Storage and storage of shots. Storage of shots with various banners. Knowing the number behind the yogo fraction

Objectives of the lesson:

1. Take the rise of the shotgunner,
2. Adding that sighting of shots with different banners,
3. Complete the knowledge of the value of the smallest common multiple.

Today, at the lesson, we continue the work on the topic “Stocking and handling shots with different banners”.

Tse we have another lesson to those in front of you are standing goal:

As in the first lesson, we were engaged in fractions with you, for which banners are mutually simple or multiples of one to one number, then today our schedule is getting more complicated, for some special occasions we happen to know the common banner of laying out banners on simple multipliers for the rule of NOC.

For example, the lesson you are guilty of is good to know the rule:

how to add up fractions with different banners and remember to zastosovuvat tse rule for the hour of the day of the day.

After 3 lessons, there will be a control work, in which there will be tasks that will be revised, as you have mastered the topic. On the control robot There will be 2 tasks on our topic: the third task - the completion of the task, the addition of shots with different banners and the fourth task: the development of tasks for the regulation of the rule. Also, today we are working with you on the standard.

1. a) Correct.

42	48	6
36	54	12
30	24	18

It is respectful to look at the whole rectangle and try to remember the numbering of the numbers, maybe remember the law.

And now try to guess the numbers of the blacks.

Who has memorized the numbers?

How can you better remember the roztashuvannya tsikh numbers?

(Numbers that are multiples of 6 are arranged in order of growth after the year's arrow, starting from the upper right rectangle)

Let's repeat the alignment of fractions with different banners and equal numbers.

Match these fractions: ; .

Stash them in order of growth.

b) It is important to look at the next series of numbers:

16, 10, 8, , 2007, 1961.

How many numbers are written?

How many guys numbers? Name them.

Name the third number.

Another number is z kintsya.

Tri-digit number.

A number that is a multiple of 5.

Multiple of 10

A multiple of 3.

A multiple of 9. What do you see the number 1961 in?

How does the number fit into others, so that it does not fit into a series of numbers?

Tsey drіb correct chi wrong?

Is the speed of chi not short?

Speed ​​up your drib.

2. Rechecking homework.

How do you compare two fractions with different banners?

How are fractions stacked with different bannermen?

How to win the shots from different bannermen?

Chi є food shodo home robot? Perevirka in the ranks of the teacher.

3. Robot with the rule for the assistant after inaccurate opinions of the academics.

In mathematics, one cannot miss a single word in certain rules. Zagalny znamennik and the smallest svіlny znamennik, such as they always run.

Listen to the parable of one measure.

When there was no electricity, I loved one place in the evenings to walk around the streets of Moscow. As if vins hit one city dweller, a bump popped up on his forehead. on the coming day, having seen the decree: "At the dark hour, dobi nadvir comes out with light." And in the evening, the same city dweller flew into the new raid. Measure thirsty at the new lighter.

Axis, - said the passerby.

Where is the candle? - Having asked for measures.

And the decree does not say that the lighter can have a candle, - that’s it.

Mer having seen another decree: "At the dark hour, finish the nadvir, come out with a lighter with a candle."

On the third day history repeated itself.

Mer is already viishov іz himself.

Do you think that you are transitory?

The order does not say that the lighter's candle can be lit.

Mer had a chance to see a decree on the third day, only after that he passed, giving you peace.

Our task is to know the rule well and remember to zastosovuvat. I repeat once again, we are working above the standard.

4. Vikonanny is right.

Razv'yazhit on the butt on the doshtsi behind the bajan.

You vyrishili butts, de bannermen mutually simple numbers and if the larger banner is short.

At this time of year, it’s time to add orders for additional delivery of shots with different bannermen.

Write a task:

If you learn to sing like that, as we scribbled with you, then you know well, how to know the NOC of two numbers and yet see a whole part from an incorrect fraction, you know that the banners are not mutually simple numbers.

If you learn to know the sleeping banner, having multiplied the banners, you will show the ignorance of the NOC, then the rules are: how to add fractions with different banners. To that, for us, as the bannermen are not mutually simple numbers and multiples of one, you need to know the NOC of the bannermen.

No. No. are written on the dosh, yak may be virishity in the class: 309 d - i, 328, 340 (repetition)

e) ; wink on doshtsi,

e) ; they repeated the short shot, on the control robot the task was done, it was not corrected to the standard.

g) (independently)

h) ; known LCM(21.15) = 3 * 7 * 5 = 105.

6. Order No. 327 write independently.

7. Repetition of earlier twisted material. No. 340.

Speed ​​fractions:

The speed of shots on the control robot is also the same as the order for the standard.

