Direct and inverse proportionality. Direct proportional dependence direct and inverse proportional dependencies 6

Mathematics - the basis and queen of all sciences, and I advise you to make friends with her, my friend. Her wise laws if you come, you will bring your knowledge, you will apply them. You can swim by the sea you can fly in space. Build people to build people: it will stand a hundred years. Do not be lazy, worry, try, knowing the salt of sciences. It's trying to prove everything, but not to twist.

3 Choosing an answer with the appropriate letter of the word of the word: 17-in; 7-l; 0.1-and; 14-C; 0,2-A; 25-k Find the missed numbers and find out the word: 3 + 37: 5 3. 0.3 +41: 45:, 7 5,6: 0.7: 2 0 +4.8: 26 Word, 9 50,050,1 0,050,337 80.45,20.2 s and l and this is a word-force. The motto of the lesson: Power-in knowledge! I'm looking for, it means I'm learning!

A straight proportional dependence is the same dependence of the quantities in which ... inverse proportional dependence is the same dependence of the values \u200b\u200bin which ... to find an unknown extreme member of the proportion ... Average member of the proportion is ... The proportion is true if ...

C) ... with an increase in one value several times, the other decreases at the same time. X) ... the work of extreme members is equal to the product of the average members of the proportion. A) ... with an increase in one value several times, the other increases with the same. P) ... We need a product of medium members of the proportion to divide into a known extreme dick. Y) ... with an increase in one value several times, the other increases at the same time. E) ... the attitude of the work of extreme members to the well-known average

4. The speed of the car and the time of its movement is inversely proportional. 5. The speed of the car and its traveled path is inversely proportional. 6. Two values \u200b\u200bare called inversely proportional if, with an increase in one of them, twice is twice as two times.

Check the answers:

Decision. K-in bulldozers time. (Min) x We define the dependence and make up the proportion: 7: 5 \u003d 210: x x \u003d 210 * 5: 7 x \u003d 150 (min). 150 min. \u003d 2.5 hours Answer: 2.5 hours
Algorithm for solving problems for direct and inverse proportional dependencies: an unknown number is indicated by the letter x. The condition is recorded in the form of a table. This establishes the type of dependence between values. A direct proportional dependence is indicated by the same directional arrows, and inversely proportional dependence - oppositely directional arrows. The proportion is recorded. Her unknown member is.

Check yourself: What values \u200b\u200bare called directly proportional? Give examples of directly proportional values. What values \u200b\u200bare called inversely proportional? Give examples of inverse proportional values. Give examples of values \u200b\u200bin which the dependence is neither directly or inversely proportional.

Homework. P; 811; 812.

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Signatures for slides:

"Direct and reverse proportional dependencies" Grade 6 Mathematics teacher MOU "Kurovskaya School No. 6" Chugreyev T. D.

Mathematics - the basis and queen of all sciences, and I advise you to make friends with her, my friend. Her wise laws if you come, you will bring your knowledge, you will apply them. You can swim by the sea you can fly in space. Build people to build people: it will stand a hundred years. Do not be lazy, work, try, knowing the salt of sciences to prove everything, but not to give up hands.

Finished the phrase: 1. A straight proportional dependence is the same dependence of the values \u200b\u200bin which ... 2. Inverse proportional dependence is the same dependence of the values \u200b\u200bat which ... 3. To find an unknown extreme member of the proportion ... 4. The average member of the proportion is equal to ... 5. The proportion is true, If ... c) ... with an increase in one value several times, the other decreases at the same time. X) ... the work of extreme members is equal to the product of the average members of the proportion. A) ... with an increase in one value several times, the other increases with the same. P) ... We need a product of medium members of the proportion to divide into a known extreme dick. Y) ... with an increase in one value several times, the other increases at the same time. E) ... the attitude of the work of extreme members to the well-known average.

