Project objectives:
Learn history
origin
percent;
Consider tasks
on interest from
practical life and
environment
contemporary
person.
Spend
research and
help
interest
computing
introduce
data in the form
tasks and diagrams

The relevance of our project

Interest is one of the most difficult topics
mathematicians, and many students
find it difficult or not able to solve at all
percentage tasks. And the understanding of percentages and
ability to calculate percentages
necessary for every person. Applied
the importance of this topic is very great and affects
financial, economic, demographic and
other areas of our life. Interest study
dictated by life itself. Ability to perform
percentage calculations and calculations are necessary
to each person, since with interest we
face in Everyday life.

Our Action Plan

We have studied in addition the topic of interest
their history
Find out what parents know
relatives
Made up your tasks for percentages
Solved some problems from the exam
Prepared a presentation

A bit of history
The word "percentage" is
latin origin:
"pro centum" - "from a hundred".
Often instead of a word
"percentage" is used
phrase "hundredth
part of the number. "Percentage
called a hundredth
numbers. 1/100=1%Percentage
were especially
common in ancient
Rome. The Romans called
interest money,
paid by the debtor
(lender) for each
a hundred.
Since the words "a hundred"
sounded like "percent", then
hundredth part was called
percent

From the Romans interest
passed on to other peoples
Europe. In Russia
the concept of percentage introduced
Peter I.
The symbol did not appear immediately.
First they wrote the word "hundred"
So:
In 1685 was in Paris
printed
book
"Management
on
commercial arithmetic,
where by mistake instead of
was typed.

2. Interest in our
life.
interest is one of
mathematical concepts
which is often found in
Everyday life. We
heard for example that
In store 20% discount
57% took part in the elections
voters
100% class progress,
the bank charges 16% per annum,
Acetic acid 70%
material contains 100% cotton
etc
Boy 100% - In conversation
means the best in everything!

Three main actions related to interest

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=v:0.01.
3. Finding a percentage
numbers.
To find the percentage
numbers, you need the ratio of these numbers
multiply by 100%.

10.

Interest
apply
1. in medicine
2. in programming
3. in stores
4. in the elections
5. in cooking
6. in statistics
7. in fabric formulations
8. in taxes
9. in solutions
10. in savings banks
11. in analysis
activities
Interest use
people of different professions

11. After conducting research in our class, we collected some data and processed them, we got the following results

Progress. In our class
2 excellent students -8% and 9
good students -36% total
44% without "3"
There are only 25 in our class
one out of 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 quarter
Row 1
3 quarter
Row 2
Row 3
4 quarter

12. Birthdays in class by season

summer
autumn
winter
Spring

13. We learned from the school accountant that

Monthly from salary
employees, employer
deducted:
- to the Pension Fund - 22%;
- social fund
insurance - 2.9%;
- social fund insurance against
accidents - 0.2%
- regional fund
medical insurance -
5.9%. Total 30.2%
tax deducted from
personal income tax salary
=13%
For example, the salary is
14500 rubles -13% personal income tax
=14500-1885=12615rub
the employee will receive

14. These are the tasks we compiled based on the information received

forest land
Severobaikalsk
occupy an area
1651527 km2. Our summer
the city has been for a long time
all in smoke, the forest burned.
What percentage of the forest
burned down during
Fire if area
fire
25234 sq. km (1.5%)

15. History of our city

We conducted a survey among
residents of the city
Severobaikalsk
Do you know the coat of arms
of our city" out of 123
65% of people surveyed
know the coat of arms, the rest
no. How many people from
does not know the interviewees
coat of arms of our
cities? (79 people
know, 44 do not know)

16.

Interest in trading:
Mom wanted
buy a down jacket
for 2700 rub. in
Economy store.
November 4th was
sale. Discount
for all goods 20%.
How many rubles
mom will buy
down jacket on
t
sale?
(2160 rub)
Discount
20%

17.

When mixing a 5% solution
acid with 40%
solution
acids received
140g 30%
solution. How
grams of each
solution was for
this taken?

18.

