Задачи на проценты

 

Kirov region administration

“Saratov town”

 

Saratov school № 24

 

 

Regional scientific conference

“Discovery”

 

 

 

 

Percent

 

 

 

Made: studentof 6^thform

Polyakova Elizaveta Dmitrievna

Teacher:

Nakorenok Dina Alexandrovna

Naryvskaya Ekaterina Igorevna

 

 

 

 

 

 

 

 

 

Saratov, 2019

Content

Introduction…………………………………………………………………..….....31.The main kinds of percent Math problems…..….……………..………...............4

2. Modern percent Math problems’ examples/ …………………………................5

3.My searches……………………............................................................................9

Conclusion..…………………………………………………………………….....10References…………………………..………………..…………….......................11

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Introduction

 

Percent (lat. Percent «one hundredth») —one hundredth; is denoted with the sign «%»; is used for meaning of part at the ratio to the whole, integral. At first I looked through the History, Geography and Biology students’ books. The searching shows the information in percent can be seen in every school stundent’s book. Then I asked 38 students two questions:

1. Is it important to study “Percent”?

2. Where can “Percent” knowledge be used?

My survey results are next: 1. Important - 34 students (89 %). Unimportant -3 students (8 %). I don’t know - 1 student (3 %).

I decided to prove the importance of “Percent” in my work and show a wide variety of using percent in a daily life.

My search goal is to study the application area of percent. More than that I would like to prove, that we can not avoid percent Math problems in our life.

My search scopes are:

-to study the main kinds of percent Math problems;

-to show the way of using “percent” by solving real Math problems from different human life fields;

-to pursue rsearch in statistics;

-to make a conclusion.

My search object are percent Math problems from our daily life.

My search subject is the way of solvingreal percent problems and using percent calculation in different fields of human being.  

Methods: searching method by using study materials and necessary information through the Internet; practical technique by percent calculating from daily life; analysis of results.

 

 

 

1.The main kinds of percent Math problems

 

There are three main kinds of percent Math problems:

 

Problem1. Find the specified percent by a given number. The given number can be multiplied of the specified percent, and then the intersection is divided by one hundred.

500 pumps were produced by a factory in a quarter. 60 % from these pumps were of the highest quality. How many pumps of the highest quality were produced by the factory?

Solving:

Find 60 % of 500 (the whole pumps’ quantity). 60 % = 0,6500 • 0,6 = 300 pumps of the highest quality.

Answer: 300 pumps of the highest quality.

 

 Problem 2. Find the specified percent by a given number and its coefficient in percent of an unknown number. The given number is divided in its percent and multiplied of 100. 

A student read 138 pages, what makes 23% of the whole number of pages in a book. How many pages are there in the book?

Solving:

So, we don’t know how many pages are there in the book. But we know that the part, what was read by the student is 23% of the whole quantity of pages in the book. As138 pages are only a part of the whole, the number of pages in the whole book is higher than 138.

 

 

Problem 3. Find percent of one number at the other. To find out percent of one number at another, they must the part, which is asked divide into the total number and multiply of 100 %.

16 watermelons from 200 ones turned out to be unripe. What percent of all watermelons make unripe ones?

Solving:

What is asked about? It is asked about unripe watermelons. We divide 16 into the whole quantity of watermelons and multiply of 100 %.

Answer: 8 % - make unripe watermelons of all ones.

 

 

 

 

2. Modern percent Math problems’ examples

 

1.«Season sale»

Problem №1. The shop “September” reduced prices for rubber shoes by 15% during the season sale. How many rubles can be saved by buying rubber shoes, if we know that they cost 1100 rubles before price reducing? 

Solving:

1.     1100:100 * 15 =165 (rubles) - sale

2.     1100-165=935 (rubles) – the shoes price during the season sale.

Answer: 935 rubles.

 

Problem №2. A customer can get a present, which costs 20 % of spent money during the New Year sale action in the shop. Can the customer hope to get a picture, which costs 365 rubles, if he or she has already spent 1850 rubles? Solving:

1.     1850 :100 *20=370 (rubles)

Answer: The customer can hope to get a present as 20 % of spent sum is more than the picture price.

 

2. «Credit»

Problem №1. A mother took out a loan 30 000 rubles for one year at interest 12% for buying a computer. She has to pay back a loan monthly with equal sum of money to return the whole sum with percent in a year. How much money has she to pay back every month?

Solving:

Let’s find how much money has the mother to pay back – to sum 30 000 we add 12% of  30000 rubles: 30000+(30000:100*12) = 33600 (rubles) – the whole debt.

33600 : 12 =2800 (rubles) – monthly debt sum.

Answer: 2800 rubles.

 

3. «Bank deposit»

A bank assess 13% interest of damages and the sum, which is payed in comes to 100 000 rubles. What sum will be assessed depositor’s bill in three years? Solving:

 1)100000+100000*0,12=112000 (rubles) – in one year. 

1.     112000+112000*0,12=125440 (rubles) – in two years.

2.     125440+125440*0,12=140492,8 (rubles) – in three years.

Answer: 140492, 8 rubles.

 

4. “Social payments”

The pension of my grandmother payment was 14 440 rubles in March. In April she got 15 760 rubles. How many percent did my grandmother's pension payment become higher?

