How to derive the whole part of the wrong fraction. Video Tutorial "Isolation of a whole part of the wrong fraction. Presentation of a mixed number in the form of incorrect fraction. Allocation of the whole part of incorrect fraction

How to highlight a whole part of the wrong fraction? In order to allocate the whole part from the wrong fraction, it is necessary: \u200b\u200bto divide the numerator with the remnant to the denominator; Incomplete private will be the whole part; The residue (if any) gives a numerator, and the divider is the valve of the fractional part. Read No. 1057, 1058, 1059, 1060. 1062, 1063. 1064. 7.

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Mixed numbers

"The summary of the lesson in mathematics" is the sample. a) 4/7 + 2/7 \u003d (4 + 2) / 7 \u003d 6/7 b, b, g (at the board) d) 7 / 9-2 / 9 \u003d (7-2) / 9 \u003d 5 / 9 e, Well, s (at the board). 12 kg of cucumbers collected in the garden. 2/3 of all cucumbers were litria. 6 / 7-3 / 7 \u003d (6-3) / 7 \u003d 3/7 2/11 + 5/11 \u003d (2 + 5) / 22 \u003d 7/22 9 / 10-8 / 10 \u003d (9-8 ) / 10 \u003d 2/10. Show fraction 2/8 + 3/8. Formulate the subtraction rule. Studying a new material:

"Comparison of decimal fractions" is the purpose of the lesson. Compare numbers: oral account. 9.85 and 6.97; 75.7 and 75,700; 0.427 and 0.809; 5.3 and 5.03; 81.21 and 81,201; 76,005 and76.05; 3.25 and 3, 502; Read the fractions: 41.1; 77.81; 21.005; 0,0203. 41.1; 77.81; 21.005; 0,0203. Ensure the number of decimal signs. Lesson plan. Discharge decimal fractions. Fixing lesson in grade 5.

"Rules rounding numbers" - 1.8. 48. Well done! 3. 3. Learn to apply the rounding rule on the examples. Try to compare. Round up integers up to dozen. 1. Remember the number rounding rule. Is it convenient to work with such a number? One hundred thousand 3. Record the result. 5312.\u003e. 2. To withdraw the rule of rounding decimal fractions to a specified discharge.

"The addition of mixed numbers" - 25. Example 4. Find the difference value of 3 4 \\ 9-1 5 \\ 6. 3 4 \\ 9 \u003d 3 818; 1 5 \\ 6 \u003d 1 15 \\ 18. 3 4 \\ 9 \u003d 3 8 \\ 18 \u003d 3 + 8 \\ 18 \u003d 2 + 1 + 8 \\ 18 \u003d 2 + 8 \\ 18 + 18 \\ 18 \u003d 2 + +26 \\ 18 \u003d 2 26 \\ 18. Lesson Abstract in grade 6