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
turn out
after mixing. Connecting the written numbers with dashes, we get the following
diagram:
5
30
40
Consider pairs 30 and 5, 30 and 40. In each pair of
subtract the smaller number and write the result
at the end of the corresponding line. It will turn out like this
scheme:
5
10
30
40
25
It concludes that a 5% solution should be taken in 10 parts,
and 40% 25 parts, .(10+25=35 parts in total, 140:35=4g-weight of one
parts, 4×10=40g, 4×25=100g.)
those. to get 140g. 30% solution must be taken
5% solution 40g, and 40% - 100g

19.

On TV I
heard that
smoking man
reduces its
life at 15% that
is 8.4 years.
What is the average
duration
life in Russia? (56)

20.

One more challenge
Vasya used to decide
right two things
on interest from
twenty. After
study of the topic on
one useful
website, Vasya became
decide correctly 16
tasks out of 20. How many
percent wiser
Vasya? Per
one hundred percent mind
counting 20 solved
tasks(70%)

21.

Here's what we learned from
our parents:

22. 1. Family budget (per month):

Name
rub
Mother
15 000
Grandmother
13 000
Total
28 000
Expenses
Remainder
21770
6230
%
100

23.

2. Distribution of family
November budget:
Utilities
2000 rub
9%
Mobile phones (all)
600 rub
2,8%
Food
6600 rub
30,3%
Clothes, shoes
4000 rub
18,4%
Credit
5000 rub
23%
Fare
520 rub
2,4%
Medications
1000 rub
4,6%
Entertainment (concert)
300 rub
1,4
Sweets
1500 rub
6,9%
Other (haircut)
250 rub
1,2%
21770
100%
Total

24.

We chose this theme because we like
mathematics and we believe that mathematics is necessary
know well.
We wanted to get a complete picture of
percent, 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.

Kramor V.S. "We repeat and
systematize the school course of algebra
and start the analysis. M., "Enlightenment"
1990
Journal "Mathematics at School."
1998 No. 5.
F.F. Nagibin "Mathematical
casket "M." Enlightenment "1988.
https://yandex.ru/images/
http://infourok.ru/
https://en.wikipedia.

Project "Interest in our life". Objectives: To summarize knowledge on the topic "Interest" and highlight the practical significance of this concept in various fields of human activity. 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 either in accounting, or in financial analysis, or 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, in the middle of the century, trade expanded and, consequently, special attention was paid to the ability to calculate interest. 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 work: “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." The task in general form: 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% - 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 the practical life and environment of 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, subtract the smaller number from the larger number and write the result at the end of the corresponding dash. 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)

“Interest in our life” was prepared by: students of grade 6 “secondary school No. 3” Klepov A, Sukmanov A. supervisor: Dremukhina T.A

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.

• Conduct research and use percentage calculations to present data in the form of problems and charts

Project objectives:

• To study the history of the origin of interest;
• Consider tasks for interest from the practical life and environment of modern man.

The relevance of our project Percentages are one of the most difficult topics in mathematics, and many students find it difficult or not able to solve percentage problems 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. Our Action Plan

• We have additionally studied the topic of interest and their history.
• Find out what parents and relatives know
• Made up your tasks for percentages
• Solved some problems from the exam
• Prepared a presentation

A bit of history

The word "percent" is of Latin origin: "pro centum" - "from a hundred". Often, instead of the word "percentage", the phrase "hundredth of a number" is used. Percentage called hundredth of a number. 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.

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.

2. Interest in our lives.

Percentages are one of the mathematical concepts that are often encountered in everyday life. We have heard, for example, that

In store 20% discount

57% of voters took part in the elections,

100% class progress,

the bank charges 16% per annum,

Acetic acid 70%

material contains 100% cotton etc

Boy 100% - In conversation means the best in everything!

Three main actions related to interest

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%.

Interest applied 1. in medicine 2. in programming 3. in stores 4. in elections 5. in cooking 6. in statistics 7. in fabric formulations 8. in taxes 9. in solutions 10. in savings banks 11. in the analysis of activities Percentages are used by people of different professions After conducting research in our class, we collected some data and processed it, we got the following results Birthdays in class by season We learned from the school accountant that

• On a monthly basis, 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 \u003d 14500-1885 \u003d 12615 rubles will be received by the employee

Here are the tasks we have compiled based on the information received 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%) History of our city

• We conducted a survey among residents of the city 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)

Interest in trading:

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)

20% discount

We learned from our chef that

% is also in canteens

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?

