6th grade students
After studying the topic "Percentage", the children were asked to study this topic in more detail. Find out where interest is applied in life and why it is needed at all. In what professions interest is often used. And we got a project on this topic. The guys studied the history of the appearance of interest, made up their life tasks for interest.
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MBOU Inyakinskaya secondary comprehensive school
Project
on the topic of:
"Percentages in our life"
Supervisor: teacher of mathematics Ustinkina S. A.
Project time: 3 lessons
And extracurricular work
December 2012
Problem.
At the lesson of mathematics, we studied the topic "Percentage". We became interested,
Where does it occur in our lives? The teacher recommended that we investigate this question. We decided to study the necessary literature, ask around parents, grandparents.
Project tasks.
- To study the history of the origin of interest;
- Consider tasks for percentages from practical life ;
- Define scope practical application percent.
Target:
- Find out where and how interest is applied in our lives. Understand how history proves the emergence of interest.
Our action plan.
- Read literature on the history of interest.
- Find out what parents and grandparents know about interest and how they apply it to their profession.
- Make up your tasks for percentages and bring as much as possible more examples life situations associated with interest.
- Gather all the material together and arrange the product of our work in the form of a brochure and presentation.
1. From the history of the emergence of interest.
The word percent off Latin word pro centum, which literally means "for a hundred" or "from a hundred". 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. Interest was especially common in Ancient Rome. The Romans called interest the money that the debtor paid to the lender for every hundred. From the Romans, interest passed to other peoples of Europe.
The % sign is believed to come from the Italian word cento (one hundred), which is often abbreviated cto in percentage calculations. From here, by further simplification in cursive, the letter t turned into a slash (/), the modern symbol for percent arose.
“The Romans took interest from the debtor (that is, money in excess of what they lent). At the same time, they said: "For every 100 sesterces of debt, pay 16 sesterces of interest."
Examples of two tasks of historical content, on the topic "Interest":
Task 1 . One poor Roman borrowed 50 sesterces from a lender. The lender made a condition: "You will return to me within the prescribed period of 50 sesterces and another 20% of this amount." How many sesterces must a poor Roman give to a lender to repay a debt?
Answer: 60 sesterces.
Task 2 A certain person borrowed 100 rubles from a usurer. An agreement was concluded between them that the debtor is obliged to return the money exactly in a year, paying another 80% of the debt amount. But after 6 months, the debtor decided to return his debt. How many rubles will he return to the usurer?
Answer: 140 rubles.
The use of the term "percentage" in Russia begins 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 applied 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 a percentage is a special kind of decimal fractions, a hundredth of a whole (taken as a unit).
2. Interest in our lives.
Percentage is one of the mathematical concepts that are often found in Everyday life. You can read or hear, for example, that
57% of voters took part in the elections,
Progress in the classroom 85%,
the bank charges 17% per annum,
milk contains 1.5% fat,
the material contains 100% cotton, etc.
Eye color in our class
Our class.
66,65%
33,35%
Distribution of area in the school area
50%
3. Tasks for percentages
The main tasks for fractions can be divided into three groups:
1. Finding percentages of a number:
To find percentages of a number, turn the percentages into decimal and multiply by that number.
2. Finding a number by its percentage:
To find a number by its percentage, you need to turn the percentage into a decimal fraction and divide the number by this fraction.
3. Finding the percentage of numbers:
To find the percentage of numbers, you need to multiply the ratio of these numbers by 100.
Here are the tasks we did:
1. A fur coat costs 2,000 rubles in a store. In the summer, at a sale, it fell in price by 23%. For how many rubles can you buy a fur coat at a sale?
2. On a wholesale basis, the price of 1 kg of watermelon is 8 rubles. The store makes a markup of 3%. At what price per kilogram will we buy a watermelon in the store?
3. My mother works at the club as a usher. A ticket to the disco costs 20 rubles. But the director said that from January 1, the ticket price will rise by 5%. How much will a disco ticket cost from January 1st?
4. I have a friend who studies at the Shilovsky Secondary School No. 1. He said that there are only 900 students in their school and all students attend various circles and sections. I was wondering, what is the percentage?