We can solve this problem through the ratio:

14 440 rubles – 100 %

15 760 rubles  - х %

Solving:

Х=15 760 *100 : 14440 =109 (%) – became the pension payment.

109 – 100 = 9 %

Answer: the pension payment became higher 9 %.

 

5. “Using of household appliances”

Allowable voltage for washing-machine (according to the pass)  is 220 V ± 5 %. What range of electrical voltage can the machine can be used in?

Solving:

220:100 *5= 11 (V).

220-11=209(V) 220+11=231 (V)

Answer: the range of electrical voltage can vary from 209 till 231 V.

 

 

6. “Salary”

A father got 36 700 rubles including award. In work contract it is denoted that accident free work is payed 15 % of base pay. What is the father’s salary without award?

Soving: 36 700 rubles – 115 %

Хrubles - 100 %

Х =36 700 *100: 115 =31 913 (rubles).

Answer: 31 913 (rubles) is the father’s salary without award.

 

7. “Travelling”

A railway adult’s ticket costs 820 rubles, student’s one costs  40% of adult’s ticket price. A family consists from two school-aged children and two adults. How much money does the family spend on tickets?

Solving:

1) 820 :100*40=328 (rubles).

2) 820 *2+328*2=2296 (rubles).

Answer: 2296 (rubles).

 

8. “Cooking”

Problem № 11. A refectory bought 50 kg of fish for cooking fried fish. Find out how many kg of scaled fish is appropriate for the dish, if the by-product norm makes 27 %?

Solving:

50 : 100 *27=13,5 (kg) –by-products

50-13,5=36,5 (kg) fish.

After talking to senior high school students I have found that it is necessary to be able to solve percent problems to passthestate exams in Math. I was glad to note that some of them we can already solve.

For example:

 

1.The price of electric kettle was made 21% higher and made 3025 rubles. How much does the kettle cost before the price was made higher?

Pay attention that 3025 rubles is the price after making it 21% higher. Let’s make a proportion: 3025 is 121%, 100% - the price before rising.

3025 rubles - 121%

х rubles     -  100%

Answer: 2500

 

2. A T-shirt cost 1200 rubles. After the price reducing it cost 972 rubles. How many percent was the T-shirt cheaper after that?

We find out what percent from 1200 makes the reduced price.

1200 rubles - 100%,

972 rubles - х %.

Make a proportion:

1200 rubles   -  100%

972 rubles      -   х %

It means that 972 is 81% from 1200 rubles.

The price was 100-81=19% cheaper.

Answer: 19

 

3. In a N town live 250000 citizens. 15 % of children and teenagers live with. 35% of citizens do not work (pensioners, students, housewives). How many citizens work?

Why do students seldom solve this kind of problems correctly? The fact is that “15 percent” or “35 percent” are relative numbers. Every time different numbers can be considered as 100%. As in the rule: in different occasions we take up everything we are comparing for 100%. So, children and teenagers make15% of 250000 of all citizens. It means that their number is 15% from 250000,

 

Answer: There are 37500 of children and teenagers in the town.

Consequently there are 250000-37500=212500 adults in the town. 35% adults do not work. Now we take up number of adults for 100%. It turns that the number of citizens who do not work is35% from  212500.

Make a proportion:

212500      -  100%

 х              -   35%

So, the number of working adults is 212500-74375=138125 men.

Be attentive  by solving such problems. Read statement of problems attentively, do not forget what you have to find out.

Answer: 138125

 

4. Railway adult’s ticket costs 720 rubles. Railway children’s ticket costs 50% from the adult’s ticket price. A group consists of 15 students and 2 adults. How much do the tickets for the whole group cost?

1) 720 :100*50=360 (rubles).

2) 720 *2+360*15=6840 (rubles).

Answer: 6840

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.     My searches

 

Girls and boys percentage in the 6 form

	Quantity of students	%
Quantity of students	20	100 %
Boys	7	35 %
Girls	13	65 %

Conclusion: The girls’ number are 30 % more in our class then boys.

 

Quality and progress in the second term

	Quantity of students	%
Quantity of students	20	100 %
Quality	12	60 %
Progress	20	100 %

 

Conclusion: The progress in our form is 40 % higher than knowledge quality.

 

 

 

 

 

 

 

 

 

 

 

 

Conclusion

 

The work is finished. It was interesting for me. I have learnt the history of percent better and found out that percents are very important in our everyday life.  To sum up everything I have searched I make a conclusion that the theme is actual.

Many life branches require knowledge of percent counting: taking on a loan, deposits, buying goods on credit, tax counting, advertisements actions: rebate counting in percentage and so on.

Nowadays everybody have to understand and to use percent.

I would like to conclude that percent knowledge and their counting are important for every modern person not only in one’s occupation but in everyday life.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

References

 

1. Виленкин, Н. Л., Жохов, В. И., Чесноков, А. С., Шварцбурд, С. И. Математика 6. – М.: Дрофа, 2006. – 288с.

2. Виленкин, Н. Л. За страницами учебника математики. – М.: Просвещение, 1989. –73с.

3. Захарова А.Е. Несколько задач «про цены».// Журнал «Математика в школе». – 2002– №8

4. Зубарева И. И. Еще раз о процентах.// Журнал «Математика в школе». – 2006– №10

5. http://mathist.narod.ru/razmerz.htm математический кружок в 5-6

 

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