into account the discounts, and most likely they will help it in these calculations.

Now the presentation, tested on my classmates, could be postponed in open access in the Internet.

On the Youtube channel, we and our sister have their own page "shkola1223". I made a film in the form of a slideshow on the pages of the presentation and posted it on our channel.

http: // www. / user / shkola1223? Feature \u003d Watch

Now if in the Youtube search system to type the request "lesson on the topic of interest", or "interest tasks", then you can get acquainted with my presentation to interactive lesson. T. K. It was developed with the support of my project manager, it may be useful to teachers and schoolchildren in preparing homework. Here are some slides from the presentation:

The main conclusions on the conducted lesson.

The results of the test showed:

v The material is outlined clear and accessible;

v Material contains full information to work with percent;

v The list of examples contribute to the best assimilation of this topic;

v The proposed memo helps to fix the material passed;

Based on test results, it can be argued that the training program is compiled successfully and it can be recommended as a tutorial on the topic "Interest" for a student of grades 5-7.

Such detailed analysis The formulas suddenly helped me in the surrender of the programming exam in courses. It was necessary to write a program to calculate some formula. All the guys condition the program was taken by simple arithmetic action, and my program calculated interest and found the total number. As a result, the exam was delivered to "excellent"!

Conclusion

In conclusion, I would like to say that the percentage is really it Majesty. Without this concept, there is now much in life it would be incomprehensible, messy. The percentage puts in order many calculations, comparisons, etc.

The topic "interest" is universal in the sense that it binds among themselves many accurate and natural sciences, household and industrial areas of life. Students are found with interest in the lessons of physics, chemistry, on the Internet, viewing the TV shows, in stores.

Be able to competently and economically carry out elementary percentage calculations should each modern student.

From a mathematical point of view, a percentage section in school mathematics is the simplest. Teach interest is first of all to teach quickly and without hesitation to translate one or another verbal wording with the participation of interest in the appropriate mathematical formulation. In such a skill, a modern person, regardless of the kind of activity and the level of education, needs continuously.

That flew half a year of interesting and hard work. Thanks to the help of the head of my project and classmates achieved objective of the project :

It is investigated and proven that the use of interest in everyday life leads to the need to study the support tasks percentage in school. The study of this topic can be carried out using interesting presentation To the lesson.

Scheduled project implementation activities are fully implemented:

I repeated the material passed by interest. I got acquainted with the use of interest in different spheres of life. I found out that now the scope of interest is very high compared with the time of their birth, when they were used only roshovshchiki. I realized that interest can be applied everywhere, and for this you need the ability to correctly calculate them.

Project tasks:

Ancutting among classmates

- The history of the question has been studied

- Systematized and summarized information on the mathematical concept of interest

- The reference tasks for interest

- Created a presentation to the lesson

Thus, the expected project results:

In the process of the study, a training program was created, which can be used for individual learning. This program can be recommended for lessons and optional classes in mathematics. Mathematics teachers can use it as toolkit To this topic, as well as to control students' knowledge.

Presentation is posted in open Internet access. This program can use all who are interested in this topic.

In this project, I looked at the simplest basic tasks per percentages. These tasks account for only the first chapter of interest calculations. In the next work, I would like to get acquainted with a simple and difficult percentage, disassemble the conditions of tasks related to the accrual of bank interest.

I believe that the project has a practical result and will be useful for schoolchildren of different ages and for teachers who can use these materials for presenting their students.

Thanks for attention!

Bibliography.

1., Mathematics: textbook for grade 5 - M.: Mnemozina, 2003.

2., I know the world. Children's encyclopedia: mathematics. - M.: "AST Publisher", 1999.

3., Sedov Calculations. M. Drop, 2003

4. http: // RU. Wikipedia. ORG / WIKI /%, http: /// StudyGuide

Application. Results of questionnaire

Questioning

26 students so answered questionnaire questions:

1) How much time on a weekday, spend on: food, homework, computer, sleep, mugs / sections and the remaining time?

From this diagram it follows that the schoolboy on average spends his day to different classes approximately equally. In addition to the fulfillment of homework, many have a lot of time on other classes.

2) How much time on weekends you spend on: various events, computer, mugs / sections, homework?