The growth of the child and its age is directly proportional. 2. With the constant width of its rectangle, its length and the area are directly proportional. 3. If the rectangle area is constant value, then its length and width - inversely proportional values. 4. The speed of the car and the time of its movement is inversely proportional.

5. The speed of the car and its traveled path is inversely proportional. 6. The revenue of the cinema cash register is directly proportional to the number of tickets sold at the same price. 7. Machine capacity and their number are inversely proportional. 8. The perimeter of the square and the length of it is directly proportional. 9. With a permanent price, the cost of the goods and its mass is back proportional to the values.

Well, in the direction of pencils! Neither paper, no pens, no chalk! Verbal counting! We will create this thing only by the strength of mind and soul! VERBAL COUNTING

Find an unknown member of the proportion? ? ? ? ? ? ?

"Direct proportional dependency" Theme of the lesson and reverse

a) Cyclist for 3h drives 75 km. How long does the cyclist drive 125km at the same speed? b) 8 identical pipes fill the pool in 25 minutes. How many minutes will the pool of 10 such pipes fill? c) Brigade of 8 workers performs a task for 15 days. How many workers will be able to fulfill this task for 10 days, working with the same productivity? d) from 5.6 kg of tomatoes receive 2 liters of tomato sauce. How many liters of sauce can be obtained from 54 kg of tomatoes? Create proportions to solve problems:

Answers: a) 3: x \u003d 75: 125 b) 8: 10 \u003d x: 2 5 V) 8: x \u003d 10: 15 g) 5,6: 54 \u003d 2: x

For the heating of the school building, coal was harvested 180 days at the rate of consumption 0.6t of coal per day. How many days will this stock, if it is spent daily by 0.5t? Decide the task

Summary: Mass (T) For 1 day Number of days by norm 0.6 180 0.5 x amounted to the proportion :; ; Answer: 216 days. Decision.

In the iron ore, 7 parts of the iron account for 3 parts of impurities. How many tons of impurities in ore, which contains 73.5 tons of iron? №793 Decide the task

The number of parts of the mass of iron 7,73.5 impurities 3 x; Answer: 31.5 kg of impurities. Decision. ; №793.

An unknown number is indicated by the letter x. The condition is recorded in the form of a table. This establishes the type of dependence between values. A direct proportional dependence is indicated by the same directional arrows, and inversely proportional dependence - oppositely directional arrows. The proportion is recorded. Her unknown member is. Algorithm for solving problems for direct and inverse proportional dependencies:

Solve the equation:

№1. On the path from one village to another at a speed of 12.5 km / h cyclist spent 0.7 hours. At what speed did he have to go to overcome this path for 0.5 h? №2. Of 5 kg of fresh plux, 1.5 kg of prunes are obtained. How many prunes will turn out to be 17.5 kg of fresh plums? Number 3. The car drove 500 km, Istiving 35l gasoline. How many liters of gasoline will need to drive 420 km? №4. For 2 hours caught 12 caras. How many karas will be caught for 3 hours? №5 Six rairs can perform some work in 18 days. How many more paintings need to be invited to work for 12 days? Independent work Decide the task, constittrating the proportion.

Solutions to tasks from independent work Solution: №1 Summary: Speed \u200b\u200b(km / h) Time (H) 12.5 0.7 x 0.5 Reply: 17.5 km / h Solution: №2 Summary: Plums (kg ) Prunes (kg) 5 1.5 17.5 x; ; kg Answer: 5.25 kg; ; ;

Solving problems from independent work Solution: №3 Solution: №5 Summary: Short Recording: Distance (km) Gasoline (L) 500 35 420 x; Answer: 29.4 liters. The number of Mals time (days) 6 18 x 12; ; Malyarov will fulfill work for 12 days. 1) 9 -6 \u003d 3 malaria needs to be invited. Answer: 3 malaria.