5. I read in the newspaper that the Eleks store is holding a sale of computer equipment with a 12% discount. I ask my parents to buy me a laptop that costs 20,900 rubles. How much will I have to pay for this laptop, taking into account the discount?
6. During the renovation of the school, out of 28 windows on the main facade, only 10 were replaced with plastic ones.
What is the percentage of plastic windows from the windows on the facade?
7. We have a school site in our school. We know that flower crops occupy 6.4 acres, which is 32% of the entire area. What is the area of the school lot?
8. Our family's monthly income is 15,600 rubles. 5,000 rubles a month are spent on food, utilities cost 900 rubles, electricity - 220 rubles. What percentage of the total budget is the cost of food, utilities and electricity.
9. The notebook costs 40 rubles. What is the largest number of such notebooks that can be bought for 650 rubles after a price reduction of 15%? (This task is taken from the USE assignments in mathematics grade 11.)
10. A person who smokes shortens their life by 15%, which is 8.4 years. What is the average life expectancy in Russia? (from statistics)
4. Conclusion.
The study of percentage is dictated by life itself. They surround us almost everywhere. People in many professions work with percentages. For example, economists, accountants, bankers and even sellers. The ability to perform percentage calculations and calculations is necessary for every person, since we encounter percentages in everyday life.
Conclusion: Percentages make it easy to compare parts of a whole, simplify calculations and are therefore very common.
In the process of doing the work, we learned a lot of new things, we think that we have done very useful work for ourselves and this will be useful in our studies.
Project "Interest in our life". Objectives: To summarize knowledge on the topic "Interest" and highlight the practical significance of this concept in various fields human activities. Learn to competently and economically carry out elementary percentage calculations. Tasks: Consider tasks, the plots of which are taken from reality. Conduct research in the school on how students are able to solve percentage problems and present the results in a diagram. Issue a "Handbook for students" with the rules for solving problems for percentages. 2008
The project was completed by students of the 8th grade: 1. Grigoriev Valera 2. Posashkova Ekaterina 3. Kusumov Bakhtiyar Project leader: mathematics teacher Mashyanova N.A. Novosarbaiskaya secondary school Contents: Contents: 1. Introduction. 2. The history of interest. 3. Definition of interest. 4. Tasks for simple interest. 5. Research results. 6. Interest at school.
Introduction. “I am a percentage,” a cry rang out, “I declare immediately. At school, every student is obliged to know me. In our time, in almost all areas of human activity, there are percentages. The concept of "percentage" cannot be dispensed with in any accounting, neither in financial analysis nor in statistics. To calculate the salary of an employee, you need to know the percentage of tax deductions; in order to open a deposit account in a savings bank, our parents are interested in the amount of interest on the amount of the deposit; to know the approximate rise in prices in the coming year, we are interested in the percentage of inflation. In trade, the concept of "percentage" is used most often: discounts, markups, markdowns, profits, seasonal changes in commodity prices, income tax, etc. All of these are percentages. %
History of interest. The hundredth of a number is called the percentage of the number and is denoted by the sign%. This concept appeared in mathematics in connection with the development of trade, when for borrowed money the lender received from the debtor any amount in excess of the debt. This amount is usually expressed in hundredths. A little later, she got a name - interest. The word "percent" comes from two Latin words: "pro" - "on" and "centum" - "one hundred", that is, in a literal translation into Russian, percent means "one hundred". The % sign was fixed to denote percent in the 17th century. It probably came from the contraction of the Latin word "centum" in "cto". In cursive, "cto" began to look like "o / o", and then - "%". From this, by further simplifying the cursive letter t into a slash, the modern symbol for percent was derived. 1% \u003d 0.01 The percentage tables compiled by the Babylonians have come down to us. These tables made it possible to quickly determine the amount of interest money. Interests were also known in India. Indian mathematicians calculated percentages using the so-called triple rule. For example, when calculating 5% of 830, they wrote: 1% is 830/100, 5% is (8305) / 100 \u003d 41.5 They also made more complex calculations. In ancient Rome, cash settlements with interest were widespread. The Roman Senate set the maximum available interest charged from the debtor. In Europe, trade expanded in the middle of the century and, consequently, Special attention applied to the ability to calculate percentages. Then it was necessary to calculate not only interest, but also interest on interest (compound interest). Often, offices and enterprises developed special interest calculation tables to facilitate calculations. These tables were kept secret, they were a trade secret of the company. The tables were first published in 1584 by Simon Stevin, an engineer from the city of Bruges (Netherlands). He is known for various scientific discoveries, as well as the use of a special notation for decimal fractions. For a long time, interest was understood exclusively as profit or 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.