From this diagram it follows that on average the guys spend on the homework 20% of the day off, and the rest of the time can devote to various events.

These questions have shown me that interest can be used to study many topics.

3) How often do you count the interest?

From this diagram it follows that more than half of our class enjoy the calculation of interest in everyday life.

4) Do you think the presence of interest is an important component in our lives?

Almost 80% of the guys from our class consider the presence of a percentage of an important component in our lives.

These two questions revealed the attitude of classmates to the theme of the daily use of interest, and confirmed the relevance of the topic of the project. After summing up the outcome of the questionnaire, I began to study the topic and creating a presentation of the lesson.

Application. Slides presentation to the lesson

Project tasks:
Explore the story
Origin
percent;
Consider tasks
per percentage out
practical life I.
ambient
Modern
man.
Spend
Research and S.
help
percentage
calculations
imagine
Data in the form
Tasks and diagrams

The relevance of our project

Interest is one of the most difficult topics
mathematics and very many students
make it difficult or do not know how to solve
interest tasks. And the understanding of interest and
Ability to produce interest calculations
necessary for every person. Applied
The value of this topic is very large and affects
financial, economic, demographic and
Other spheres of our lives. Explore interest
dictated life itself. Perform ability
Interest calculations and calculations are necessary
every person since with percents we
Follow in everyday life.

Plan of our actions

We have learned further the subject interest
their history
Found out that parents know,
relatives
Accounted for their interest tasks
Some tasks from the exam decided
Prepared a presentation

A little of the story
The word "percentage" has
Latin origin:
"Pro Centum" - "from one hundred".
Often instead of the word
"Percentage" use
The phrase "Cottaya
Part of the number ". Percentrate
called a hundredth part
numbers. 1/100 \u003d 1% percent
were especially
Completed in ancient
Rome. Romans called
percent money
who paid the debtor
(Body) for each
hundred.
Since the words "on a hundred"
sounded as "percentage", then
Cottage began to call
percentage

From Romans interest
switched to other peoples
Europe. To Russia
The concept of percentage introduced
Peter I.
The symbol did not appear immediately.
First wrote the word "hundred"
So:
In 1685 In Paris was
Printed
book
"Guide
by
commercial arithmetic ",
where by mistake instead
It was scored.

2. Associates in ours
Life.
Interest is one of
mathematical concepts
which is often found in
Everyday life. we
heard for example that
In the store 20% discount
57% took part in the elections
voters
Performance in class 100%,
Bank charges 16% per annum
Acetic acid 70%
Material contains 100% cotton
etc
Patzan 100% - in conversation
means the best in everything!

Three major actions related to interest

1. Finding percent of the number.
To find in% from B, it is necessary in · 0.01.
2. Finding a number by its percentages.
If it is known that in% of the number x is equal to, then
X \u003d Q: 0.01.
3. Finding a percentage
numbers.
To find interest
numbers, the attitude of these numbers
Multiply 100%.

10.

Interest
Applied
1. In medicine
2. In programming
3. In stores
4. In the election
5. In cooking
6. In statistics
7. In the composition of the fabrics
8. In taxes
9. In solutions
10. In Sberbank
11. In Analyz
activities
Interest is used
People of different professions

11. After conducting research in our class, we collected some data and processing them we received such results.

Checkout. In our class
2 excellent students -8% and 9
GOODSHIES -36% TOTAL
44% without "3"
In our class only 25
Man from no 12 boys 48% and 52% girls-13
18
17
17
16
16
15
14
12
10
8
10
9
8
8
6
4
2
2
2
2
2
0
1 quarter
Boys
Girls
2 quarters
Row 1.
3 quarters
Series 2.
Row 3.
4 quarters

12. Birthdays in class at the time of year

summer
fall
winter
Spring

13. From the school accountant, we learned that

Monthly from salary
employees, employer
Executed:
- into the pension fund - 22%;
- Social Foundation
insurance - 2.9%;
- Foundation Soc. Insurance OT
Accidents - 0.2%
- regional fund
health insurance -
5.9%. TOTAL 30.2%
The tax is deducted from
wages worker NDFL
=13%
For example, the salary is
14500ruble -13% NDFL
\u003d 14500-1885 \u003d 12615rub
will receive an employee

14. These tasks we accounted for relying on the information received.

Forest land
Sverobaikalsk
occupy Square
1651527 km2. In the summer of our
The city was for a long time
All in smoke, the forest burned.
How many percent of the forest
burned during
Fire, if the area
Fire
25234kv.km (1.5%)

15. The history of our city

We conducted a survey among
residents of G.
Severobaikalsk
"Do you know the coat of arms
of our city "out of 123
surveyed 65% of people
know the coat of arms, the rest
not. How many people are
Interviewed does not know
The coat of arms of ours
Cities? (79 people
Know 44 do not know)

16.