Additional task: №6. The mining enterprise is required to purchase 5 new cars for a certain amount of money at a price of 12 thousand rubles. for one. How many such cars will be able to buy an enterprise if the price for one car becomes15 thousand rubles? Solution: №1 Short record: Number of machines (pcs) Price (thousand rubles) 5 12 x 15; cars. ; Answer: 4 cars.

Homemade Test No. 812 № 816 № 818

Thank you for the lesson!

Preview:

Chugreyev Tatyana Dmitrievna 206818644

Mathematics lesson in the 6th grade

on the topic "Direct and inverse proportional dependencies"

Developed
mathematic teacher
Maou "Kurovskaya School No. 6"
Chugreyev Tatyana Dmitrievna

Objectives lesson:

educational - to actualize the concept of "dependence" between the values;

Developing - through the solution of tasks, formulation of additional issues and tasks to develop creative and mental activity of students;

Independence;

Self-esteem skills;

Educational- to educate interest in mathematics as part of universal culture.

Equipment: TSO necessary for the presentation: computer and projector, leaves for recording answers, cards for the stage of reflection (three each), pointer.

Type of lesson: lesson applying knowledge.

Forms of organization of the lesson: Frontal, collective, individual work.

During the classes

1. Organizing time.
   

The teacher reads: (Slide number 2)

Mathematics - the basis and queen of all sciences,
And I advise you to make friends with her, my friend.
Her wise laws if you do,
His kidnight will bring
You will apply them.
You can swim by the sea you swim,
You can fly in space.
Home Build People You can:
It will stand for a hundred years.
Do not be lazy, work, try,
Knowing salt sciences.
To prove everything try
But not downtrend.

2. Check the studied material.

1. Finish the phrase:(Slide 3). (Children first perform the task on their own, writing on the leaves only letters corresponding to the correct answer. Then you raise your hand. After that, the teacher reads the question aloud, and I am responsible).

1. Direct proportional dependence is such a dependence of the values \u200b\u200bat which ...
2. Inverse proportional dependence is such a dependence of the values \u200b\u200bat which ...
3. To find an unknown extreme member of the proportion ...
4. The average member of the proportion is ...
5. The proportion is true if ...

C) ... with an increase in one value several times, the other decreases at the same time.

X) ... the work of extreme members is equal to the product of the average members of the proportion.

A) ... with an increase in one value several times, the other increases with the same.

P) ... We need a product of medium members of the proportion to divide into a known extreme dick.

Y) ... with an increase in one value several times, the other increases at the same time.

E) ... the attitude of the work of extreme members to the well-known average.

Answer: Success. (slide 6)

1. Oral account: (slides 6-7)

Well, in the direction of pencils!

Neither paper, no pens, no chalk!

Verbal counting! We will create this business

Only the strength of mind and soul!

The task: Find an unknown member of the proportion:

Answers: 1) 39; 24; 3; 24; 21.

2)10; 3; 13.

1. Message Topics lesson.slide number 8. (Ensures the motivation of schoolchildren's teachings.)

• The topic of our lesson "Direct and inverse proportional dependencies".
• In previous lessons, we considered a direct and inverse proportional dependence of quantities. Today, at the lesson, we will solve different tasks using the proportion by setting the type of communication between the data. Repeat the basic property of proportions. And the next lesson ending on this topic, i.e. Lesson - test work.

1. Stage of generalization and systematization of knowledge.

1) Task1.

Create proportions to solve problems:(work in notebooks)

a) Cyclist for 3h drives 75 km. How long does the cyclist drive 125km at the same speed?

b) 8 identical pipes fill the pool in 25 minutes. How many minutes will the pool of 10 such pipes fill?

c) Brigade of 8 workers performs a task for 15 days. How many workers will be able to fulfill this task for 10 days, working with the same productivity?

d) from 5.6 kg of tomatoes receive 2 liters of tomato sauce. How many liters of sauce can be obtained from 54 kg of tomatoes?