Percent definition. Percentages Percentages are numbers that are a special case of decimal fractions. A percentage is a fraction of 1/100 or 0.01. One hundredth of a quantity is called a percentage of a quantity. 1/100 = 1% or 0.01 = 1% For example. Out of every 100 participants in the lottery, 7 participants received prizes. 7% - This is 7 out of 100, 7 people out of 100 people.
To express a percentage as a decimal or natural number, you need to divide the number before the % sign by 100. For example: 58% = = 0.58 To go back, the reverse action is performed. Thus: To express a number as a percentage, you need to multiply this number by 100. For example: 0.58 \u003d \u003d (0.58 100)% \u003d 58%
Tasks for simple interest. In the simplest percentage problems, a certain value "a" is taken as 100% (an integer), and its part "b" is expressed by the number "p%". Problem 1. How to find a few percent of the number "a"? To find a few percent of a number, you need to multiply this number by the corresponding fraction.
Task 3. How to find the percentage of two numbers, or find out what percentage the number "b" is from the integer "a"? To find out how many percent the number "b" is from the number "a", you need to divide "b" by "a" and multiply the result by 100%.
Research: “How do students in our school know how to solve percentage problems?” The topic "Percentage" is given little time in mathematics lessons. This topic is studied in grades V-VI, after which it is rarely returned to. We offered students from grades 6 to 11 to solve the following tasks: (the study was conducted in the spring of 2008)
Tasks: 1 option. 1. 70% of all students are present in the class. What percentage of all students are absent? 2. Express as a percentage 2/5 of all residents of the city. 3. Find 15% of 30,000 rubles. 4. How much will it be if 30,000 rubles. Increase by 15%? 5. How many percent are 500 rubles. from 200 rub.? 6.40% of a certain amount is 100 rubles. What is this amount? Option 2. 1. We dug up 45% of the field. What percentage of the field remains to be dug up? 2. Express as a percentage ¾ of all residents of the city. 3. Find 35% of 10,000 rubles. 4. How much will it be if 10,000 rubles. reduce by 35%? 5. How many percent are 600 rubles. from 400 rub.? 6.30% of a certain amount is 150 rubles. What is this amount?
The number of correctly completed tasks (in percent). grades Average score 653%12%53%6%29%35%31% 783%58%42%25%25%33%44% 8100%50%33%33%17%42%46% 980%73% 80%7%67%60%61% %78%78%44%78%56%72% %71%71%29%100%100%79%
Conclusion. Most mistakes were made in the task of the form: "Increase (decrease) the number by a few percent." task in general view: 1) The number a was increased by p%. It became: a + a p / 100 \u003d a (1 + p / 100) 2) The number a was reduced by p%. It became: a - a p / 100 = a (1 - p / 100) For example: 1) The number 120 will be increased by 25%. For example: 1) The number 120 will be increased by 25%. 120(1+ 25/100) = 120 1.25 = (1+ 25/100) = 120 1.25 =150 2) Decrease the number 120 by 25% 2) Decrease the number 120 by 25% 100) = 120 0.75 = (1 - 25/100) = 120 0.75 = 90
Different types of problems with percentages 1. Determining the percentage of a number Find: 25% of 120. Solution: 1) 25% = 0.25; 2) ,25 \u003d 30. Answer: Determination of a number by its known part, expressed as a percentage Find the number if 15% of it is equal to 30. Solution: 1) 15% \u003d 0.15; 2) 30: 0.15 \u003d 200. or: x is a given number; 0.15.x = 300; x = 200. Answer: After considering these simplest problems, we can consider problems like: 1. How many percent is 10 more than 6? 2. How many percent is 6 less than 10? Solution: 1. ((10 - 6).100%)/6 = 66 2/3% 2. ((10 - 6).100%)/10 = 40%
4. What happens to the price of a product if it is first increased by 25% and then lowered by 25%? Solution: Let the price of goods x rub. 1) x + 0.25x = 1.25x; 2) 1.25x - 0.25.1.25x \u003d 0.9375x 3) x - 0.9375x \u003d 0.0625x 4) 0.0625x / x. 100% = 6.25% Answer: The original price of the item has decreased by 6.25%. 5. Fresh mushrooms contained 90% water by weight, and dry 12%. How many dry mushrooms will be obtained from 22 kg of fresh ones? Solution: 1) 22. 0.1 = 2.2 (kg) - mushrooms by weight in fresh mushrooms; 2) 2.2: 0.88 = 2.5 (kg) - dry mushrooms obtained from fresh ones. Answer: 2.5 kg. When solving problems on percentages, one has to deal with the concept of "percentage content", "concentration", "% solution". Therefore, I propose tasks for these concepts.
