The rule for finding a number by its fraction:

To find a number for a given value of its fraction, you need to divide this value by a fraction.

Let's consider how to find a number by its fraction, with specific examples.

Examples.

1) Find the number 3/4 of which is 12.

To find a number by its fraction, divide this number by this fraction. To, you need to multiply the given number by the inverse of the fraction (that is, by the inverted fraction). To, you need to multiply the numerator by this number, and leave the denominator unchanged. 12 and 3 by 3. Since the denominator is one, the answer is an integer.

2) Find a number if 9/10 is 3/5.

To find a number for a given value of its fraction, divide this value by this fraction. To divide a fraction into a fraction, multiply the first fraction by the inverse of the second (inverted). To multiply a fraction by a fraction, multiply the numerator by the numerator, and the denominator by the denominator. We reduce 10 and 5 by 5, 3 and 9 - by 3. As a result, we got the correct irreducible fraction, which means this is the final result.

3) Find a number whose 9/7 are equal

To find a number based on the value of its fraction, divide this value by this fraction. Mixed number and multiply it by the inverse of the second (inverted fraction). Reduce 99 and 9 by 9, 7 and 14 - by 7. Since we received an incorrect fraction, it is necessary to select the whole part from it.

Sections: Mathematics

Lesson topic:"Finding a part of a whole and a whole according to its part."

The purpose of the lesson:

1. Learn to find a fraction of a number and a number by its fraction.
2. To generalize the concept of an ordinary fraction and actions with ordinary fractions.

Equipment: Multimedia projector, Power Point presentation ( Application ).

DURING THE CLASSES

I. Organizational moment

Students are seated in groups (5-6 people). You can offer to diagnose your mood at the stages of the lesson. Each student is given a card on which he highlights the "character" of his mood.

II. Knowledge update

We are already familiar with the concept of an ordinary fraction.
- What does the numerator of the fraction show? (Into how many parts the whole was divided).
- What does the denominator of the fraction show? (How many parts were taken).

- Consider the drawing and answer the questions:

Students are encouraged to reproduce it.

III. Verbal counting. (Best counter)

Each team is presented with a task on the screen. The teams take turns completing the task.

1st team

2nd team

3rd team

4th team

It sums up which team is the best counter.

IV. Dictation

The dictation is carried out with subsequent self-examination. It is possible to carry out a carbon copy, students hand over one copy to the teacher for verification.

1. Insert the missing number instead of x:

2. Reduce the fraction:

3. Arrange the fractions in descending order:

4. Perform actions:

5. Turtles - giants live on the islands of the Pacific Ocean. They are so large that children can ride while sitting on their shell. The following task will help us find out the name of the world's largest turtle.

After passing the solution, students check the answers.

V. New material

The teacher offers to solve the problems (5-7 minutes are given for thinking them over)

1. There were 12 birds sitting on a branch. Then they flew away. How many birds flew away?

2. In your math class for the third quarter 6 people got the mark "5". This amounts to the number of all students in the class. How many students are there in the class?

Then the solution is verified and shown on the slide.

1 way: 12: 3 2 = 8 (birds)

Method 2: 12 = 8 (birds)

2 task. 6: = 6 = 34 (people)

The teacher draws attention to the fact that two types of tasks can be distinguished:

1. To find part of the number, expressed as a fraction, you need this number multiply for a given fraction.
2. To find number according to its frequency and, expressed as a fraction, you need divide for this fraction the number corresponding to it.

Students are encouraged to memorize this rule right in the classroom and retell each other in pairs.

The teacher focuses on the following: for those who find it difficult to determine the type of problem, I advise you to pay attention to prepositions what , This ... These prepositions are found in the problems of finding numbers by its fraction.

Vi. Securing new material

On the slide, the condition of six problems and the students are asked to sort them into two columns by type.