Mathematics lesson in 4th grade Theme: allocation of a whole part of the wrong fraction Theme of the lesson: allocation of a whole part of incorrect fraction. Didactic goal: Create conditions for the formation of new educational information. Objectives and objectives of the lesson: 1. To form the concept of a mixed number. 2. Place the ability to allocate the whole part of the wrong fraction. 3. Develop computational skills. 4. Develop the ability to analyze and solve text objectives to find a part of the number and the number by part of it. 5. Develop logical thinking Pupils. Planned learning outcomes, formation Wood: subject: to expand the concept of the number, form the ability to translate incorrect fractions into mixed numbers and apply the knowledge and skills when performing various tasks. MetaPered: develop the ability to see the mathematical task in the context of the problem situation in other disciplines, in the surrounding life. Cognitive UUD: develop ideas about the number; the ability to work with a textbook, additional sources of information (analyze, extract the necessary information); The ability to make a generalization, conclusions, establish causal links. Communicative Wood: to bring up respect for each other, develop the ability to join the training dialogue with the teacher, with classmates, observing the norms of speech behavior, the ability to ask questions, listen and answer the questions of others, the ability to put forward the hypothesis. Regulatory Wood: Determine the purpose of the task, learn to plan the stages of work, control your actions, detect and correct errors, critically evaluate the results of its work and work of all, based on the existing criteria, form the ability to mobilize for forces and energy, to overcoming obstacles. Personal Wood: Forming training motivation , initiative, develop the skills of competent oral and written mathematical speech, the ability to self-esteem its actions. Resources: multimedia projector, presentation. Type of lesson: Studying a new material. Stage lesson Teacher's activities Activities of the student organizational moment Greeting, checking the preparedness for the training session, organizing the attention of children. . Turn on in the business rhythm lesson. Methods used, techniques, shapes of verbal formulated Uud be able to draw up their thoughts in oral form (Communicative Wood). The ability to listen and understand the speech of others (Communicative Wood). As you understood from the read, today we will continue to work on the fractions. Guys, at the lesson you must open new knowledge, but, as you know, every new knowledge is related to what we have already studied. Therefore, we will start with repetition. The oral account of the actualizes of knowledge and skills practical answers are recorded in the column, check the responses on the slides. In the lesson, vote to be able to sequence actions (regulatory Wood). To be able to convert information from one form to another (cognitive UUD). Delivering your thoughts in oral and writing (communicative Wood). Blitz poll: what rules you used when: 1. The crushing amount has fallen. 2. There were a difference fraction. 3. A number of part. 4. A part in the number. Talk rules. Participation in a conversation with the teacher. To be able to draw up your thoughts (Communicative Wood). Be able to navigate in your knowledge system: to distinguish a new one from the already known with the help of a teacher (cognitive Wood). The ability to listen and understand the speech of others (Communicative Wood). Goaling E and Motivation 3. Setting the problem of verbal to be able to draw up their thoughts in oral form (Communicative Wood). Be able to navigate in. . His knowledge system: to distinguish a new one from the already known with the help (cognitive teachers of Wood). Children express options for their solutions. 4. "Formulation of the problem and the objective of the lesson, select the whole part from this fraction. What do you offer? What do you think, what is the purpose of the lesson we will put? Formulate the purpose of the lesson and the topic of students. Purpose: Learn to allocate the whole part of the wrong fraction of verbal, practical to be able to extract new knowledge: to find answers to questions using a textbook, your own life experience and information obtained on (cognitive lesson Wood). To be able to draw up their thoughts orally; Listen and understand the speech (communicative other Wood). So, any irregular fraction can be represented as a mixed number. An integer part is a natural number, and the fractional part is the correct fraction. . . Drawing up an algorithm. Vitely practical, reproductive analysis on working lesson to vote to be able to be a collectively drawn up plan (regulatory Wood). Be able to sequence actions (regulatory Wood). Be able to draw up your thoughts in oral and writing; Listening and understanding the speech of others (Communicative Woods) to be able to sequence actions (regulatory Wood). Be able to do work on the proposed plan (regulatory Wood). Having to prove the lesson to assimilate new knowledge and methods of assimilation 5. Recreation of the new: explanation on the board. Write down the shot 16/5 in the form of a private as a rule was used to select the whole part to allocate from the wrong fraction to allocate the whole part from the wrong part: to divide the numerator to the denominator; The received incomplete private write to be able to make the necessary adjustments to effect after its completion based on its assessment and taking into account the nature of the errors made (regulatory Wood). The ability to self-esteem on the criterion for the success of educational activities (Personal Wood). the basis of the whole part of the fraction; residue to write to the fraction numerator; Divider Write to the denomoter. 16: 5 \u003d 3 (OST. 1)) 3 - an integer 1 - numerator 5 - denominator 16/5 \u003d 3 1/5 Reading the rule in the textbook on P. 26, No. 3 - at the board 1 Example with an explanation. Rest with commenting. №4 (A, B, B) - independently. Multi-test. m In an integer, n and b of parts in the fraction is always a whole numerator. The guys tell a rule to find a whole need to multiply 6. Formulate new knowledge. We confirm your statement by the rule in the textbook. 7. Primary fixing 8. Fizkultminutka 9. Repeating the studied entry on the board: M / N \u003d B Highlight where in the fraction of the integer and part? How to find an integer? Applying the rule solve equation. Parts p. 28, task10. What additional questions can be put? Pp. 27, №8 - at the board (A, B, B) - 3 student decide. The rest are solved in pairs (d). Checking the task analysis. Self record solution. Answering questions, analyze their work in the lesson summing up the lesson, verbal, analysis 10. The result of the lesson: what did you study in the lesson? Select a whole part of incorrect fraction. Visible to what conclusion came? It is necessary that it is necessary to separate from the wrong fraction to allocate its numerator to the denominator, the private will be the whole part, the residue with the numerator, and the divider denomoter. And now you will check ourselves as you learned this. Perform yourself. (mutual test). Information about the homework Reflection 11. Homework: C. 26, №4 (g, d, e), learn the rule on with. 26 and p. 28 №11 If you think that you understood the topic of today's lesson, then coloring leaflets with green pencil. What is not if you think sufficiently learned the material yellow. If you think you did not understand the topic of today's lesson red. Self-assessment is able to evaluate the correctness of the performance of an adequate retrospective assessment. (Regulatory Wood). Based on the ability to self-esteem the criterion on the success of training activities (Personal Wood).