Percentage content. Percentage solution. Task: How many kg of salt in 10 kg of salt water, if the percentage of salt is 15%,15 = 1.5 (kg) of salt. Answer: 1.5 kg. The percentage of a substance in a solution (for example, 15%), sometimes called a % solution, for example, a 15% salt solution. Task: The alloy contains 10 kg of tin and 15 kg of zinc. What is the percentage of tin and zinc in the alloy? Solution: The percentage of a substance in an alloy is the part that the weight of this substance makes up from the weight of the entire alloy. 1) = 25 (kg) - alloy; 2) 10/% = 40% - percentage of tin in the alloy; 3) 15/% = 60% - the percentage of zinc in the alloy; Answer: 40%, 60%.
Concentration. If the concentration of a substance in a compound by mass is p%, then this means that the mass of this substance is p% of the mass of the entire compound. Example. The concentration of silver in an alloy of 300 g is 87%. This means that pure silver in the alloy is 261 g,87 = 261 (g). In this example, the concentration of a substance is expressed as a percentage. The ratio of the volume of a pure component in solution to the entire volume of the mixture is called the volumetric concentration of this component. The sum of the concentrations of all components that make up the mixture is equal to 1. In this case, the concentration is a dimensionless quantity. If the percentage of a substance is known, then its concentration is found by the formula: k \u003d p 100% k - the concentration of the substance; p is the percentage of the substance (in percent).
Additional tasks. 1. There are 2 alloys, one of which contains 40% and the other 20% silver. How many kg of the second alloy must be added to 20 kg of the first in order to obtain an alloy containing 32% silver after fusion together? Solution: Let x kg of the second alloy be added to 20 kg of the first alloy. Then we get (20 + x) kg of the new alloy. 20 kg of the first alloy contains 0.4. 20 \u003d 8 (kg) silver, x kg of the second alloy contains 0.2 x kg of silver, and (20 + x) kg of the new alloy contains 0.32. (20+x) kg of silver. Let's make an equation: 8 + 0.2x = 0.32. (20+x); x = 13 1/3. Answer: 13 1/3 kg of the second alloy must be added to 20 kg of the first to obtain an alloy containing 32% silver. 2. 5% salt solution was added to 15 liters of 10% salt solution to obtain an 8% solution. How many liters of 5% solution were added? Solution. Let x l of 5% salt solution be added. Then the new solution became (15 + x) l, which contained 0.8. (15 + x) l salt. 15 liters of a 10% solution contains 15.0.1 \u003d 1.5 (l) of salt, x l of a 5% solution contains 0.05x (l) of salt. Let's make an equation. 1.5 + 0.05x = 0.08. (15 + x); x \u003d 10. Answer: 10 liters of a 5% solution were added.