1. The store accepted 156 kg of fish for sale. 1/3 of all fish were carp. How many kg of carp did the store receive?
2. Conducted 18 experiments, this was 2/9 of the entire series of experiments. How many experiments do you need to carry out?
3. The teacher checked 20 notebooks. This made up 4/5 of all notebooks. How many notebooks should the teacher check?
4. Out of 72 fifth-graders, 3/8 go in for athletics. How many students are involved in this sport?
5. 30 paintings were selected for the exhibition. This made up 2/3 of the paintings in the museum. How many paintings are on display?
6. 3/4 of its length was cut from a rope 18 m long. How many meters of rope are left?

Vii. Lesson summary

The teacher returns students to the lesson goal, proposes to distinguish two types of problems on fractions and algorithms for their solution. Papers with mood diagnostics are collected.

VIII. Homework: P. 9.6, No. 1050, 1058, 1060.

how to find the whole by its part? (formula) and got the best answer

Answer from Squad_not_noticing_the_loss_of_fighter [guru]
Finding the whole by part;

Example:

Solution: 420: 3/5 = 700 (kg).

Answer from Timexer_Player[newbie]
Finding the whole by part;
To find the largest number of a given part of it,
divide this value by the fraction expressing the given part.
Example:
The carcass weight of a bull is 3/5 of its live weight.
What is the live weight of a bull to weigh 420kg?
Solution: 420: 3/5 = 700 (kg).

Answer from Juriy marjenko[newbie]
To find the number by its part, the part must be divided by the numerator and multiplied by the denominator

Answer from Pavel Chuprakov[newbie]
Here's a little stash you can easily remember:
Find part of the whole
No need to disturb anyone
We need this number
Multiply by this fraction

Answer from Adamson show[newbie]
Finding the whole by part;
To find the largest number of a given part of it,
divide this value by the fraction expressing the given part.
Example:
The carcass weight of a bull is 3/5 of its live weight.
What is the live weight of a bull to weigh 420kg?
Solution: 420: 3/5 = 700 (kg).

Answer from Olvina Salikhzhanova[newbie]
To find the part x of an integer a, you need to divide the number a corresponding to an integer by the denominator m and multiply the result by the numerator k of the fraction that expresses this part.

Answer from Mi S Slonopotam[guru]
numerator divided by denominator - get whole part and remainder (fraction)

Answer from Lily[expert]
to find the whole by part, divide by the denominator and multiply by the numerator

Topic: Finding a part of a whole and a whole in its part

Target: To systematize, expand, generalize and consolidate the knowledge gained on the topic “Finding a part from a whole and a whole in its part. Informatics among us "
Tasks:
To intensify the knowledge of students about the concepts of fraction, solving problems on fractions.
To teach students to solve problems on a topic, to be able to distinguish ways of solving problems.
Application of the obtained theoretical knowledge in solving practical problems.
Expand the horizons of students in the field of computer science.
Stages of the lesson.

Goal setting - 2 min.
Basic knowledge update - 8 min.
Consolidation and generalization of the material. - 23 minutes
Summing up the lesson and setting homework. - 5 minutes.

Expected results: students must learn to apply the necessary methods of solution to a particular problem, must be able to solve problems, be able to perform calculations of fractions.

During the classes:

Organizing time. - 2 minutes.
Greetings, students.
Goal setting - 2 min.
Guess the puzzle.

What word is encrypted here? That's right, the internet.
What topic are we studying with you now? (right, "Finding a part from a whole and a whole according to its part")
How will the Internet relate to this topic? (we will solve problems on this topic for knowledge of the Internet0
Who can formulate the topic of today's lesson? (The Internet is among us)
Do you know what the Internet is? (Tell their versions)
Internet - (from Lat. Inter - between and net - network), a global computer network that connects both users of computer networks and users of individual (including home) computers.
Updating basic knowledge- 8 minutes
Perform verbally:
A) Find the part of the number:
3/4 from 16;
2/5 from 80;
7/10 from 120;
3/5 from 150;
6/11 from 121;
5/6 from 108

B) Find a number if:
3/8 of it are equal to 15;
2/5 of it are equal to 30;
5/8 of it are equal to 45;
4/9 of it are equal to 36;
7/10 equals 42;
2/11 equals 99.

