Minus ix module. The value of the module of the number. Geometric sensor module
In mathematics, as in life, situations are often encountered, de negative numbers do not seem to have any practical sense: for example, we cannot drive by kilometer machines (we can’t drive kilometers, it’s not respectful, in some kind of orange) The values are always positive. The very fact in mathematics is a special term - module.
So is the modulus of a number?
Show me what you are saying.
Let’s admit that it’s worth it on the ground and you can collapse forward or backward. Meaning point of direction. 
Otzhe, ty robish croc forward and referring to the point with the coordinate. 
Tse means, how ti pishov come from a mistsya, de standing on the crochet(Single vidrizka). Tobto, see from the cob to the point, children in the bag have appeared, so it goes.
But you can collapse and go back!
If you go to the right point from the coordinate of moving the crochet to the back side, then you will end up at the point from the coordinate. 
Yak vіdstan bulo passed in the first and in another way? Obviously, I’ll see, I’ll pass in the first and in another way, if we are the same and in the same three, even offending points (i), in some of them, I’m leaning in the same way from the point, from which there is a lot of ruch (). 
In such a rank, we have come close to the witness module... Go, the module will show you from any point to the coordinate image to the cob point of coordinates.
So, the modulus of the number will be. The module of the number is also suitable, so you can't be negative!
Modulus - tse absolute value
The module is simple to use:
(- be-yake number).
Also, we know the modulus of the number i:
Basic power of the module
The mi axes have come close to the first power of the module: the module cannot be a negative number.
Tobto, if - the number is more positive, then the module will be more important.
what is it.
If the number is negative, then the module is more expensive than the number:
how much
And yaksho? Well zychayno! Yogo module is also available:
yaksho, then, abo.
The third vipliv, the moduli of the other numbers, tobto:
Now play with it:
Views: 9; 3; 16; eight; 17.
It's easy to deliver, isn't it?
And if the axis is in front of you, the number is:
Yak bootie here? Yak rozkriti module in the whole vipad? Screenplay for the same script. With a selection of signs, there is a sign swirling next to the sign of the module, and then the open module:
- if the value of the viraz is greater than zero, then it is simply the fault of the sign of the modulus,
- if the wieraz is less than zero, then the blame of the z-pid sign of the module, zmіnyuchi at the tsomu sign, as they robbed the price earlier in the butts.
Well, will I try? estimated:
(Forgetting, what is the root?)
Yaksho, what is the sign of maє? Well zychayno,! And, it means, the sign of the module is open, zmіnyuchi is the sign of the virazi:
Rose? Todi try it yourself:
indications:
By the same authorities, Volodya module?
First, if we need to multiply the numbers in the middle of the modulus sign, we can easily multiply the moduli of the numbers. Tobto:
Dangle with mathematical language, module create numbers additional add-on modules of qix numbers.
for example:
Well, why do we need to distribute two numbers (rotation) under the sign of the module? So then, well, for many! Rozib'єmo on two edges of the number (swing) under the sign of the module:
for wash, shho (so yak zero delay is not possible).
Varto will remember one more power of the module: the module of sumi numbers depends on less than dorіvnyu sumi modules of qix numbers:
Why so? It's as simple as that! Yak mi pam'yataєmo, the module is positive. If the module is signified, it can be a number: it is positive, so it is negative. It is permissible that the numbers and the offense are positive. Todi live viraz to the right wing. Visible on the butt:
If there is a modulus sign, one number is negative, but not positive, liva viraz is hungry to appear less than right:
Everything is clear, I can’t see a couple of things corny authorities module.
As for us, such a hang is in front of us:
What can we do with tsim viraz? The meaning of x is not familiar to us, but then it is already known, well, but to mean. The number is greater than zero, but you can simply write down:
The axes mi і came to the іnsh power, as in the backward viglyadі it can be represented as follows:
And why should this hang:
Otzhe, we need to add a sign pіd module. And why is the need for a sign here? Surely, dumb, like a memory, what if the number in the square is greater than zero! Yaksho not pam'yataєsh, marvel at the topic. And why should I go? And the axis scho:
Great, right? Dosage by hand. And now a specific butt for fastening:
Well, why should I? It's funny!
Do you have any problems? Todi go ahead and train on the butts!
1. Know the meaning of viraza, yaksho.
2. Do any numbers have a module?
3. Know the meaning of the virus:
If not everything is clear and difficult in the solutions, then let's get it out:
solution 1:
Otzhe, by means of the meanings in the Otrimaєmo viraz:
Solution 2:
Yak mi pam'yataєmo, opposite numbers modulo rivn. This means that the value of the module is equal to two numbers: i.
Solution 3:
a)
b)
v)
G)
Having captured everything? It's time to go to the fold!
I'll try to forgive the viraz
Decision:
Now, my memory is that the value of the module cannot be less than zero. If the number is positive after the sign of the modulus, then we can simply display the sign: the modulus of the number will be more significant to the number. If the modulus sign is a negative number, then the modulus value is one opposite to the number (that is, the number taken from the "-" sign).
In order to know the module, be it a virazu, for a cob it is necessary to use it, it is more positive or negative.
Enter, meaning the first viraz on the module.
Otzhe, viraz under the sign of the module is negative. Another viraz with the modulus sign is positive, as there are two positive numbers.
The absolute value of a number a- the price of the display from the cob of coordinates to the point A(a).