Description of the presentation on individual slides:
1 slide
Description of the slide:
The project "Interest in our life" was prepared by: students of grade 6 "Secondary School No. 3" Klepov A, Sukmanov A. supervisor: Dremukhina T.A
2 slide
Description of the slide:
Find out where and how interest is applied in our lives. To expand knowledge about the use of percentage calculations in tasks and in different areas of human life. Target:
3 slide
Description of the slide:
Conduct research and use percentage calculations to present data in the form of tasks and diagrams Project objectives: To study the history of the origin of interest; Consider tasks for interest from practical life and environment modern man.
4 slide
Description of the slide:
The relevance of our project Interest is one of the most difficult topics in mathematics, and many students find it difficult or do not know how to solve problems with percentages at all. And the understanding of percentages and the ability to make percentage calculations are necessary for every person. The applied value of this topic is very high and affects the financial, economic, demographic and other spheres of our life. The study of percentage is dictated by life itself. The ability to perform percentage calculations and calculations is necessary for every person, since we encounter percentages in everyday life.
5 slide
Description of the slide:
Our plan of action We additionally studied the topic of interest and their history We found out what parents and relatives know We made our tasks for percentages We solved some problems from the Unified State Examination We prepared a presentation
6 slide
Description of the slide:
A bit of history The word "percent" is of Latin origin: "pro centum" - "from a hundred." Often, instead of the word “percent”, the phrase “hundredth of a number” is used. A hundredth of a number is called a percentage. 1/100=1% Interest was especially common in Ancient Rome. The Romans called interest the money that the debtor (lender) paid for every hundred. Since the words “per hundred” sounded like “percent”, the hundredth part was called a percentage.
7 slide
Description of the slide:
The symbol did not appear immediately. First they wrote the word "hundred" like this: In 1685. in Paris, the book "Guide to commercial arithmetic" was printed, where by mistake was typed instead. From the Romans, interest passed to other peoples of Europe. In Russia, the concept of interest was introduced by Peter I.
8 slide
Description of the slide:
2. Interest in our lives. Percentages are one of the mathematical concepts that are often encountered in everyday life. We heard, for example, that In the store, a 20% discount, 57% of voters took part in the elections, academic performance in the class is 100%, the bank charges 16% per annum, Acetic acid 70% material contains 100% cotton, etc. Boy 100% - In a conversation means the best in everything!
9 slide
Description of the slide:
Three Basic Percentage Activities 1. Finding percentages of a number. To find y% of v, you need v·0.01. 2. Finding a number by its percentage. If it is known that y% of the number x is equal to b, then x=b:0.01. 3. Finding the percentage of numbers. To find the percentage of numbers, you need to multiply the ratio of these numbers by 100%.
10 slide
Description of the slide:
Percentages are used 1. in medicine 2. in programming 3. in stores 4. in elections 5. in cooking 6. in statistics 7. in fabric compositions 8. in taxes 9. in solutions 10. in savings banks 11. in activity analysis people of different professions
11 slide
Description of the slide:
After conducting research in our class, we collected some data and processed it, we got the following results
12 slide
Description of the slide:
13 slide
Description of the slide:
We learned from the school accountant that every month the employer deducts from the salary of employees: - to the Pension Fund - 22%; - social insurance fund - 2.9%; - social fund accident insurance - 0.2% - regional health insurance fund - 5.9%. Total 30.2% Tax deducted from the salary of an employee Personal income tax = 13% For example, the salary is 14500 rubles -13% Personal income tax = 14500-1885 = 12615 rubles will be received by the employee
14 slide
Description of the slide:
These are the tasks we compiled based on the information received. The forest lands of the city of Severobaikalsk occupy an area of 1651527 km2. In the summer, our city was covered in smoke for a long time, the forest was burning. How many percent of the forest burned down during the Fire, if the fire area is 25234 sq. km (1.5%)
15 slide
Description of the slide:
The history of our city We conducted a survey among the residents of Severobaikalsk "Do you know the coat of arms of our city" out of 123 respondents, 65% of people know the coat of arms, the rest do not. How many of the respondents do not know the coat of arms of our city? (79 people know, 44 do not know)
16 slide
Description of the slide:
Interest in trade: Mom wanted to buy a down jacket for 2700 rubles. in the Economy store. And on November 4th there was a sale. 20% discount on all goods. How many rubles will mom buy a down jacket on sale? (2160 RUB) t Discount 20%
17 slide
Description of the slide:
When mixing a 5% acid solution with a 40% acid solution, 140 g of a 30% solution were obtained. How many grams of each solution was taken for this?