Check the answers. (Slide number 10) (self-esteem: put + or - pencil innotebook; analyze errors)

Answers: a) 3: x \u003d 75: 125 c) 8: x \u003d 10: 15

b) 8: 10 \u003d x: 2 5 g) 5.6: 54 \u003d 2: x

Decide the task

№788 (p. 130, vilenkin textbook)(after parsing yourself)

In the spring, when working on landscaping the city on the street, Linden was planted. It was 95% of the linden planted lip. How much did the Lipa planted if 57 Lipa began?

• Read the task.
• What two values \u200b\u200bsays in the task?(on the number of lips and their percentages)
• What is the relationship between these values?(directly proportional)
• Make a brief record, proportion and solve the task.

Decision:

; ; x \u003d 60.

Answer: 60 Lipa planted.

Solve the task: (Slide №11-12) (after the disclamation decrease independently; mutual test, then the solution is displayed on the screen Slide No. 23)

For the heating of the school building, coal was harvested 180 days at the rate of consumption 0.6t of coal per day. How many days will this stock, if it is spent daily by 0.5t?

Decision:

Short record:

Make a proportion:

; ; Days

Answer: 216 days.

№793 (p. 131) (Semoration field yourself; self-control.

(Slide №13)

In the iron ore, 7 parts of the iron account for 3 parts of impurities. How many tons of impurities in ore, which contains 73.5T iron?

Solution: (Slide №14)

Answer: 31.5 kg of impurities.

So, we formulate an algorithm for solving problems with the help of proportions.

Algorithm Solving Tasks for Direct

and inverse proportional dependencies:

1. An unknown number is indicated by the letter x.
2. The condition is recorded in the form of a table.
3. This establishes the type of dependence between values.
4. A direct proportional dependence is indicated by the same directional arrows, and inversely proportional dependence - oppositely directional arrows.
5. The proportion is recorded.
6. Her unknown member is.

Repetition of the material studied.

№763 (s) (p. 125) (commenting at the board)

6. Stage of control and self-controlling knowledge and ways of action.
(Slide number 17-19)

Independent work(10 - 15 min) (Mutual: On ready-made slides, students check each other independent work, exposing + or -. The teacher at the end of the lesson collects notebooks for viewing).

Decide the task, constituting the proportion.

№1. On the path from one village to another at a speed of 12.5 km / h cyclist spent 0.7 hours. At what speed did he have to go to overcome this path for 0.5 h?

Decision:

Short record:

Make a proportion:

; ; KM / C.

Answer: 17.5 km / h

№2. Of 5 kg of fresh plux, 1.5 kg of prunes are obtained. How many prunes will turn out to be 17.5 kg of fresh plums?

Decision:

Short record:

Make a proportion:

; ; kg

Answer: 5.25 kg

Number 3. The car drove 500 km, Istiving 35l gasoline. How many liters of gasoline will need to drive 420 km?

Decision:

Short record:

Make a proportion:

; ; L.

Answer: 29.4 liters.

№4 . For 2 hours caught 12 caras. How many karas will be caught for 3 hours?

Answer: There is no answer. These values \u200b\u200bare neither directly proportional or inversely proportional.

№5 Six raws can perform some work in 18 days. How many more paintings need to be invited to work for 12 days?

Decision:

Short record:

Make a proportion:

; ; Malyarov will fulfill work for 12 days.

1) 9 -6 \u003d 3 malaria needs to be invited.

Answer: 3 malaria.

Additional (slide №33)

№6. The mining enterprise is required to purchase 5 new cars for a certain amount of money at a price of 12 thousand rubles. for one. How many such cars will be able to buy an enterprise if the price for one car becomes15 thousand rubles?

Decision:

Short record:

Make a proportion:

; ; cars.

Answer: 4 cars.

1. Stage of summing up lessons

• What did we know in the lesson?(Concepts of direct and inverse proportional dependence of two values)
• Give examples of directly proportional values.
• Give examples of inverse proportional values.
• Give examples of values \u200b\u200bin which the dependence is neither directly or inversely proportional.