How from incorrect fraction to allocate a whole part? And got the best answer

Answer from Katy [Active]
In order to translate a number, it is necessary to divide the numerator with the remnant to the denominator. To find out how much "whole" times contain. And this is incomplete private and will be the whole part. Then the residue (if any) gives a numerator, and the divider is the denominator of the fractional part (so that it is clearer you need a denominator to multiply by the integer that you received earlier, and then from the numerator to subtract what you got now)
For example: 136/28 \u003d 4 as many as 24/28, this is a reduction fraction \u003d 4 as long as 6/7
I divided into 28 and received 4. Then to find out the numerator, multiplied 28 to 4 it turned out 112, and out of 136 output 112. To reduce, the numerator and denominator should be divided into the same number (in this case it is 4)
Good luck!

Answer from Andrei Polyakov[newcomer]
25/22, 22/22 is one whole, and 3/22 remains, and Togo 1 and 3/22

Answer from Kinogolik[guru]
to divide the numerator to the denominator, the number to the comma is a whole part, then intend to multiply the denominator and subtract it from the source numerator. This digit will be a numerator.
for example: 88/16 \u003d 5.5
16*5=80
88-80=8
5 8/16=5 1/2

Answer from Vadim Culpinov[guru]

Answer from Anna[newcomer]
for example 1000/9 .... Easily 1000 share for 9 ... Get 111This integer and the residue goes to the numerator and the denominator remains the same 9 ....

Answer from Єranche[newcomer]
try to calculate on the calculator))
excavated the numerator to the denominator and write down the number to the left of the comma.
if you need to highlight the fractional part:
you multiply the allocated part to the denominator and the resulting number is deducted from the numerator. I.e:
79/3
1. We allocate the integer: 26
2. The allocated integer part multiply to the denominator: 26 * 3
3. The resulting number is deducted from Nizer 79- (26 * 3)
uRA.

Answer from Alexey Lauthit[guru]
the numerator is divided into the denominator, the resulting number is recorded as an integer and the residue in the form of a numerator and the denominator remains the same

Answer from EOMAN GAYKO[expert]
damn, so I first learned to do it. Only then the Internet appeared, I learned to use it and I found this site very soon)

Answer from _Dafna_[active]
for example, 23/3 - share the numerator to the denominator for the calculator (if it is near), take the first number, multiply to the denominator and you get a whole part of this fraction. From the numerator, you submit the number that turned out when multiplying the denominator, and get the right fraction. In the answer you write a whole part and next to the correct fraction.
If there is no calculator near, then there are already a little intuitively share the same actions.
The most good fractions, which in the denominator costs 2, 5 or 10 🙂

Answer from Le Chiffre.[expert]
Highlight how many denominator fits in a numerator times, then subtract the signator from the numerator, the denominator remains unchanged.

Answer from Alexey Antoshechkin[newcomer]
233 Delica in numbers and know Birch first and twisted

Answer from MI S Slonopotam[guru]
the numerator is divided into the denominator - get a whole part and the residue (fraction)

Answer from Elena[active]
As for 3/2, it seems true. It is necessary to simply separate the numerator with the remnant to the denominator. Then a private is a whole part, the residue is a numerator, and the divider is a denominator (i.e., as it was and remained). for example
48/13. We divide 48 to 13 we get 3 and in the residue 9. So it means 48/13 \u003d 3 as many as 9/13
Source: Mathematics

Answer from Pavel Chuprakov[newcomer]

Answer from sergey Nesterenko[newcomer]
1) To translate the wrong fraction into a mixed, it is necessary: \u200b\u200bto divide the numerator to the denominator with the residue, an incomplete private is a whole part, the balance is the numerator and the denominator is the same.
2) To make a mixed fraction to turn into incorrect, it is necessary: \u200b\u200ba whole part multiply the denominator and add a numerator, the resulting number will go to the numerator, and the denominator remains the same.