8. Pouch for the lesson.

a) How do you add up and see fractions with different banners?
b) Displaying a badge.
c) Head home: item 11,

For the lesson

Addition of shots with the same banners

Adding fractions of two types:

1. Adding shots with the same banners;
2. Storage of shots from various bannermen.

On the back of the head, stacking shots with the same banners. Everything is simple here. To add fractions with the same banners, it is necessary to add up their numbers, and leave the banner without change.

For example, we store fractions i. We add up numbers, and we leave the banner without change:

Whose butt can be easily understood, as if guessing about the pizza, as it was divided into chotiri parts. If you add pizza to pіtsy, then we’ll wide pіtsy:

butt 2. Add up the fractions.

Vіdpovіdі viyshov have the wrong word. As soon as the task is over, then the wrong fractions are taken care of. In order to find an incorrect fraction, it is necessary to see a part of a new whole. In our view, the whole part is easy to see - two divided into two will be one:

Whose butt can be easily understood, as if guessing about the pizza, as it is divided into two parts. If you add more pizza to the pizza, then you will see one whole pizza:

butt 3. Add up the fractions.

Well, I’m still adding numbers, but the banner is left without change:

Whose butt can be easily understood, as if guessing about the pizza, as it is divided into three parts. If you add more pizza to pіtsy, then we'll add pіtsy:

Example 4. Know the meaning of Viraza

Whose butt folds just like that, like in front. Chiselniks must be folded, and the banner should be left without change:

Let's try to picture a solution for help little one. If you add pizza to pizza and add pizza, then you will see 1 qila and more pizza.

Like a bachite at the addition of shots with the same banners, there is nothing folding. Learn the following rules:

1. Sob to add fractions with the same banners, it is necessary to add up their numbers, and leave the banner without change;

Adding shots with different banners

Now we learn how to add fractions with different banners. If the fractions are stacked, the banners of their fractions may be the same. Ale, however, do not start the stench.

For example, you can stack fractions, shards of stink can make the same banners.

And the axis of the fraction and it is impossible to fold it at once, the shards of these shots are different banners. In such cases, the fractions should be brought to the same (scorched) banner.

Іsnuє kіlka ways to bring shots to the same banner. Today, we can only look at one of them, the shards in other ways can be folded for the cob.

The essence of this method lies in the fact that on the back of the head (NOK) znamenniks in both fractions. Let's let the NOC divide the first shot on the banner and take the first additional multiplier. Similarly, it is necessary to go with another fraction - NOC divide another fraction on the standard and take another additional multiplier.

Then the numbers and banners of fractions multiply by additional multipliers. As a result of these diy, the fractions of some of them had different banners, they turn to shots, those of which have the same banners. And we know how to add such fractions.

butt 1. Let's add fractions

We know the least significant multiples of the banners of both fractions. The denominator of the first fraction is the number 3, and the denominator of the other fraction is the number 2. The least significant multiple of these numbers is 6

LCM (2 and 3) = 6

Now turn to fractions. We divide the NOC into the standard of the first shot and take away the first additional multiplier. NOC is the number 6, and the banner of the first fraction is the number 3. Divide 6 by 3, take 2.

Otrimane number 2 is the first additional multiplier. Let's write it down to the first fraction. For whom the scythe line over the fraction is small, and we write over it the knowledge of the additional multiplier:

Similarly, we fix it with another fraction. Dilimo NOK on the banner of another fraction and we will take another additional multiplier. The NOC is the number 6, and the standard of the other fraction is the number 2. Divide 6 by 2, take 3.

Otrimane number 3 is another additional multiplier. Let's write it down to another fraction. I still know a small scythe line over another fraction and write over it the knowledge of the additional multiplier:

Now we have everything ready for storage. Lost to multiply the numerals and banners of fractions on their own supplementary multipliers:

Marvel at what we have come to. Mi dіyshli of that, that the fractions of some of them were different banners, turned into fractions of those of the same banners. And we know how to add such fractions. Let's finish this butt to the end:

Otzhe, the butt is completed. Add to come out.

Let's try to picture a solution for help little one. If you add pizza to the pizza, then you will see one whole pizza and one more six pizza:

The reduction of shots to the same (scorched) banner can also be depicted as a small one. Grafted fractions to the zagalny banner, we took away fractions i. Qi two fractions are represented by the same pieces of pizza. Vіdminnіst will be less in the fact that once again the stench will be divided into the same parts (pointing to the same banner).