1. Home Task (Slide21)
   № 812, 816, 818.

Thanks for the lesson Slide №22

Mathematics lesson in the 6th grade

on the topic "Direct and inverse proportional dependencies"

Developed
mathematic teacher
MOU "Mikhailovskaya School name
Hero Soviet Union V.F. Nesterova "
Kleimenova D.M.

Objectives lesson :

1. Didactic :

promote the formation and consolidation of skills and skills to solve problems with the help of proportions;

to teach two quantities in conditions of tasks and establish the type of dependence between them;

write a brief record and make a proportion;

fasten the skills and ability to solve equations having a type of proportion.

2. Developing :

develop memory, attention, continue the development of mathematical speech students;

promote the development of creative activities of students and interest in the subject matter of mathematics.

3. Educational :

educate accuracy, form interest in mathematics;

educating the ability to carefully listen to the opinion of others, upbringing self-confidence, education of the culture of communication.

Equipment: TSO necessary for the presentation: computer and projector, leaves for recording answers, cards for the stage of reflection (three each), pointer.

Type of lesson: lesson applying knowledge.

Forms of organization of the lesson: Frontal, collective, individual work.

LESSON STRUCTURE:

Organizational moment, greeting, wishes.

Check the studied material.

Message Topics lesson.

Repetition of the material studied.

Stage of control and self-controlling knowledge and ways of action.

Stage of summing up lesson.

Homework.

Reflection.

During the classes

Organizing time. (Slide 3)
(Greeting, fixation of missing, checking students' preparedness to learning process, distribution of leaves and cards for reflection, checking the preparedness of the classroom to occupation, organization of attention of the schoolchild).

Teacher reads: (Slide number 3)

Mathematics - the basis and queen of all sciences,
And I advise you to make friends with her, my friend.
Her wise laws if you do,
His kidnight will bring
You will apply them.
You can swim by the sea you swim,
You can fly in space.
Home Build People You can:
It will stand for a hundred years.
Do not be lazy, work, try,
Knowing salt sciences.
To prove everything try
But not downtrend.

2. Check the studied material.

(identifies problems in the knowledge and methods of students' activity and determines the causes of their occurrence, eliminates the discovered gaps during the test.)

Oral survey: (Slide №4)

What is called the attitude of two numbers?

How to find a fraction from the number?

What is proportion?

What values \u200b\u200bare called directly proportional?

What shows the attitude of two numbers?

How to find a number on his fraction?

The main property of proportion.

What values \u200b\u200bare called inversely proportional?

Finish the phrase: (Slide 5). (Children first perform the task on their own, writing on the leaves only letters corresponding to the correct answer. Then you raise your hand. After that, the teacher reads the question aloud, and I am responsible).

Direct proportional dependence is such a dependence of the values \u200b\u200bat which ...

Inverse proportional dependence is such a dependence of the values \u200b\u200bat which ...

To find an unknown extreme member of the proportion ...

The average member of the proportion is ...

The proportion is true if ...

FROM) …with an increase in one value several times, the other decreases at the same time.

X) ... the work of extreme members is equal to the product of the average members of the proportion.

A) ... with an increase in one value several times, the other increases with the same.

P) ... We need a product of medium members of the proportion to divide into a known extreme dick.

Y) ... with an increase in one value several times, the other increases at the same time.

E) ... the attitude of the work of extreme members to the well-known average.

Answer: SUCCESS.(slide 6)

Graphic dictation (slides 7-10).

"Yes" and "no" do not say

And the icon is depicting.

"Yes" the "+" icon, no icon "-".

(Students, work independently. Answers are recorded on leaves. Self-test using slide number. After the lesson, the teacher brings the leaflets)

If the area of \u200b\u200bthe rectangle is a constant value, then its length and width - inversely proportional values.