Interest in trade:
Mom wanted
Buy yourself down jacket
for 2700 rubles. in
Shop "Economy".
On November 4 was
sale. Discount
For all goods 20%.
For how much rubles
Mom buy
Down jacket
T.
SALE?
(2160 rubles)
Discount
20%

17.

When mixing 5% solution
Acids with 40%
Solution
Acids received
140g 30%
Solid. how many
Grams of each
The solution was for
Is it taken?

18.

Consider an old way to solve this task.
Each other is written by the content of acid solutions, to the left
them I.
approximately in the middle - the acid content in solution that should
come out
After mixing. By connecting the written numbers by the screenshots we get such
Scheme:
5
30
40
Consider the pairs of 30 and 5, 30 and 40. In each pair of
larger number will delete less and the result write
At the end of the corresponding screak. It turns out such
Scheme:
5
10
30
40
25
It is concluded from it that 5% of the solution should be taken 10 parts,
and 40% of 25 parts ,. (10 + 25 \u003d 35 hours of total, 140: 35 \u003d 4g-weight of one
parts, 4 × 10 \u003d 40g, 4 × 25 \u003d 100g.)
those. To get 140g. 30% solutions need to take
5% solution 40g., And 40% - CSO - 100g

19.

On TV I.
I heard that
Smoking man
Reduces its own
life is 15% that
It is 8.4 years.
What is middle
Duration
Life in Russia? (56)

20.

Another task
Previously, Vasya decided
Correct two tasks
per percentage out
twenty. After
Thread Study by
one useful
website, Vasya became
Deciding correctly 16.
Tasks from 20. How much
percent Posnel
Vasya? Per
100% mind
We consider 20 solved
Tasks (70%)

21.

But what we learned from
Our parents:

22. 1. Family budget (per month):

Name
rub
Mum
15 000
Grandmother
13 000
TOTAL
28 000
Costs
Residue
21770
6230
%
100

23.

2. Family distribution
budget for November:
Utilities
2000 rubles
9%
Mobile phones (all)
600 rubles
2,8%
Food
6600 rubles
30,3%
Clothes, shoes
4000 rubles
18,4%
Credit
5000 rubles
23%
Fare
520 rubles
2,4%
Medicine
1000 rubles
4,6%
Entertainment (concert)
300 rubles
1,4
Sweets
1500 rubles
6,9%
Other (haircut)
250 rubles
1,2%
21770
100%
TOTAL

24.

We chose this topic because we like
mathematics and we believe that mathematics
Know well.
We wanted to get full ideas about
Percentages about their role in everyday life.
We thought how important it is, to understand and know
interest and decided: to be good
specialists and to be 100% successful, it is necessary
study well.

25.

Kmmm V.S. "Repeat I.
We systematize school Course Algebra
and the beginning of the analysis. " M., "Enlightenment"
1990.
Magazine "Mathematics at school."
1998.№5.
F.F. Nagibin "Mathematical
Box »M." Enlightenment "1988.
https://yandex.ru/images/
http://infourok.ru/
https: //ru.wikipedia.

Work plan:

Introduction ....................................................................................... 2.

Chapter 1. What we know about interest ...................................................... 4

1.1. The history of the occurrence of interest ................................................ 4

1.2. What is the percentage? .................................................. .........................................five

1.3. Why do you need interest? ....................................................................................................................... ..6

Chapter 2. Role percent modern world…………………………………7

2.1. Percentages around us .................................................................. .7

2.2. Tasks per percent .................................................................. 8

2.3. Study with the help of interest ............................................. 9

Conclusion. Conclusions ..................................................................... 13.

List of used literature ............................................. 14

"Mathematics consists of 50 percent

from formulas and evidence

and by 50 percent of imagination "

Introduction

Subject My work is "the role of interest in the modern world"

The relevance of our project.