Answer from tanya Vorsa[newcomer]
In order to allocate the whole part from the wrong fraction, the numerator should be divided into the denominator
the number is written in the form of an integer, and the residue in the form of a numerator, and the denominator is the same.

In this article we will talk about mixed numbers. First we give the definition of mixed numbers and give examples. Further we will stop in touch between mixed numbers and irregular fractions. After that, we show how to translate a mixed number to the wrong fraction. Finally, study reverse processwhich is called the allocation of the whole part of the incorrect fraction.

Navigating page.

Mixed numbers, definition, examples

Mathematics agreed that the amount of N + A / B, where N is a natural number, A / B - the correct ordinary fraction, can be recorded without a mark of addition. For example, the amount of 28 + 5/7 can be briefly recorded as. This entry was called mixed, and the number that corresponds to this mixed record was called a mixed number.

So we approached the determination of a mixed number.

Definition.

Mixed number - this is a number equal to the sum of the natural number N and the correct ordinary fraci A / B, and recorded in the form. With the number N called in a whole part of the number, and the number A / B is called fractional part of the number.

By definition, the mixed number is equal to the amount of its whole and fractional part, that is, the equality that can be written and so :.

Here examples of mixed numbers. The number is a mixed number, a natural number 5 - a whole part of the number, and the fractional part of the number. Other examples of mixed numbers are .

Sometimes you can meet the numbers in a mixed record, but having a fractional part of the wrong fraction, for example, or. These numbers understand the amount of their whole and fractional part, for example, and . But such numbers are not suitable for determining the mixed number, since the fractional part of the mixed numbers should be the correct fraction.

The number is also not a mixed number, since 0 is not a natural number.

Communication between mixed numbers and irregular fractions

Trace communication between mixed numbers and irregular fractions best on examples.

Let the tray lies the cake and another 3/4 of the same cake. That is, in the sense of addition on the tray there is 1 + 3/4 cake. After writing the last amount in the form of a mixed number, we state that the cake is located on the tray. Now the whole cake will be cut into 4 equal shares. As a result, there will be 7/4 cake on the tray. It is clear that the "number" of the cake at the same time has not changed, therefore.

From the considered example, such a connection is clearly visible: any mixed number can be represented as an incorrect fraction..

And now let the tray are 7/4 cake. Folding out of four pieces a whole cake, 1 + 3/4 will be on the tray, that is, the cake. From here it is seen that.

From this example it is clear that wrong fraction can be represented as a mixed number. (In the particular case, when the numerator of the wrong fraction shares aimed at the denominator, the irregular fraction can be represented as a natural number, for example, since 8: 4 \u003d 2).

Translation of a mixed number in the wrong fraction

To perform various actions with mixed numbers, it turns out to be a useful skill representing mixed numbers in the form of incorrect fractions. In the previous paragraph, we found out that any mixed number can be translated into the wrong fraction. It's time to figure out how such a translation is carried out.

We write an algorithm showing how to translate a mixed number in the wrong fraction:

Consider an example of the translating mixed number in the wrong fraction.

Example.

Imagine a mixed number in the form of incorrect fraction.

Decision.

Perform all the necessary steps of the algorithm.

The mixed number is equal to the sum of its whole and fractional part :.

After writing a number 5 as 5/1, the last amount will take the form.

To complete the translation of the initial mixed number in the wrong fraction, it remains to perform fractions with different denominators: .

A brief record of the whole solution is as follows: .

Answer:

So, to carry out the transition of a mixed number to the wrong fraction, you need to perform the following chain of actions :. As a result, received which we will use in the future.

Example.

Record the mixed number in the form of incorrect fraction.

Decision.