The growth of the child and its age is directly proportional.

With constant width of the rectangle, its length and area are directly proportional.

The speed of the car and the time of its movement is inversely proportional.

The speed of the car and its traveled path is inversely proportional.

The revenue of the cinema cash register is directly proportional to the number of tickets sold at the same price.

Machine capacity and their amount are inversely proportional.

The perimeter of the square and the length of it is directly proportional.

With a permanent price, the cost of goods and its mass is back proportional to the values.

Answer: + - + + - + + - - -(Slide number 10)

Get an assessment. (Slide №11)

8 -9 correct answers - "5"

6-7 correct answers - "4"

4-5 correct answers - "3"

Oral account: (slides 12-13)

Well, in the direction of pencils!

Neither paper, no pens, no chalk!

Verbal counting! We will create this business

Only the strength of mind and soul!

The task: Find an unknown member of the proportion:

Answers: 1) 39; 24; 3; 24; 21.

2)10; 3; 13.

Message Topics lesson. slide number 14. (Ensures the motivation of schoolchildren's teachings.)

The topic of our lesson "Direct and inverse proportional dependencies".

In previous lessons, we considered a direct and inverse proportional dependence of quantities. Today, at the lesson, we will solve different tasks using the proportion by setting the type of communication between the data. Repeat the basic property of proportions. And the next lesson ending on this topic, i.e. Lesson - test work.

Demonstratedslide number 15.

Stage of generalization and systematization of knowledge.

1) Task1.

Create proportions to solve problems:(work in notebooks)

but)Cyclist for 3h drives 75km. How long does the cyclist drive 125km at the same speed?

b) 8 identical pipes fill the pool in 25 minutes. How many minutes will the pool of 10 such pipes fill?

c) Brigade of 8 workers performs a task for 15 days. How many workers will be able to fulfill this task for 10 days, working with the same productivity?

d) from 5.6 kg of tomatoes receive 2 liters of tomato sauce. How many liters of sauce can be obtained from 54 kg of tomatoes?

Check the answers. ( Slide number 16) (self-esteem: put + or - pencil innotebook; analyze errors)

Answers:a) 3: x \u003d 75: 125c) 8: x \u003d 10: 15

b) 8: 10 \u003d x: 2 5 g) 5.6: 54 \u003d 2: x

2) Fizkultminutka. (Slide number 17-22)

Because of the desk we quickly got up

And on the spot they stumbled.

And then we smiled,

Above-above reached out.

Sat down - got up, sat down - got up

Over a minute of forces they scored.

Strain your shoulders

Raise, lower,

Right to the left turn

And at the desk again sit down.

3) Decide the task (Slide number 23)

№788 (p. 130, vilenkin textbook)(after parsing yourself)

In the spring, when working on landscaping the city on the street, Linden was planted. It was 95% of the linden planted lip. How much did the Lipa planted if 57 Lipa began?

Read the task.

What two values \u200b\u200bsays in the task?(on the number of lips and their percentages)

What is the relationship between these values?(directly proportional)

Make a brief record, proportion and solve the task.

Decision:

;
; x \u003d 60.

Answer: 60 Lipa planted.

4) Decide the task: (slide №24-25) (after the parsing decrease independently; mutual test, then the solution is displayed on the screen Slide No. 23)

For the heating of the school building, coal was harvested 180 days at the rate of consumption 0.6t of coal per day. How many days will this stock, if it is spent daily by 0.5t?

Decision:

Short record:

Make a proportion:

;
;
Days

Answer: 216 days.

5) №793 (p. 131)(Semoration field yourself; self-control.

(Slide №26)

In the iron ore, 7 parts of the iron account for 3 parts of impurities. How many tons of impurities in ore, which contains 73.5T iron?

Decision: (Slide №27)

;
;

Answer: 31.5 kg of impurities.

6) Summing up the total stage. (Slide №28)

So, we formulate an algorithm for solving problems with the help of proportions.