18 slide
Description of the slide:
Consider the old way of solving this problem. One under the other, the acid contents of the available solutions are written, to the left of them and approximately in the middle - the acid content in the solution, which should be obtained after mixing. Connecting the written numbers with dashes, we get the following scheme: 30 5 40 Consider the pairs 30 and 5, 30 and 40. In each pair of more subtract the smaller one and write the result at the end of the corresponding line. The following scheme will be obtained: 10 30 5 40 25 From it it is concluded that 5% solution should be taken 10 parts, and 40% 25 parts,. (10 + 25 = 35 parts in total, 140:35 = 4g-weight of one part, 4 × 10=40g, 4×25=100g) i.e. to get 140g. 30% solution you need to take a 5% solution 40g., And 40% solution - 100g
19 slide
Description of the slide:
I heard on TV that a person who smokes shortens his life by 15%, which is 8.4 years. What is the average life expectancy in Russia? (56)
Municipal educational institution "Secondary school of the village of Cherkasskoye, Volsky district of the Saratov region"
PROJECTON THE TOPIC OF:
"PERCENTAGE AROUND US"
Completed by: Chelobanova Diana,
Utkina Tatyana students
Teacher: Lapteva O.A.
2016-2017 academic year year
Educational project passport
7th grade students Diana Chelobanova, Tatyana Utkina.
MOU "Secondary School with. Cherkasy"
"Interest around us"
1.subject - mathematics
2. project type :
1) by dominant activities - research;
2) in terms of content - natural science;
3) by the number of participants - collective;
4) by the breadth of coverage of content - interdisciplinary;
5) in terms of time - short;
4. name of the topic:"Interest";
5. creative title: "Interest around us"
6 .annotation:
At present, the understanding of interest and the ability to make percentage calculations are necessary for every person: the applied value of this topic is very great and affects the financial, demographic, environmental, economic, sociological and other aspects of our life.
Any person should be able to freely solve the problems offered by life itself, be able to calculate the various offers of shops, credit departments and various banks and choose the most profitable ones.
7.problem
Do we need to know about percentages
8. target:
expand the concept of interest;
show the breadth of applications in life percentage calculations
9.task: search for information, analysis of the information received;
10. fundamental question: What knowledge can you live without? modern world?
11.problematic issues:
Where was interest born?
How are interest related to the natural sciences?
Where can interest be used in school life?
Do adults solve percentage problems in everyday life?
12.work plan: work with textbooks, literature and video information, analysis of the proposed explanations;
13.form of work: collective;
14.presentation form: presentation
1 7 . informational resources: http:// en. wikipedia. org/ wiki/%25
http:// school21. m- sk. en/ npk_ d_ mat/ lobkov/ lobkov. htm
18.used information technologies: powerpoint, Microsoft Word;
19.materials and equipment:
Projector, computer.
20. Project manager:
teacher of mathematics Lapteva O.A.
Percent. Basic concepts.
Types of tasks for interest
Application of percentage calculations in various types human life
Examples of Modern Percentage Problems
Interest in school life.
Conclusion
Conclusions.
Literature.
Wherever you go, wherever you go,
But whatever you say...
You will meet percentages everywhere
On life path
The purpose of our project
expand the concept of interest;
to carry out interdisciplinary communication through this topic;
show the breadth of application in life percentage calculations.