The first baby depicts drib (chotiri pieces out of six), and the other baby depicts drib (three pieces out of six). Having folded qі shmatochki mi otrimuєmo (sіm shmatochkіv іz six). This drib is wrong, we saw a part of it in the new whole. As a result, they took away (one whole pizza and one shot of pizza).

It is significant that we have painted this butt for you already in a report. AT initial mortgages it is not accepted to write so blatantly. It is necessary to take into account the knowledge of the NOC of both banners and the additional multipliers before them, and also to multiply the known additive multipliers to the numbers and banners. Perebuvaya at school, we had a chance to write down the butt like this:

Ale є th zvorotny beck of the medal. As the first stages of the development of mathematics do not make reports, then begin the vinification of the family “And the stars from that number?”, “Why do fractions raptly transform into other fractions? «.

In order to make it easier to stack fractions with different bannermen, you can speed up with an offensive cover instruction:

1. Know the NOC of standard shots;
2. Razdіliti NOK on the banner of skin shot and take an additional multiplier for skin shot;
3. Multiply the numbers and banners of fractions by your additional multipliers;
4. Fold the fractions, like the same flags;
5. If you have an incorrect twang, then you see the whole part;

butt 2. Know the meaning of Viraza .

Quickly follow the instructions, as directed higher.

Krok 1. Know the NOC of banners in fractions

We know the NOC of the banners of both shots. Denominators of fractions of numbers 2, 3 and 4

Krok 2. Divide the NOC on the standard of skin shot and take off the additive multiplier for skin shot

Dilimo NOK on the banner of the first shot. The NOC is the number 12, and the standard of the first fraction is the number 2. We divide 12 by 2, we take 6. We took away the first additional multiplier 6. We write yoga over the first fraction:

Now we divide the NOC on the banner of another shot. The NOC is the number 12, and the signifier of the other fraction is the number 3. We divide 12 by 3, we take 4. We took away another additional multiplier 4. We write it over another fraction:

Now we divide the NOC on the banner of the third fraction. The NOC is the number 12, and the signifier of the third fraction is the number 4. We divide 12 by 4, we take 3. We took away the third additive multiplier 3. We write it down over the third fraction:

Krok 3. Multiply the numbers and the signs of the fractions by your additional multipliers

We multiply the numbers and banners by our additional multipliers:

Krok 4. Add up the fractions, which have the same banners

We came to the point where the fractions of some were different banners, turned into fractions, like the same (glorious) banners. I lost my ability to add up qi fractions. We store:

The addition did not fit in one row, so we transferred the viraz, which was gone, to the next row. Tse allowed in mathematics. If the viraz does not move one row, then transfer it to the next row, when it is required, obov'yazkovo put a sign of equality (=) on the end of the first row and on the cob of a new row. The sign of equivalence on the other row is to talk about those who are continuing the viraz, like a buv on the first row.

Krok 5

We've got the wrong word. We can see a whole part in it. We see:

Otrimali vіdpovіd

Viewing shots with the same standard

There are two types of shots:

1. Viewing shots with the same standard
2. Watching shots from various banners

Spochatku vіdnіmannya shots with the same standard. Everything is simple here. In order to see another fraction from one, it is necessary to see the number of the first fraction, and to deprive the banner of the other fraction.

For example, we know the meaning of viraz. In order to break this butt, it is required, according to the number of the number of the first shot, to take the number of the other shot, and the banner to be left without change. So i zrobimo:

Whose butt can be easily understood, as if guessing about the pizza, as it was divided into chotiri parts. Yakshcho vіd pіtsi vіdrіzati pіtsi, then viyde pіtsi:

butt 2. Know the meaning of virase.

Well, I know the same from the number of the first fraction, I can see the number of the other fraction, and the banner is left without change:

Whose butt can be easily understood, as if guessing about the pizza, as it is divided into three parts. Yakshcho vіd pіtsi vіdrіzati pіtsi, then viyde pіtsi:

Example 3. Know the meaning of Viraza

Whose butt folds just like that, like in front. From the numeral of the first fraction, it is necessary to see the numerals of the second fractions:

Like a bachite at the sight of shots with the same banners, there is nothing folding. Learn the following rules:

1. In order to see another fraction from one, it is necessary from the number of the first fraction to see the number of the other fraction, and to deprive the banner without changing;
2. If there is a wrong breeze in the veins, then it is necessary to see a part in a new whole.

Watching shots from various banners

For example, you can see shots for shots, shards and shots can make the same banners. And the axis of the shot cannot see the shot, the shards of these shots are different banners. In such cases, the fractions should be brought to the same (scorched) banner.