Algorithm Solving Tasks for Direct

and inverse proportional dependencies:

An unknown number is indicated by the letter x.

The condition is recorded in the form of a table.

This establishes the type of dependence between values.

A direct proportional dependence is indicated by the same directional arrows, and inversely proportional dependence - oppositely directional arrows.

The proportion is recorded.

Her unknown member is.

5. Repetition of the material studied. (Slide №29)

№763 (s) (p. 125)(commenting at the board)

6. Stage of control and self-controlling knowledge and ways of action.
(Slide No. 30-32)

Independent work (10 - 15 min) (Mutual: On ready-made slides, students check out independent work, exposing + or -. The teacher at the end of the lesson collects a notebook to view).

Decide the task, constituting the proportion.

№1. On the path from one village to another at a speed of 12.5 km / h cyclist spent 0.7 hours. At what speed did he have to go to overcome this path for 0.5 h?

Decision:

Short record:

Make a proportion:

;
;
KM / C.

Answer: 17.5 km / h

№2. Of 5 kg of fresh plums, 1.5 kg prunes are obtained. How many prunes will turn out to be 17.5 kg of fresh plums?

Decision:

Short record:

Make a proportion:

;
;
kg

Answer: 5.25 kg

№3. The car drove 500 km, Istiving 35l gasoline. How many liters of gasoline will need to drive 420 km?

Decision:

Short record:

Solving tasks from Vilenkin, Zhokhov, Chesnokov, Schwarzburd for grade 6 in mathematics on the topic:

1 for 3.2 kg of goods paid 115.2 p. How much should you pay for 1.5 kg of this product?
DECISION

2 Two rectangles have the same area. The length of the first rectangle is 3.6 m, and the width is 2.4 m. The length of the second is 4.8 m. Find it width.
DECISION

782 Determine whether direct, reverse, or is not a proportional relationship between values: by car traveled with a constant speed, and the time of its movement; the cost of goods purchased at one price and its number; square square and its length; mass of steel bar and its volume; the number of workers performing some work with the same labor productivity, and the execution time; the cost of goods and its number bought for a certain amount of money; the age of man and the size of his shoes; the volume of the cube and the length of his rib; the perimeter of the square and its length; the shot and its denominator, if the numerator does not change; The fraction and its numerator, if the denominator does not change.
DECISION

783 steel ball with a volume of 6 cm3 has a mass of 46.8 g. What is the mass of the ball from the same steel if its volume is 2.5 cm3?
DECISION

784 of 21 kg of cotton seed received 5.1 kg of oil. How many oil will come out of 7 kg of cotton seed?
DECISION

785 For the construction of a stadium of 5 bulldozers cleared the platform for 210 minutes. How long does 7 bulldozers get this platform?
DECISION

786 To transport the cargo, it took 24 cars with a loading capacity of 7.5 tons. How many cars need a loading capacity of 4.5 t to transport the same cargo?
DECISION

787 To determine the germination of seeds sown peas. Of the 200 seed pea, 170 sat down. What percentage of the peas gave shoots (germination)?
DECISION

788 During the Sunday, the Linden was planted on the landscaping of the city on the street. It began 95% of all landlined Lip. How many of them were planted if 57 Lipa began?
DECISION

789 In the ski section 80 students are engaged. Among them are 32 girls. What percentage of the participants of the section make girls and boys?
DECISION

790 The plant was supposed to pay 980 tons in the plan for the plan. But the plan was carried out by 115%. How many tons began to pay the plant?
DECISION

791 For 8 months, the worker fulfilled 96% of the annual plan. How many percent of the annual plan will perform a 12-month worker if it works with the same performance?
DECISION

792 For three days, 16.5% of the entire beet was removed. How much days need to remove 60.5% beets, if working with the same performance?
DECISION