Interest is one of the difficult topics of mathematicians. Understanding interest and ability to perform interest calculations are necessary for each person. The applied value of this topic is very large and affects the various spheres of our life. Faced with interest for the first time, we suddenly notice that they accompany us everywhere - not only at school (in the lessons of mathematics, physics, chemistry, biology, geography, etc.), but also in everyday life: in the store, at work , in the bank, in the media, the Internet and many other things. Oriented in the world of interest at a good level is not so easy! The ability to perform percentage calculations and calculations are necessary to each person. List where and how the percentage is used infinitely, so we decided to study how the percentage is important in our modern life. How it is used as it is used in the store, in the bank and how our life depends on. We tried to study and based on the statistics on our school. Question I set up at the beginning of this work"How often in the modern world we use interest?"

These materials identified the object, the subject and purpose of our study.

Object research is a mathematical concept percentage.

Subject of study: understanding interest and ability to produce interest calculations and systematize the information received.

Purpose of the study: explore the use of knowledge about interest and find out how often interest is found in our lives; Top up the knowledge bank to the tasks about calculating interest in different spheres of life.

Research tasks:

learn about the history of interest;

Determine the concept of "percentage";

Determine the sphere practical application percent;

consider the various types of tasks percent from the practical life of a modern person;

Draw conclusions;

Conduct a study on the basis of our school, and submit results in the form of charts and tables.

Methods which I used the study - this is a questionnaire, analysis, measurement, comparison and generalization.

Practical significance: This topic is now very relevant, for the concept of "loan" is firmly included in the life of a modern person. People take bank loans and, as a rule, cannot correctly calculate interest payments. Anyone should be able to freely solve the tasks offered by life itself, be able to calculate the various offers of shops, credit departments and various banks and choose the most profitable. Text tasks per percentages are included in the materials of GIA and EGE.

Chapter 1. What we know about interest.

The idea of \u200b\u200bexpressing parts of the whole constantly in the same stakes caused by practical considerations was born in antiquity in Babylonians who used six-month fractions. Already in the clinical tables, Babylonians contain tasks for calculating interest. We have reached the charts compiled by Babylonians, which allowed to quickly determine the amount of interest money. Interest and in India were known. Indian mathematicians calculated interest, applying the so-called triple rule, i.e. using the proportion. They could produce more complex calculations using interest. Monetary calculations with interest were especially common in ancient Rome. The Romans called the interest of money, which paid the debtor to the lender for each hundred. From the Romans, interest crossed to other peoples. In the Middle Ages in Europe, due to the wide development of trade, much attention paid to the ability to calculate interest. The% sign occurs, as believed from the Italian word CENTO (STR), which in percentage calculations often written abbreviated CTO. From here, by further simplification, a modern symbol occurred to designate a percentage.

There is another version of this sign. It is assumed that this sign occurred as a result of ridiculous typos, perfect by a typewriter. In 1685, a book was published in Paris - a manual for commercial arithmetic, where, by mistake, the typewriter instead of CTO printed%.

The word "percentage" firmly entered the lexicon of our people.

Interest as a certain income obtained from a unit of capital for a unit of time appeared in ancient times. Already in the laws of Moses, it is said about banning to charge interest. IN Ancient Greece In particular, the change in the Delia Temple, the attention of interest was practiced. The interest is repeatedly mentioned in the ancient Roman legislation relating to later times. It affects the question of interest and Aristotle in their philosophical writings, speaking of the unrestricted interest of interest. Decimal fractions that are now playing in mathematics big role, appeared relatively recently. The first decimal fraction was recorded by Vieta (1540-1603). Systematic learning about frauds outlinedSimon Stevein In 1585, and the theory of decimal fractions substantiated Gerigon in 1634. But widespread decimal fractions only inXIX. in., after the introduction of the decimal system of measures.

For the first time published tables for calculating interest in 1584Simon Stevein - Engineer from the city of Bruges (Netherlands).Stevein Known a remarkable diversity of scientific discoveries, including a special record of decimal fractions.