Zagalny znamennik is known for this very principle, as we were honored when stacking shots from different znamenniks. We are aware of the NOC znamennikіv both shots. Let's let the NOC divide the first shot on the banner and take the first additional multiplier, which is written over the first shot. Similarly, the NOC divides the standard of another fraction and takes another additional multiplier, which is written over another fraction.

Let's multiply the fractions by additional multipliers. As a result of these operations, the fractions of some of them had different banners, are converted to shots, those of which have the same banners. And we already know how to virahuvat such fractions.

example 1. Know the meaning of virazu:

Many fractions are made by different banners, so it is necessary to bring them to the same (zagalny) banner.

We know the NOC of the znamenniks in both fractions. The denominator of the first fraction is the number 3, and the denominator of the other fraction is the number 4. The least significant multiple of these numbers is 12

LCM (3 and 4) = 12

Now turn to fractions

We know the additional multiplier for the first fraction. And to that we divided the NOC into the banner of the first shot. The NOC is the number 12, and the sign of the first fraction is the number 3. We divide 12 by 3, we take 4. We write the four over the first fraction:

Similarly, we fix it with another fraction. Dilimo NOK on the banner of another fraction. The NOC is the number 12, and the standard of another fraction is the number 4. We divide 12 by 4, we take 3. We write a triple over another fraction:

Now we have everything ready for the vіdnimannya. Lost to multiply fractions by additive multipliers:

Mi dіyshli of that, that the fractions of some of them were different banners, turned into fractions of those of the same banners. And we already know how to virahuvat such fractions. Let's finish this butt to the end:

Otrimali vіdpovіd

Let's try to picture a solution for help little one. Yakshcho vіd pіtsi vіdrіzati pіtsi, then viyde pіtsi

This is the report version of the decision. Perebuvayuchy at school, we had a chance to turn the stock shorter. It would look like a solution in this way:

Bringing shots and up to a sleeping banner can also be depicted as a small one. Grafting qi fractions to a sleeping banner, we took fractions away. The number of fractions is depicted by the same small pieces of pizza, and once again the stench will be divided into the same parts (brought to the same banner):

The first baby depicts a drіb (highest pieces out of twelve), and the other baby - a drіb (three pieces out of twelve). Vіdrіzavshi vіd eight shmatochkіv three shmatochki us otrimuєmo five shmatochkіv і twelve. Drib and describe five stitches.

butt 2. Know the meaning of Viraza

The number of fractions is made by different bannermen, it is necessary for that coop to bring them to the same (zagalny) banner.

We know NOK znamennikіv tsikh drobіv.

The denominators of fractions of numbers 10, 3 and 5. The smallest multiple of these numbers is 30

LCM(10, 3, 5) = 30

Now we know the additive multipliers for skin shot. Therefore, we divided the NOC into a banner of skin shot.

We know the additional multiplier for the first fraction. The NOC is the number 30, and the standard of the first fraction is the number 10. We divide 30 by 10, we take the first additional multiplier 3. We write yoga over the first fraction:

Now we know the additional multiplier for another fraction. Let's divide the NOC into a banner of another fraction. The NOC is the number 30, and the standard of another fraction is the number 3. We divide 30 by 3, we take another additional multiplier 10. We write yoga over another fraction:

Now we know the additional multiplier for the third fraction. Let's divide the NOC on the banner of the third fraction. The NOC is the number 30, and the signifier of the third fraction is the number 5. We divide 30 by 5, we take the third additional multiplier 6. We write it over the third fraction:

Now everything is ready for viewing. Lost to multiply fractions by additive multipliers:

Mi dіyshli of the fact that the fractions of some of them were different banners, turned into fractions of some of the same (zagalnі) banners. And we already know how to virahuvat such fractions. Let's hang the butt.

The extension of the butt does not fit on one row, so we can transfer the extension to the next row. Don't forget about the equal sign (=) on the new row:

Vidpovidi wiyshov have the right drіb, and nibi us all in power, ale wine is too bulky and ugly. The need to grow її is simpler. What can you rob? You can speed it up.

To speed up the drіb, it is necessary to spread out the numeral and banner on (ND) numbers 20 and 30.

Also, we know GCD of numbers 20 and 30:

Now we turn to our butt and divide the number and banner of the fraction for the knowledge of the GCD, then for 10

Otrimali vіdpovіd

Multiplying a fraction by a number

In order to multiply the fraction by the number, it is necessary to multiply the number of the fraction by the whole number, and leave the banner without change.

butt 1. Multiply drib by the number 1.