793 In Iron Ore, 7 parts of the iron account for 3 parts of impurities. How many tons of impurities in ore, which contains 73.5 tons of iron?
DECISION

794 To prepare the borsch for every 100 g of meat, it is necessary to take 60 g of beets. How many beets should be taken on 650 g meat?
DECISION

796 Present in the form of a sum of two fractions with a numerator 1 each of the following fractions.
DECISION

797 From numbers 3. 7, 9 and 21, make up two faithful proportions.
DECISION

798 Average members of the proportion of 6 and 10. What could be the extreme members? Give examples.
DECISION

799 With what value x is correct proportion.
DECISION

800 Locate the ratio of 2 minutes to 10 C; 0.3 m2 to 0.1 dm2; 0.1 kg to 0.1 g; 4 h to 1 day; 3 dm3 to 0.6 m3
DECISION

801 where on coordinate ray The number C must be located so that the proportion is correct.
DECISION

802 Close table sheet of paper. For a few seconds, open the first string and then closing it, try to repeat or write three numbers of this line. If you are correctly played all the numbers, go to the second line of the table. If an error is made in any row, write several sets from the same, the number of two-digit numbers and train in memorization. If you can reproduce at least five two-digit numbers without errors, you have good memory.
DECISION

804 Is it possible to draw up a faithful proportion of the following numbers.
DECISION

805 from the equality of works 3 · 24 \u003d 8 · 9 Make three faithful proportions.
DECISION

806 Cut length AB is 8 dm, and the length of the CD segment is 2 cm. Find the ratio of the lengths of the AB and CD. What part of the ab is the CD length?
DECISION

807 Pourevka in the sanatorium costs 460 p. The trade union pays 70% of the cost of the voucher. How much does the rest pay for the rest?
DECISION

808 Find the value of the expression.
DECISION

809 1) When processing the part of the casting, a mass of 40 kg in waste was gone 3.2 kg. What percentage is the mass of the details from the casting? 2) When sorting the grain of 1750 kg into waste, 105 kg took place. What percentage of grain stayed?

Two values \u200b\u200bare called directly proportionalIf with an increase in one of them several times the other increases at the same time. Accordingly, with a decrease in one of them several times, the other decreases at the same time.

The relationship between such values \u200b\u200bis a direct proportional dependence. Examples of direct proportional dependence:

1) at a constant speed, the path passed directly proportionally depends on time;

2) the perimeter of the square and its side is directly proportional;

3) the cost of goods purchased at one price is directly proportional to its quantity.

To distinguish direct proportional dependence on the reverse, you can use the proverb: "The farther in the forest, the more firewood."

Tasks on direct proportional values \u200b\u200bare conveniently solved by proportion.

1) For the manufacture of 10 parts you need 3.5 kg of metal. How much metal will go to the manufacture of 12 such details?

(I argue like this:

1. In the filled column, put the arrow in the direction from a larger number to the smaller.

2. The more details, the more metal is needed for their manufacture. It means that it is directly proportional to the dependence.

Let x kg of metal need for the manufacture of 12 parts. We make a proportion (in the direction from the beginning of the arrows to its end):

12: 10 \u003d x: 3.5

To find, it is necessary to divide the work of extreme members to a well-known average member:

So, it will take 4.2 kg of metal.

Answer: 4.2 kg.

2) For 15 meters of tissue paid 1680 rubles. How much are 12 meters of such fabric?

(1. In the filled column, put the arrow in the direction from a larger number to the smaller.

2. The smaller the fabric is bought, the less you need to pay for it. It means that it is directly proportional to the dependence.

3. Therefore, the second arrow is equally directed from the first).

Let x rubles stand 12 tissue meters. We make a proportion (from the beginning of the arrows to its end):

15: 12 \u003d 1680: x

To find an unknown extreme member of the proportion, the product of medium members Delim on a well-known extreme member of the proportion:

So, 12 meters are 1344 rubles.

Answer: 1344 rubles.