Relevance of the topic choice:
Percentages are one of the mathematical concepts that are often encountered in everyday life. At present, the understanding of interest and the ability to make percentage calculations are necessary for every person: the applied value of this topic is very great and affects the financial, demographic, environmental, economic, sociological and other aspects of our life. This topic is now very relevant, because the concept of "credit" (whether it be a mortgage, or a car loan, consumer credit) has firmly entered the life of a modern person. People take bank loans and, as a rule, cannot correctly calculate the interest payments. Any person should be able to freely solve the problems offered by life itself, be able to calculate the various offers of shops, credit departments and various banks and choose the most profitable ones. Percentage word problems are included in OGE materials and USE
1. Percentage. Basic concepts.
The word "percent" comes from the Latin pro centum, which literally means "per hundred", "one hundred" or "per hundred". In popular literature, the emergence of this term is associated with the introduction of the decimal number system in Europe in the 15th century. Interest was especially common in ancient Rome. The Romans called interest the money that the debtor paid to the lender for every hundred.
It is believed that the concept of percentage was introduced by the Belgian scientist Simon Stevin. In 1584 he published percentage tables. The use of the term "percentage" in Russia begins at the end of the 18th century. For a long time, interest was understood exclusively as profit or 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.
The origin of the percent designation is interesting. There is a version that the% sign comes from the Italian pro cento (one hundred), which in percentage calculations was often abbreviated as cto. From here, by further shortening in cursive, the letter t turned into a slash (/), the modern percent sign arose
There is also an assumption that the % sign arose as a result of a typo. In Paris, in 1685, a book was printed - a guide to commercial arithmetic, where the compositor mistakenly printed the% sign.
2. Types of problems for interest
There are three main types of interest problems:
Task 1. Find the specified percentage of the given number.
Given number is multiplied by the specified percentage, and then the product is divided by 100.
Task 2. Find a number given another number and its value as a percentage of the desired number.
The given number is divided by its percentage and the result is multiplied by 100.
Task 3. Find the percentage expression of one number from another.
The first number is divided by the second and the result is multiplied by 100.
3. Application of percentage calculations in various types of human life
Faced with percentages for the first time, we suddenly notice that they accompany us everywhere - not only at school (at the lessons of mathematics, physics, chemistry, biology, geography, etc.), but also in everyday life: in the store (especially in pre-holiday discounts), at work (raising and lowering salaries), at the bank, in the media, on the Internet, and much more. Navigate the world of interest on good level not so easy! I bring to your attention a selection of tasks for percentages.
4. Examples of Modern Interest Problems
Task
At the seasonal sale, the store reduced the prices of shoes by 24%. How many rubles can you save when buying sneakers if they cost 593 rubles before the price cut?
Insurance problem.
Our car dealership offers you to immediately conclude an agreement on car theft insurance for 100,000 rubles. Determine what percentage of the value of your car will be paid to you in the event of theft.
Conclusion
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.
In my work, I showed the use of the concept of percentage in solving real problems only from some areas of human life. In the course of our research, we came to the conclusion that percentages help us:
Competently understand a large flow of information
Invest correctly
Properly take loans, choosing a more profitable option.
Make great purchases and save on discounts
Solve math problems.
It is difficult to name an area where interest would not be applied.
As you know, conclusions are based on analysis. People do not know a more convenient way to analyze than percentage. It is the most accurate and easy to use. Its essence is clear even to a child.
It is very difficult to fully consider the use of interest calculations in life, since interest is used in all spheres of human life.
Literature.
Vilenkin, N. L. Behind the pages of a mathematics textbook. - M.: Education, 1989. - S. 73. Vilenknn, N. L., Zhokhov, V. I., Chesnokov, A. S., Schwarzburd, S. I. Mathematics 6. - M .: Bustard, 2000 .
Project on:
Supervisor: teacher of mathematics Doronkina N.N.
Problem.
In the lesson of mathematics, we studied the topic "Percentage". We are interested in this topic. We wanted to know where interest occurs in our lives. We decided to study the necessary literature, communicate with parents and acquaintances.
Target:
Find out where and how interest is applied in our lives.
Project objectives.
Study the history of the origin of interest.
Consider tasks for interest from life.
Determine the scope of practical application of interest.
Our action plan.
Find out what adults know about percentages and how they apply them in their profession.
Make up your goals with percentages.
Collect all the material and arrange it in the form of a brochure.