Multiply the numeral fraction by the number 1

The record can be understood as taking half 1 time. For example, if you take the pizza 1 time, then you will see the pizza

From the laws of multiplication, we know that the multiplicand and the multiplier are remembered by the months, then the tver will not change. Yakshcho viraz, write it down, then tver like that and earlier you will be equal. I’m still familiar with the rule of multiplying an integer number and a fraction:

Tsey record can be understood, like taking half of one. For example, if there is one whole pizza and we take half of it, then we will see a pizza:

butt 2. Know the meaning of Viraza

Multiply the number of the fraction by 4

Vіdpovіdі viyshov have the wrong word. We can see in the whole part:

Viraz can be understood as taking two quarters 4 times. For example, if you take a pizza 4 times, then you will see two whole pizzas

How to remember the multiplier and the multiplier with the missions, take away the viraz. Vono tezh dorivnyuvatime 2. This viraz can be understood, like taking two birds from four or three birds:

A number that can be multiplied by drib, and the banner of the fraction is allowed, as if the stink of a sleeping dilnik, greater than one.

For example, viraz can be calculated in two ways.

First way. Multiply the number 4 by the number of the fraction, and deprive the banner of the fraction without change:

Another way. Chotirka, which is to multiply, and four, which is in the standard shot, you can speed it up. Speed ​​\u200b\u200bfour fours can be on 4, but the largest sleeping time for two fours is the four itself:

Viyshov the very same result 3. After the short fours, the new numbers are established: two singles. Ale multiplying one with a trio, and farther subdivided into one does not change anything. Therefore, the solution can be written in short:

The speed can be scribbled just the same, if we failed to speed in the first way, but at the stage of multiplying the numbers 4 and 3 we were wrong to speed the speed:

And the axis of viraz can be counted only in the first way - multiply 7 by the fractional banner, and remove the banner without changing:

It is connected with this, that the number 7 and the banner of the shot do not make a sleeping dilnik, greater than one, and apparently do not rush.

Deyakі uchnі pomilkovo skorochuyut number, scho to multiply, і number of fractions. Robiti is not possible. For example, the next notation is not correct:

The speedy fraction of the transfer, scho and numeral and banner will be divided by the same number. In the situation with the viraz, it was robbed only in the number book, the shards of writing down everything is the same, what to write down. Bachimo, who rozdil vykonan only in the numeral book, but in the znamennik no podіl is not seen.

Reproduction of shots

To multiply fractions, it is necessary to multiply their numbers and banners. If you see the wrong thing, you need to see a part in a new whole.

example 1. Know the meaning of virase.

They took it away. Bazhano speedy drib. The fraction can be shortened by 2. Then there is a residual decision on the future of the attack:

Viraz can be understood as taking a pizza from half of the pizza. Let's say we have half of the pizza:

How are sons like half and two thirds? It is necessary to divide the back half into three equal parts:

І take two of them:

We have a pizza. Guess how the pizza looks, divided into three parts:

One piece in the middle of the pizza and taken by us two pieces are matimut the same size:

In other words, go about one and the same rozmir pіtsi. Therefore, the meaning is worthy

butt 2. Know the meaning of Viraza

We multiply the number of the first fraction by the number of the other fraction, and the standard of the first fraction by the standard of the other fraction:

Vіdpovіdі viyshov have the wrong word. We can see in the whole part:

Example 3. Know the meaning of Viraza

We multiply the number of the first fraction by the number of the other fraction, and the standard of the first fraction by the standard of the other fraction:

At vidpovіdі viyshov the correct drіb, but be kind, like yogo speed. In order to speed up the drіb, it is necessary to divide the numeral and banner of this fraction into the largest splnny dіlnik (ND) of numbers 105 and 450.

Otzhe, we know the GCD of numbers 105 and 450:

Now let's divide the number and banner of our vіdpovіdі on GCD, as we knew at once, tobto on 15

Giving a whole number to a fraction

Whether it be a whole number, you can look at a fraction. For example, the number 5 can be yak. You can’t change its meaning on the first five, the shards of viraz mean “the number of five divided by one”, but, apparently, one five:

Return numbers

At the same time, we get to know the other topic of mathematics. Vaughn is called "turning numbers".

Appointment. Return toa a number is called, like when multiplied bya give loneliness.

Let's imagine the appointment of the zminnoy a number 5 and try to read the meaning:

Return to 5 a number is called, like when multiplied by 5 give loneliness.

Can you know such a number, like multiplying by 5 gives one? It appears, it is possible. Let's imagine a five at a sight of a fraction:

Let's multiply this drіb on ourselves, only we remember the calendar and the banner by the moons. In other words, let's multiply the drіb by itself, only flips:

What do you see after what? If we continue to wield the butt, then we take one:

Mean return to 5, є number, shards with a multiplier of 5 come out alone.