1.2 What is the percentage?

So what is the percentage? The percentage is one hundredth share of the number, for its designation, use a special icon -%.For a long time, percentages were understood only by profit and loss for every 100 rubles. They were used only in trade and cash transactions. Then the area of \u200b\u200btheir application has expanded, interest is found in economic and financial calculations, statistics, science and technology. Today, the percentage is a private type of decimal fractions, a hundredth fraction of a whole (adopted per unit).

The sign% happened, as believed from the Italian word "cento."(STR), which in percentage calculations was often written abbreviated"cto." From here by further simplification in the rapid of the letter "t."In the inclined line there was a modern sign to designate the percentage.

One percentage is a hundredth share. The definition of one percent can be recorded by equality:

1% = (1/100)*100%=0,01 * 100%

5% = 0,05* 100%

23% = 0,23* 100%

130% = 1,3* 100%

The origin of interest, in the specified sense, there are assumptions that they originally arose as a special type of income, which received owners for returning to the use of fruitful property, for example: pets, fruit gardens, etc. Later began to let into account and cash The use of which also began to charge. The word "percentage", as you know, Latin origin. But already all the middle ages instead of Latin "procento."It turned out the distribution of Italian"percento."Or, more often,"procento.».

The ability to perform interest calculations is necessary to each person! In percentage, the implementation of the work, labor productivity, the savings, fuel, electricity, etc. is calculated, and other interests are applied in physics, chemistry, meteorology, technique, statistics, with all sorts of banking operations. Using percent, it is convenient to determine the content of one substance in the other; Measure changes in the production of goods, the growth of monetary income and other interests are very convenient to use in practice, as they express parts of integers in the same hundredths. This makes it possible to simplify calculations and easy to compare parts of each other and with integer. This year we learned how to perform three main actions with interest:

Being percent of the number;

Finding a number by its percentage;

Finding the interest rate of numbers.

If we are talking about the percentage of this number, then this number is taken for 100%. For example, 1% salary is a hundredth part of the salary; 100% salary is 100 hundredths of salary. Those., All salary. Income tax with salary is taken in the amount of 13%, i.e. 13 hundredths from salary. The inscription "60% cotton" on the label indicates that the material contains 60 hundredths of cotton, i.e. More than half consists of pure cotton. 3.2% fat in milk means that 3.2 hundredths of the mass of the product make up fat (or other words, every 100 grams of this product contains 3.2 grams of fat).

As is known from practice, with the help of interest often show a change in one or another value. This form is a visual numerical characteristic of a change that characterizes the importance of the change. For example, the level of adolescent crime rose by 3%, there is nothing terrible in this - perhaps this figure reflects only natural level fluctuations. But if he rose by 30%, then this is already talking about the seriousness of the problem and the need to study the causes of such a phenomenon and the adoption of relevant measures.

Chapter 2. The role of interest in the modern world.

2.1. Percentages around us.

Faced with interest for the first time, we suddenly notice that they accompany us everywhere - not only at school (in the lessons of mathematics, physics, chemistry, biology, geography, etc.), but also in everyday life: in the store (especially in The time of pre-holiday discounts), at work (increase and decrease in the salary), in the bank, in the media, the Internet and many other things.Interest in the modern world:

52.5% of voters took part in the elections;

Industrial production decreased by 11.3%;

The inflation rate is 8%;

Milk contains 3.2% fat.

Now in the world of 580 million people use the Internet, and the number of them grows every year by 4%.

Knowledge of interest calculations can be used not only in the lessons, but also in everyday life. The tasks cover various spheres of human activity - finance, demography, sociology, ecology.

Interest apply in a number of professions. Consider some of them in more detail. For example, my attention was attracted by such areas of professions as medicine, ecology, trade and many others. We will bring examples of some of them.

In medicine, percentages are used when processing instruments, syringes using a 3% and 5% saming solution (disinfectant). It is also used by a 5% solution of self-exchange during the cooking of the BCG vaccine.

In ecology - the Earth's atmosphere is a good air familiar to us. It is a mixture of gases in which 78% is nitrogen, about 21% - oxygen, and 1% falls on other gases. Only 3% of water on Earth - fresh, and most of it is contained in glaciers. And only 1.1% water on Earth is suitable for drinking. Water reflects 5% of sun rays, while snow is about 85%. Under the ice ocean penetrates only 2% of sunlight.