1. From the history of interest.
The word percent is from the Latin word pro centum, which literally means "per hundred" or "one hundred". 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. Interest was especially common in ancient Rome. The Romans called interest the money that the debtor paid to the lender for every hundred. From the Romans, interest passed to other peoples of Europe.
The % sign is believed to come from the Italian word cento (one hundred), which is often abbreviated cto in percentage calculations. From here, by further simplification in cursive, the letter t turned into a slash (/), the modern symbol for percent arose.
“The Romans took interest from the debtor (that is, money in excess of what they lent). At the same time, they said: "For every 100 sesterces of debt, pay 16 sesterces of interest."
Examples of two tasks of historical content, on the topic "Interest":
Problem 1. One poor Roman borrowed 50 sesterces from a lender. The lender made a condition: "You will return to me within the prescribed period of 50 sesterces and another 20% of this amount." How many sesterces must a poor Roman give to a lender to repay a debt?
Answer: 60 sesterces.
Task 2. A certain person borrowed 100 rubles from a moneylender. An agreement was concluded between them that the debtor is obliged to return the money exactly in a year, paying another 80% of the debt amount. But after 6 months, the debtor decided to return his debt. How many rubles will he return to the usurer?
Answer: 140 rubles.
The use of the term "percentage" in Russia begins 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 applied 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 a percentage is a special kind of decimal fractions, a hundredth of a whole (taken as a unit).
2. Interest in our life.
Percentages are one of the mathematical concepts that are often encountered in everyday life. You can read or hear, for example, that
57% of voters took part in the elections,
class performance 93%,
the bank charges 17% per annum,
milk contains 1.5% fat,
the material contains 100% cotton, etc.
3. Tasks for interest.
The main tasks can be divided into percentages into three groups:
1. Finding percentages of a number:
To find a percentage of a number, you need to turn the percentage into a decimal fraction and multiply by that number.
2. Finding a number by its percentage:
To find a number by its percentage, you need to turn the percentage into a decimal fraction and divide the number by this fraction.
3. Finding the percentage of numbers:
To find the percentage of numbers, you need to multiply the ratio of these numbers by 100.
Here are the tasks we did:
1. The client took a bank loan of 12,000 rubles for a year at 16%. He must repay the loan by depositing the same amount of money into the bank every month, so that in a year he will pay back the entire amount taken on credit, together with interest. How much should he pay to the bank every month?
2. On a wholesale basis, the price of 1 kg of watermelon is 8 rubles. The store makes a markup of 3%. At what price per kilogram will we buy a watermelon in the store?
3. My aunt works at the club as a usher. A ticket to the disco costs 40 rubles. But the director said that from January 1, the ticket price will rise by 5%. How much will a disco ticket cost from January 1st?
4. I study at Tumskaya school No. 46. There are only 356 students and 83 children from large families in the school. I was wondering, what is the percentage? (social passport of the school)
5. I read in the newspaper that the Eleks store is holding a sale of computer equipment with a 12% discount. I ask my parents to buy me a laptop that costs 20,900 rubles. How much will I have to pay for this laptop, taking into account the discount?
6. During the renovation of the school, out of 28 windows on the main facade, only 10 were replaced with plastic ones. What is the percentage of plastic windows from the windows on the facade? (USE in mathematics)
8. Income tax is 13% of wages. Wage Nadezhda Nikolaevna is equal to 16,400 rubles. How much will she receive after deducting income tax? Give your answer in rubles. (from real life)
9. The notebook costs 40 rubles. What is the largest number of such notebooks that can be bought for 650 rubles after a price reduction of 15%? (USE in mathematics)
10. A person who smokes shortens his life by 15%, which is 10.2 years. What is the average life expectancy in Russia? (from statistics)
4. Conclusion.
The topic "Percentage" that we studied in class is very important. Interest is all around us. People in many professions work with percentages. For example, economists, accountants, bankers, sellers. The ability to perform percentage calculations and calculations is necessary for every person, since we encounter percentages in everyday life.
Percentages make it easy to compare parts of a whole, simplify calculations and are therefore very common.
In the process of doing the work, we learned a lot of new things, did very useful work for ourselves, and this will be useful to us in our studies and in life.