The return number can also be known whether there is any other whole number.

You can also know the return number for any other fraction. For whom it is enough to turn over її.

Subdivided a fraction by a number

Let's say we have half of the pizza:

Let's divide її equally into two. How many pіci can be removed by the skin?

It can be seen that after the bottom of the half of the pizza came two equal pieces, leather from which the pizza was stored. Mean skin distance pіtsi.

In a real initial process, it is not necessary to have so much money to add shots with the same banners - there will be enough money from a handyman. More respect is given to us by the leaders, for the hour of their victory, the entire value is taken as one. Moreover, the back of the head is represented її more simply like 2/2, 3/3 thinly. magnitude.

163 . The girl read 2/5, then 1/5 of the book. Have you read part of the book?

164 . Tourists passed 1/7, then 3/7 of the whole route. What part of the route did he lose?

165 . Two tractor drivers mowed 5/9 bows, and the first tractor driver mowed 2/9 bows. Yaku part of the bow beveled by another tractor driver?

166 . The first tractor driver zorav 2/7 of the field, the other - 3/7 of the field. The stench roared at once 10 ha. Designate the area of ​​the field.

167 . Solve tasks 150 (a–c), vicorist vodnimannya shots.

168 . Solve problems 154 (1–2), vicorist in the form of fractions.

169 . 1) Gorobts were sitting on the hills. If the third of the gorobtsіv flew, they were gone

2) Who has won 3/4 of his pennies and lost 200 in the new one nar. How many pennies will you win?

3) On the first day, tourists passed 2/5 of the planned route, and on the other day they lost 15 km. Yaka dozhina route?

4) Your collection has 200 stamps. Behind rest river the number of stamps in the collection increased by 1/4. How many brands did the collection have for that?

170 . Before the deadline, the turner finished 2/8 of the deadline, after the deadline - 3/8 of the deadline, after which youmu had to grind 24 details. How many details can I grind?

171 . W « Arithmetic » L.M. Tolstoy. The man and the squad took pennies from one screen, and nothing was lost. A person taking 7/10 of all pennies, and a team of 690 nar. How much was all the pennies?

172 . Untie in two ways the production of Egyptian papyruses.

1) How many quarters and quarters to give at once 15. Know
number.

2) The number of that yoga half is added 9. Know the number.

173 . Fold the problem, similar to the Egyptian tasks, and untie it in two ways.

Starting from the offensive task in the decisions, the addition of shots with different bannermen is added. If this material was not twisted in the 5th class, then the task, tied with shots, which was left out, should be taken up to the 6th class.

174 . a) The skin of the first pipe resembles 1/2 of the pool, and the other - 1/3 of the pool. Yaku part of the pool is reminiscent of insulting trumpets for 1 year sleeping robot?

b) The first brigade can be vikonati for the day 1/12 of the task, and the other - 1/8 of the task. How often do two brigades go to work for a day of sleepy work?

c) Passenger car for a year passes 1/10 times between places, and vintage - 1/12 times a year. On the yak part tsієї vіdstanі are approaching for 1 year car for an hour ruhu nazustrich one to one?

175 . a) Two tractor drivers for 1 day with a sleepy robot digged 2/3 of the field. The first tractor driver zorav 1/2 of the field. Yaku part of the field was torn by another tractor driver?

b) Two cars, which are going to travel one by one, approached for 1 year on 1/3 of the distance between two places. The first car passed 1/8 of the line. How often did a friend's car pass through the countryside?

c) Through two pipes for a skin year, 1/3 of the pool is reminiscent. Through the first pipe for 1 year reminiscent of 1/10 of the pool. Like a part of the pool will be remembered for 1 year through another pipe?

176 . From the barrels they poured 1/2 water, which was in it, then 1/3, 1/15 and 1/10. Yaku part of the driver wilted?

177 I drank a cup of black caviar and topped it up with milk. Then I drank 1/3 cup and topped it up with milk. Then I drank 1/6 cup and topped up with milk. Zreshtoyu, I finished my cup to the end. Why did I drink more: cavi chi milk?

178 . Old timestamp. 1) Two walkers went out at the same time one to one from two forces. The first one can pass between two villages for 8 year, and the other for 6 year. For some part of the country, the stench is approaching year?

2) Three Teslas are hired for everyday life; the first day was 2/33, the second was 1/11, the third was 7/55. How did all the robots destroy all the stench of the day?

3) For the listing of the creative work, 4 copywriters were hired; the first moment and one rewrite twir at 24 days, the other at 36 days, the third at 20 and the fourth at 18 days. How can I rewrite part of the stench in one day, how can I work it out at once?