We use the formula for translating the mixed number to the wrong fraction. In this example n \u003d 15, a \u003d 2, b \u003d 5. In this way, .

Answer:

Allocation of the whole part of incorrect fraction

In response, it is not customary to record the wrong fraction. Wrong fraction is pre-replaced either equal to it. natural number (When the numerator is divided by a denominator), or the so-called allocation of the whole part of the wrong fraction is carried out (when the numerator is not divided by the denominator).

Definition.

Allocation of the whole part of incorrect fraction - This is a replacement of a fraction equal to her mixed number.

It remains to find out how to select the whole part of the wrong fraction.

It is very simple: the irregular shot A / B is equal to a mixed number of the form, where q is an incomplete private, and R is the residue from division A on b. That is, the whole part is equal to incompletely private from division A on B, and the residue is equal to the partial part.

We prove this statement.

To do this, it is enough to show that. We translate mixed in the wrong fraction as we did in the previous paragraph :. Since q is an incomplete private, and R is the residue from dividing A on B, then the equality A \u003d B · Q + R (if necessary, see

§ 1 Selection of a whole part of incorrect fraction

In this lesson, you will learn to translate the wrong fraction into a mixed number by selecting the whole part, as well as on the contrary, to get an incorrect fraction from a mixed number.

First, let's remember what a mixed number and the wrong fraction.

Mixed number is a special form of a number of numbers that contains a whole and fractional part.

Incorrect fraction is a fraction, the numerator of which is greater than or equal to the denominator.

Consider the task:

We divide 8 candies on three guys. How much will everyone get?

To find out how much sweets will get every child, you need

But in response it is not accepted to record the wrong fraction. It is pre-replaced either equal to it with natural number (when the numerator is divided by the denominator), or the so-called allocation of the whole part of the wrong fraction is carried out (when the numerator is not divided by the denominator).

The allocation of the whole part of the incorrect fraction is to replace the fraction equal to it with a mixed number.

In order to allocate the whole part from the wrong fraction, you need to split the numerator to the denominator with the residue. At the same time, incomplete private will be a whole part, the residue is a numerator, and the divisor is a denominator.

Let's return to the task.

So, 8 divide by 3 with the residue, we get in incomplete private 2 and in the residue 2.

§ 2 Presentation of a mixed number in the form of incorrect fraction

Let's do the following task:

We divide 49 to 13, we get in incomplete private 3 (it will be the whole part) and in the residue 10 (it will be written in the fractional part numerator).

To perform various actions with mixed numbers, it turns out to be a useful skill representing mixed numbers in the form of incorrect fractions. It's time to figure out how such a translation is carried out.

To present a mixed number in the form of an incorrect fraction, a denominator of a fraction is to multiply by a whole part and add a numerator to the resulting product. As a result, we obtain the number that will be the numerator of the new fraction, and the denominator remains unchanged.

The first step is to multiply the whole part 5 to the denominator 7, we get 35.

The second step is to the resulting product 35 add numerator 4, there will be 39.

Now we write 39 into the numerator, and in the denominator will leave 7.

Thus, in this lesson, you learned to translate the wrong fraction into a mixed number, for this you need a numerator to divide the denominator with the residue. Then incomplete private will be a whole part, the residue is a numerator, and the divisor is the denominator of the fractional part of the mixed number.

You also got acquainted with the presentation of a mixed number in the form of incorrect fraction. In order to present a mixed number in the form of an incorrect fraction, the denominator of the fractional part of the mixed number is to multiply to the integer and add a numerator to the resulting product.

List of references:

1. Mathematics grade 5. Vilekin N.Ya., Zhokhov V.I. et al. 31st ed., Ched. - M: 2013.
2. Didactic materials in mathematics grade 5. Author - Popov MA - year 2013
3. Calculate without errors. Works with self-test in mathematics 5-6 classes. Author - Minaev S.S. - year 2014
4. Didactic materials in mathematics grade 5. Authors: Dorofeyev G.V., Kuznetsova L.V. - 2010 year
5. Control and independent work on mathematics grade 5. Authors - Popov MA - year 2012
6. Mathematics. Grade 5: studies. For students, general education. Institutions / I. I. Zubareva, A. G. Mordkovich. - 9th ed., Even. - M.: Mnemozina, 2009