Consolidation and generalization of material... - 23 minutes
Where and when do you think the Internet appeared? (express opinions)
In 1957, after the Soviet Union launched the first artificial earth satellite, the US Department of Defense decided that in case of war, the US needed a reliable information transmission system. The US Defense Advanced Research and Development Agency has proposed developing a computer network for this.

Now we will solve several problems.

Alena has 140 photos uploaded on her personal page on the Odnoklassniki website. 2/7 of the total number of photos were uploaded to the Personal Photos album, 1/4 to the Hobby album, 3/35 to the Rest album, 5/28 to the Family album, and the rest to the On photos of friends ”. How many photos does Alena have in each album?
140: 7 * 2 = 40 (f) "Personal photos"
140: 4 * 1 = 35 (f) "Hobby"
140: 35 * 3 = 12 (f) "Rest"
140: 28 * 5 = 25 (f) "Family"
140 - 40 - 35 - 12 - 25 = 28 (f) "In the photo of friends"

Misha has 276 emails in his e-mail, which is 3/5 of the number of letters in Kolya's e-mail. How many more letters does Misha have?
276: 3 * 5 = 460
460 – 276 = 184.

On a flash card designed for 4G bytes (1G bytes = 1024 M bytes) there are various files. Photos occupy 3/16 of all memory, movies - 1/8 more (of all memory) than photos, text documents - 5/64 more (of all memory) than photos. How many M bytes are there for each file?
4 * 1024 = 4096
4096: 16 * 3 = 768 (M bytes) in the photo
4096: 8 * 1=512
768 + 512 = 1280 (M bytes) for films
4096: 64 *5 = 320
320 +768 = 1088 (M bytes) for text documents.

Guys, what do you need the Internet for?
Communication;
Information;
Games.
What social networks do you know? (express their opinion)
Let's call the pros and cons of social media:
"Pros":
Communication;
Information.
"Minuses":
Negative health effects;
Internet addiction;
Immersion in the virtual world;
Danger from strangers.

Let's solve the following problem.

Among the pupils of the 5th grade of one of the schools, a questionnaire was held on the topic “Social networks and children”. To the question “How much time a day do you spend on the Internet”, 3/10 of the number of all surveyed schoolchildren answered “5-6 hours”. How many schoolchildren spend this time on the Internet every day if 150 children participated in the survey?
150: 10 * 3 = 45 (children).
45 children! This is a very large number! After all, every day they waste so much time sitting at the computer.
Guys, what do you think, what harm to health can be caused by spending a long time on the Internet?
Possible student responses:
Deterioration of vision;
Decreased physical activity;
Psychological stress;
The person loses the ability to communicate;
Rachiocampsis;
Headaches;
Sleep disturbance.

You see how much negative you can earn by sitting for several hours on the Internet!

5. Summing up the lesson and setting homework... - 5 minutes.
What new have you learned in the lesson today?
What do you think is the best time to spend on the Internet every day?
What will you mainly use the Internet for?
Do you think that 5-6 hours of Internet surfing every day is the norm?
Homework: prepare a message on the topic "History of the Internet"
Announcement of estimates.
Thank you for the lesson!

Open lesson in mathematics in grade 5b.

Teacher: Bambutova M.I.

Topic: How to find a part of a whole and a whole in its part.

Purpose: to learn to solve problems of finding a part from a whole and a whole in its part.

Educational: deduce a rule for finding a part from a whole and a whole in its part,

solve problems of finding a part from a whole and a whole in its part.

Developmental: develop memory and mathematical speech

Educational: educate communication skills.

Lesson plan:

1) Introductory-motivational stage.

1. Org. Moment

2. Updating basic knowledge

Answer the questions (slide)

1) What does a fraction stand for?

2) What does a fraction stand for? ?

3)

Formulation of the problem:

1 task:

2 tasks per slide

1) draw a rectangle with sides 2cm and 5cm. What is its area?

Solve the problem

1) The area of ​​the rectangle is 10 cm 2. Shaded parts of the area of ​​the rectangle. What is the area of ​​the filled part of the rectangle?