179 . 1) The typist overruled a third of the manuscript, then 10 sides. As a result, she handed over half of the entire manuscript. How many sides of the manuscript?

2) Old-fashioned manager. Passing, who overtook another, having asked: « Yak is far from the village, yak is ahead of us? » Vіdpovіv іnshiy passable: « See that village, which one you are walking towards, the third part of everything is between the villages, and if you pass 2 versts, then you will be exactly in the middle between the villages » . How many versts was left for the first passerby to walk?

180 . Head of Adam Rize (XVI century). Three of them played the same amount. Before the first one happened 1/4 tsієї sumi, a part of the other 1/7, and a part of the third 17 florins. How big is the whole win?

Problem solving from the problem book Vilenkin, Zhokhov, Chesnokov, Schwarzburd for grade 5 on the topic:

§ 5. Zvichaynі fractions:
26. Addition of shots with the same banners

1005 Tomatoes with a mass of 5/16 kg and ogirkіv with a mass of 9/16 kg made a lettuce. Yaka masa salad?
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1006 The weight of the weight is 73/100 tons, and the weight of the package is 23/100 tons. Find the weight of the weight together with the package.
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1007 On the first day, potatoes were planted on 2/7 of the plot, and on the next day, on 3/7 of the plot. To what part of the dacha was planted with potatoes in two days?
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1008 One brigade took 7/10 tons of flowers, and the other 3/10 tons less. How many flowers did the other brigade win?
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1009 In two days, 10/11 fields shone. On the first day, 4/11 fields shone. What part of the field was shone another day?
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1010 The tank is 3/5 filled with gasoline, 1/5 of the tank was poured into the barrel. How about part of the tank was filled with gasoline?
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1012 Know the meaning of virus
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1013 Z 11 greenhouses of the vegetable state are 4 planted with tomatoes, and 2 with chickpeas. What part of the greenhouse is occupied with ogirki and tomatoes? Solve the problem in two ways.
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1014 r. For planting the fox, they saw a plot with an area of ​​300 hectares. Yalin was planted on 3/10 of the plot, and pine on 4/10 of the plot. How many hectares are occupied with yalina and pine at once?
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In 1015 the brigade decided to prepare 175 choices for the plan. On the first day, she prepared 9/25 qilkost, the next day 13/25 qilkost. How many virobiv did the brigade prepare in two days? How many virobiv їy have lost their preparation?
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1016 Potato plants were planted on 11/17 of the field of the sheep state. Ogirki planted on 1/17 of the field more, lower with carrots, that on 8/17 of the field is smaller, lower with potatoes. What part of the field is sown with ogirkas and that with carrots? How is a part of the field occupied by potatoes, and carrots and carrots at once?
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1019 We have planned 2 q 70 kg of fruit. Apples were folded 5/9 of all fruits, and pears 1/9 of fruits. How many more apples are there for pears? Solve the problem in two ways.
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1020 The first day the tourist travels 5/14 of the whole route, and the next day 7/14. Apparently, in two days a tourist travels 36 km. How many kilometers do you store the entire route of a tourist?
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1021 The first sermon took 5/13 of the book, and the other 2/13 of the book. As you can see, the first notice took 12 sides more, less than the other. How many sides of the whole book?
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1022 Speeding up jealousy 4/25 + 12/25= 16/25
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1024 260 people cancel the tour. How many buses do you need to book, so a skin bus can have no more than 30 passengers?
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1025 To christen a child. Let's christen up a child, dozhina of some kind
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1026 Find the coordinates of the point A, B, C, D, E, M, K (Fig. 128) and match the coordinates with 1.
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1027 Calculate the perimeter and area of ​​\u200b\u200bthe tricot ABC (Fig. 129)
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1030 Find the given value of x, with some fractions x/15 will be correct, and fractions 8/x will be incorrect.
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1031 Name 3 improper fractions, the number of which is greater, below 100. Name 3 improper fractions, the number of which is greater than 200.
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1033 Dovzhina of a rectangular parallelepiped 8 m, width 6 m and height 12 m. Find the sum of the area of ​​the largest and smallest faces of the parallelepiped.
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1034 For the preparation of 750 m of viscose fabric, 10 kg of cellulose are needed. For 1 m3 of wood, you can take 200 kg of pulp. How many meters of viscose fabric can be taken from 20 m3 of wood?
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1035 Combination lock has six buttons. To do this, you need to press the buttons of the song sequence and dial the code. How many options for the code for which lock?
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1036 Untie equal: a) (x - 111) 59 = 11918; b) 975 (x - 615) = 12675; c) (30 901 - a): 605 = 51; d) 39765: (b - 893) = 1205.
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1037 Solve the problem: 1) Z 30 of the visage day has passed 23. What part of the visage day has passed? 2) 40 swans floated on the stake. Of these, 30 were white. How did the white swans stack up a part of all the swans?
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1038 Find the value of the virus: 1) 76 (3569 + 2795) - (24 078 + 30 785); 2) (43 512-43 006) 805 - (48 987 + 297 305)
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1039 During the first year, the snow was cleared 5/17 of the condition of the road, and for another year, 9/17 of the condition of the road. Yaku part of the road was cleared in the snow for two years? On a part of the road, less than the first year was cleared, less than another?
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1040 On the cloth for the first lyalka, 6/25 m of fabric was stained, and on the cloth for the other lyalka, 9/25 of the fabric. How many fabrics were stained on the cloth? How much more fabric was stained on the cloth of another lyalka, lower on the cloth of the first lyalka?