Trade also applies interest knowledge. Such as challenges for price increases, the calculation of real income from trade, change in turnover compared with the previous period. Also, the seller has to go to trade reports monthly. It is necessary to calculate how much the plan is executed.

Modern life makes interest tasks relevant, since the sphere of the practical application of interest calculations is expanding. Issues of inflation, price increases, the increase in the value of shares, the decline in purchasing power concerns each person in our society. Planning a family budget, favorable investment of money in banks, impossible without the ability to carry out simple interest calculations. Percentages help us easily calculate how the rate of inflation reduces the purchasing powerfulness of money and conclude about their advantageous investment.

2.2 Interest Tasks in the modern world.

Having studied more than this topic, I decided to make several interest tasks on my own. These are the tasks turned out.

Task 1. Payment for services through the terminal.

I put money on the phone through the terminal in the store. I had 20 rubles on the phone. I replenished my account for another 100 rubles. Commission is 11%. What amount will I have on the phone now?

Decision:
11%=0,11
1) 100 * 0.11 \u003d 11 (rub) - Commission
2) 100- 11 \u003d 89 (rub) came to my phone
3) 20 + 89 \u003d 109 (rub) has become only on the phone
Answer: 109 rub.

Task 2. Deposits in Sberbank

The contribution of "replenish" in Sberbank has an annual increase of 4.80%. The deposit amount of 30,000 rubles. How many rubles will increase the contribution at the end of the year?

Decision.

1). 4,80%=0,048

2). 30 000 * 0.048 \u003d 1440 (rub).

Answer: The amount of the deposit for the year will grow by 1440 rubles.

A task 3 . Discounts to pensioners.

In many pharmacies for pensioners, there is a 10% discount. My grandmother bought medications for the amount of 720 rubles. How much money will she pay the discount?

Decision.

one). 720: 10 \u003d 72 (rub) - discount.

2). 720-72 \u003d 648 (rub)

Answer: My grandmother will pay 648 rubles.

A task 4 . Good bought.

We decided to go to the store with my mother and buy me updates. Chose a sweater for 800 rubles. and a jacket for 1500 rubles. But the store took a share on this day. And we made a 20% discount on the sweater and 30% on the jacket. Very good purchase turned out. Question: How many rubles and I saved my mother?

Decision:

(800 * 20) : 100 \u003d 160 (rub.) - Discount on the sweater.

(1500 * 30): 100 \u003d 450 (rub.) - Jacket discount

160 + 450 = 610 ( rub.)

Answer: My mother and I saved 610 rubles.

2.3. Research with interest.

I conducted a study on our database schools MBOU Boocinskaya Sosh. All results issued in percentage, using tables and diagrams. The first thing I decided to figure out is how our parents know a lot about interest. For this, I am a small questionnaire and asked the parents to answer her.

Questionnaire "What do you know about interest?"

Dear parents, I, student of the 6th grade, working on the project "Interest in the modern world" and ask you to answer in writing to my questions.

1. Do you consider the topic: "Interest in the modern world" important?

2. Do you meet in everyday life with interest? If so, give some examples.

3. Do you know how to calculate interest?

4. What role is the interest in your life play?

The results of the survey.

Yes - 80%

No - 16%

I don't know - 4%

Do you meet in everyday life with interest? If so, give some examples.

In the bank - 70%

In the store - 20%

On the Internet - 10%

Do you know how to calculate interest?

Yes - 85%

Not always - 10%

No - 5%

What role is the interest in your life?

Big-80%

No - 12%

Secondary - 4%

No answer - 4%

Output: For most adults, the percentage plays an important role. Most parents are familiar with this concept. Interest plays a big role in their lives.

Next, I conducted a study on the basis of our school. Our school is small, so for a start I decided to find out how much the boys study in it, and how many girls. In total, 52 people study our school, of which 27 boys are 60% and 25 girls - 40%.

Then I decided to figure out what progress of students in our school. To do this, I revealed the number of excellent students and good. These are the results from me.

In the first quarter we had 4% of excellent students and 33% of the gooders. In the second quarter, we had 8% of excellent students and 29% of the gooders. According to these results, it can be concluded that the level of excellent students increased by 4%.