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:

Consider the pairs 30 and 5, 30 and 40. In each pair, subtract the smaller number from the larger number and write the result at the end of the corresponding line. You get the following scheme:

It concludes that a 5% solution should be taken in 10 parts,

and 40% 25 parts, .(10+25=35 parts in total, 140:35=4g-weight of one

parts, 4×10=40g, 4×25=100g.)

those. to get 140g. 30% solution must be taken

5% solution 40g, and 40% - 100g

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)

One more challenge

Vasya used to solve two problems correctly with percentages out of twenty. After studying the topic on one useful site, Vasya began to solve 16 problems out of 20 correctly. By what percentage did Vasya become smarter? For one hundred percent mind we consider 20 solved problems (70%)

Task from the exam

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%? (19)

Here is what we learned from our parents:

1. Family budget (per month):

Name
Mother
Grandmother
Total
Expenses Remainder

2. Distribution family budget on November:

Utilities	2000 rub
Mobile phones (all)	600 rub
Food	6600 rub
Clothes, shoes	4000 rub
Credit	5000 rub
Fare	520 rub
Medications	1000 rub
Entertainment (concert)	300 rub
Sweets	1500 rub
Other (haircut)	250 rub
Total

Drawing conclusions

• We chose this topic because we like mathematics and we believe that mathematics should be good.
• We wanted to get a complete understanding of percentages, their role in everyday life.
• We thought about how important it is to understand and know the percentages and decided: in order to be good specialists and be 100% successful, you need to study well.

• Kramor V.S. "We repeat and systematize the school course of algebra and the beginning of analysis." M., "Enlightenment" 1990.
• Journal "Mathematics at School." 1998 No. 5.
• F.F. Nagibin "Mathematical Box" M. "Enlightenment" 1988.
• https://yandex.ru/images/
• http://infourok.ru/
• https://en.wikipedia.

Rootless Dina, Gudkova Anna

Project Manager:

Pavlova Olga Viktorovna

Institution:

MBOU secondary school in the village of De-Kastri, Ulchsky district, Khabarovsk Territory

In this research project in mathematics on the topic "Interests around us" students study the history of the origin of interest, consider the tasks of practical application, and also explore the possibilities of using interest in everyday life, everyday life.

In the proposed research project in mathematics on the topic "Percentages around us", the authors define the percentage as a unit for comparing data with different parameters, and also prove the need to use percentages.

In the presented research work in mathematics on the topic "Interests around us", students search for information on the Internet, analyze the material found on the history of interest, as well as on the use of interest in a person's daily life.

In the process of project work in mathematics "Percentages around us", students consider and solve problems for finding a percentage of a number, finding a number by its percentage, and also for finding the percentage of two numbers.

Introduction
Methodological characteristics of the study.
1. Interest is around us.
1.1. History of interest.
1.2. Problem solving.

• Task 1. Finding a percentage of a number.
• Task 2. Finding a number by its percentage.
• Task 3. Finding the percentage of two numbers.

1.3. interest in life.
Conclusion
Bibliography
Applications.

Introduction

Relevance. At school, we met in mathematics lessons with percentages. - one of the mathematical concepts that are often encountered in everyday life. We became interested when humanity first learned about percentages, how they were used in solving practical problems. We were also interested in the question of whether we can often meet with interest in everyday life. Based on the above, we have identified the following goals and objectives for the work.

Problem: People often come across percentages in their lives, but cannot solve them correctly.

Object of study: percentage as a universal unit of comparison of various data.

Subject of study: practical problems with percentages.

Hypothesis: If there are data with different parameters, it is more convenient to compare them using percentages.

Goals of the work:

• Define percentage as a unit for comparing data with different parameters;
• Prove the need to use percentages.

Tasks:

1. To study the history of the origin of interest;
2. Consider the tasks of practical application;
3. Explore the possibilities of using percent».

Research methods: collection and study of information, identification of problems in solving problems by means of a survey.

Research novelty: work in this direction in the conditions of MBOU secondary school in the village of De-Kastri has not been previously carried out.