2) The shaded part of the rectangle is 4 cm 2, which is part of the entire rectangle. What is the area of ​​the rectangle?

Answer the questions: ( )

part of the whole , and in what whole by part ?

What we find in problem 1 (whole by its part), what we find in problem 2 (part of the whole)

Task 2: Read the tasks and answer the questions:

1) Field area - 50 hectares. During the day, a team of tractor drivers plowed the fields. How many hectares did the team plow in a day?

2) In a day, the team plowed 20 hectares, which was the area of ​​the entire field. What is the area of ​​the field?

Answer the questions: ( distribute tasks in the form of a card)

What value is taken as a whole in each problem?

In which of the problems this value is known and in which not?

In which of the tasks you want to find part of the whole , and in what whole by part ?

What are these tasks? (reciprocal)

What do these tasks have in common? What were we looking for in these tasks?

-Part of the whole and whole in its part.

So what is our topic today? ?

Topic: How to find a part of a whole and a whole in its part .(slide)

The correct solution to the last two problems can be found in the textbook on page 95.

So we solved 4 problems, summarize all the problems and derive a rule for finding a part from a whole and a whole in its part.

Students try, to help them scatter the phrase, you need to put together in a logically correct sentence, which will be the rule.

which expresses this part.

corresponding to the whole,

To find a part of a whole

divide by the denominator

and multiply the result by the numerator of the fraction

need a number

To find a part of a whole, you need to divide the number corresponding to the whole by the denominator and multiply the result by the numerator of the fraction that expresses this part.

and multiply the result by the denominator of the fraction,

need a number

divide by numerator

which expresses this part.

To find the whole by its part,

corresponding to this part,

To find an integer by its part, you need to divide the number corresponding to this part by the numerator and multiply the result by the denominator of the fraction that expresses this part.

Collect this rule on the board.

Students recite this rule to each other.

3. Primary anchoring. Game "Sorting tasks".

Workshop on problem solving. Option 1 solves the problem of finding a part of the whole, Option 2 solves the problem of finding the whole by its part.

1. There are 80 students in the choir, ¼ of them are boys. How many boys are there in the choir?

2. There are 20 boys in the choir, which is ¼ of all students in the choir. How many students are there in the choir?

3. A small deciduous forest clears the air from 70 tons of dust per year. And the coniferous forest is ½ of this amount. How much dust does a coniferous forest filter out per year?

4. 7/12 of the kerosene contained there was poured out of the barrel. How many liters of kerosene was in the barrel if 84 liters were poured out of it?

5. The girl skied 300 m, which was 3/8 of the entire distance. How long is the distance?

6. 2/5 of the skating rink was cleared of snow, which is 200 sq.m. Find the area of ​​the entire ice rink?

7. The girl read ¾ of the book, which is 120 pages. How many pages are in the book?

8. Squirrel has prepared 600 nuts in total. In the first week, she harvested 20% of all nuts. How much protein did you collect in the first week?

9. Find the number NS, 1/8 of which is equal to 1/24.

10. The girl collected 40 plums, which is 1/3 of all plums. How many plums were collected in total?

11. Mom bought 6 kg of sweets. Vitya immediately ate 2/3 of all the candies and felt bad. After how many sweets did Viti have a stomach ache?

12. The boy collected 80 nuts, which is 2/3 of all collected nuts. How many nuts were harvested?

13. There were 40 chickens in the hen house. In a week, the fox stole 3/8 of all the chickens. How many chickens did the fox carry?

14. Alice fell into the fabulous well and flew 90 m in 1 minute. What is the depth of the well if in 1 minute Alice flew ¾ of the entire distance?

15. Before the ball, the stepmother gave Cinderella a lot of work. It took Cinderella 6 hours to complete 3/5 of this work. How long will it take for Cinderella to do all the work?

4. Reflection. The rule is to pronounce.

5. Homework: learn a rule, make a card with tasks to find a part of a whole and a whole in its part (3 tasks for each rule).