To hang a part in parts of a whole, a part needs to be divided on a whole.

Task 1. There are four students in a class of 30 students per day. What part of the day?

Solution:

Suggestion: the class has a day of learning.

Knowing the fraction of a number

For those who need to know a part of the whole, for those who need to know a part of the whole, the following rule is true:

If a part of the whole is expressed by a fraction, in order to know that part, you can add a fraction to the banner and multiply the result by її numeral.

Task 1. Bulo 600 rubles, they spent so much money. How many pennies did you spend?

Solution: to know about 600 rubles, you need to divide the sum into 4 parts, we know how many pennies to make one fourth part:

600: 4 = 150 (p.)

Suggestion: spent 150 rubles.

Task 2. Bulo 1000 rubles, they spent so much money. How many pennies were stained?

Solution: From your mind, we know that 1000 rubles are made up of five equal parts. We know how many rubles to add up one p'yata part of 1000, and then we know how many rubles to add two fives:

1) 1000: 5 \u003d 200 (p.) - one fifth part.

2) 200 2 \u003d 400 (p.) - two and a half parts.

Tsі dvі dії poєdnat: 1000: 5 2 \u003d 400 (r.).

Suggestion: 400 rubles were stained.

Another way to know a part of the whole:

In order to know a part of the whole, you can multiply the number by drib, which turns into a part of the whole.

Task 3. According to the statute of the cooperative, for the eligibility of the svіtnyh zborіv, the new may have the least number of members in the organization. The cooperative has 120 members. For which warehouse can a call be made?

Solution:

Suggestion: Calls can be made for presence of 80 members of the organization.

Knowing the number behind the yogo fraction

For the completion of the task, for those who need to know the whole in the yoga part, the following rule is true:

As if a part of a random integer is expressed as a fraction, in order to know the whole, you can divide the fraction into a number book and multiply the result by its standard.

Task 1. They spent 50 rubles, it was like the first sum. Find out the cob sum.

Solution: according to the description of the manager, that 50 rubles is 6 times less than the cob sum, i.e. the primary sum is 6 times more, lower than 50 rubles. To know the qiu sumu, you need to multiply 50 by 6:

50 6 = 300 (r.)

Suggestion: the first amount is 300 rubles.

Task 2. They spent 600 rubles, but it turned out to be the first sum of pennies. Find out the cob sum.

Solution: Let's take into account that the number that is joking is made up of three thirds of the chasm. Over the mind two-thirds of the number, 600 rubles are added. We know one third of the first sum, and then we will make three thirds of the first sum (the first sum):

1) 600: 2 3 = 900 (p.)

Suggestion: the first amount is 900 rubles.

Another way to know the whole part:

In order to know the whole behind the magnitude of the part that bends it, you can divide the magnitude into fractions that bend the part.

Task 3. Vіdrіzok AB, equal 42 cm CD. Know the dozhina vіdrіzka CD.

Solution:

Suggestion: dozhina vіdrіzka CD 70 div.

Task 4. Kavuni was brought to the store. The store sold before the end, after the end - brought kavuns, and lost 80 kavuns to be sold. Did you bring skilki of all cavuns to the store?

Solution: on the back of the head, if a part of the number of brought kavunivs is to become the number 80. For whom, it is acceptable to take as a single total the number of brought kavunivs and we can see the number of kavunivs from it, so far away to sell (sell):

Later, we found out that 80 kavuns should be counted among the total number of brought kavuns. Now we know how many kavuns in the total number of kavuns to become, and then we add up the skіlki kavuns (the number of brought kavuns):

2) 80: 4 15 = 300 (kavuniv)

Suggestion: 300 kavuniv were brought at the store in a flash.