And I became wondering how many people live in my barrage village. For this, I went to the administration and found out that in 2010 the inhabitants were 789 people, and in 2015 there were 744 people. I decided to find out how much percent decreased the population of the village of Batings. I got the computation, it turned out that in 5 years the inhabitants decreased by 6%.

Conclusion.

So, in our work, I showed the application of the concept of a percentage in solving real problems only from some spheres of human life. The ability to perform interest calculations is necessary to each person! In percentage, the performance of the work, labor productivity, the savings, fuel, electricity, etc. is calculated.

In the course of work on this project, I concluded that interest helps us:

Competently understand the big stream of information;

Perform profitable purchases, saving on discounts;

Competently take loans, choosing a more profitable option.

Solve mathematical tasks.

Percentages are creating miracles. Knowing them, the poor can become rich. Cheerful yesterday in the trade transaction, the buyer today reasonably requires the percentage of trading discount. The savings investor learns to live percentage, competently posting money on a profitable business. It is difficult to name the area where interest was not applied.

Application in the life of interest calculations is very difficult to consider very difficult, since interest is applied in all spheres of human life. This topic leaves a wide field for further research.

Output: The role of interest in everyday life is very large. The topic "interest" is universal in the sense that it binds among themselves many accurate and natural sciences, household and industrial areas of life. We meet with percentages in the lessons, when reading newspapers, view the TV shows, in stores. Be able to competently and economically carry out elementary percentage calculations should each modern student. Recently, the exam in mathematics is carried out in uniformand in control and measuring eME Materials There is a task percentage. Therefore, it is necessary to know as much as possible and be able to use this topic.

Slide 1.

Slide description:

The project "Interest in our life". Objectives: to summarize knowledge on "interest" and allocate the practical significance of this concept in various fields of human activity. It will learn to competently and economically carry out elementary percentage calculations. Tasks: consider tasks whose stories are taken from reality. Conduct studies at school on how students are able to solve interest tasks and present results in the form of a chart. Release the "Directory for Students" with the rules for solving interest tasks. 2008

Slide 2.

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Slide 3.

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Slide 4.

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The history of the occurrence of interest. The hundredth fraction of the number is called the percentage of the number and denote the sign%. This concept appeared in mathematics in connection with the development of trafficking, when the money taken in the debt was received from the debtor any amount over debt. Usually this amount was expressed in hundredths. Somewhat later she had a name - interest. The word "percentage" occurred from the two Latin words: "Pro" - "on" and "centuries" - "one hundred", that is, in a literal translation into Russian, the percentage means "on a hundred". The% stated sign for interest in the XVII century. It probably occurred from the reduction of the Latin word "Centum" in "CTO". When cogvopsy "CTO" began to look like "O / O", and then - "%". Hence, by further simplification in the cursor, the letter T in the inclined line there was a modern symbol for the designation of interest. 1% \u003d 0.01 to us reached the interest tables made up by more than Babylonians. These tables allowed to quickly determine the amount of interest money. Interest and in India were known. Indian mathematicians calculated interest, applying the so-called triple rule. For example, when calculating 5% of 830 recorded: 1% is 830/100, 5% are (830 ∙ 5) / 100 \u003d 41.5 they produced more complex calculations. In ancient Rome, cash payments with interest were widespread. The Roman Senate established the most affordable percentage charged from the debtor. In the middle of the century, trade expanded and, therefore, special attention was paid to the ability to calculate interest. Then I had to count not only interest, but also interest from percent (complex interest). Often, the offices and enterprises to facilitate the calculations developed special charts for calculating interest. These tables kept secret, made up the commercial secret of the company. For the first time, the tables were published in 1584 by Simon Stevin - an engineer from the city of Bruges (Netherlands). He is known different scientific discoveries, as well as the use of a special record of decimal fractions. For a long time, percentages were understood only by profit or loss for every 100 rubles. They were used only in trade and cash transactions. Then the area of \u200b\u200btheir application has expanded, interest is found in economic and financial calculations, statistics, science and technology.

Slide 5.

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Slide 9.

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Tasks for simple percentages. In the simplest tasks for percentages, some value "A" is accepted for 100% (integer), and its part "B" is expressed by the number "R%". Task # 1. How to find a few percent of the number "A"? To find a few percent of the number, it is necessary to multiply this number to the corresponding fraction.

Slide 10.