For the intelligence of the price, for the present a be it a number, for example 3, and I'll try to read it again:
The absolute value of a number 3 - the price of the display from the cob of coordinates to the point A(3 ).
It is becoming clear that the module is priceless, as it is known to be. Let's try to see the cob of coordinates to point A ( 3 )
View from the cob of coordinates to point A ( 3 ) Dorіvnyuє 3 (three units or three crocs).
The module of the number is denoted by two vertical lines, for example:
The module of number 3 is meant like this: | 3 |
The module of the number 4 is meant like this: | 4 |
The module of the number 5 is meant like this: | 5 |
We were whispering the module of the number 3, and we were talking about it, so it’s on the way to 3. So it’s written:
Read yak: "Module number three to three"
Now we will try to know the absolute value of the number -3. I know that it will turn up to the value and put it in the new number -3. Only replace points A vikoristovuєmo new point B... speck A we already vikoristovuvali in the first butt.
Modulo numbers - 3 name from the cob of coordinates to the point B(—3 ).
The appearance of one point before the last cannot be negative. That is, the module of any negative number, being seen, may not be negative. The modulus of the number -3 will be the number 3. Look at the cob of coordinates to point B (-3) one in the same three units:
Read yak: "Module of the number minus three for three"
The modulus of the number 0 is 0, that is, a point with a coordinate 0 is taken from a cob of coordinates, so that a cob of coordinates is displayed to a point O (0) back to zero:
"Zero module to zero"
Robimo visnovka:
- The modulus of a number cannot be negative;
- For a positive number і zero, the modulus is more important to the number itself, and for a negative one - to the opposite number;
- The same numbers may be equal to the number of modules.
opposite numbers
Numbers that are known only by signs antiarrow... For example, the numbers -2 and 2 є are opposed. The stench comes from signs. Number -2 has a minus sign, and 2 has a plus sign, ale mi yogo is not bachimo, so plus, as they said earlier, do not write for the tradition.
Then add other numbers:
The same numbers may be equal to the number of modules. For example, we know modules for -2 and 2
On the little one you can see that the cob appears from the coordinates to the points A (-2)і B (2) however, two crocs.
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Meta lesson
Knowing schoolchildren with such mathematical understandings, like the module of the number;
Navchit schoolchildren on the basis of the knowledge of the modules of numbers;
Zakrіpiti vivcheniy materіal for additional help;
zavdannya
Zakrіpiti knowledge of children about the module number;
For the additional solution of the test enterprises, they reconsider, as they have acquired the scientific materials;
Prodzhuvati and get interested before the lessons of mathematics;
Vykhovuvati at schoolchildren in a logical way, extra nutrition and sitting.
lesson plan
1. The head of the understanding and the value of the module of the number.
2. Geometric zm_st of the module.
3. The module of the number of power.
4. Decision of equalities and irregularities, such as revealing the module of the number.
5. Historical statement about the term "number module".
6. Zavdannya for the consolidation of knowledge passed by those.
7. Homework.
The head of the understanding about the module of the number
The modulus of the number accepts the name of the number itself, since there is not a negative meaning, but the number is negative, but with an opposite sign.
Tobto, the modulus of a small space number a is the same number:
And, the module of the negative drive number x will be the opposite number:
The record will look like this:
For more affordable intelligence, the butt is guided. So, for example, the modulus of the number 3 will be 3, and also the modulus of the number -3, є 3.
Z ts'go viplivє, so on the modulus of the number the absolute value depends on respect, that is, її is absolutely meaningful, but without the urahuvannya of the sign. If they speak more simply, then it is necessary to show the sign from the number.
You can start and see the module of a number like this: | 3 |, | x |, | and | etc.
So, for example, the modulus of the number 3 is denoted | 3 |.
Likewise, on the other hand, the module of the number of nikoli is not negative: | a | ≥ 0.
| 5 | = 5, | -6 | = 6, | -12.45 | = 12.45 і etc.
Geometric module sensor
The module of the number is called vidstan, as it is displayed in single forms from the cob of coordinates to a point. At the same time, the module is open from a geometric point of view.
It is a coordinate line and is significant on two points. Let the number of points be given by such numbers, like -4 and 2.
Now let’s brutally respect the Danish babies. Mi bachimo, the point is marked on the coordinate straight line A according to the number -4; Zvidsy viplya, so dovzhina vіdrіzka OA dorіvnyu to chotir units. In general, dovzhina is like OA, so the number 4 will be the modulus of the number -4.
It is meant and recorded in the given vypadku the modulus of the number in the following rank: | -4 | = 4.
Now vizmemo, and on the coordinate straight line point B.
Tsya point In the future, it will show the number +2, and it will be found, like a bachimo, from the ear of the road to the emergence of two single ones. Three vipliv, so dovzhina vіdrizka OB dorіvnyuє two odinits. The number 2 will be the modulus of the number +2.
The record will look like this: | +2 | = 2 abo | 2 | = 2.
And now there is a bag. As long as you are not aware of the number a and meaningfully on the coordinate straight point A, then in the same way you go from point A to the ear, so that it’s just like the number a.
The record will look like this: | a | = OA.
The module of the number of power
And now, let's try to see the power of the module, look at all the variations and write down the letters behind the other:
In a word, the modulus of a number is not a number, but to mean the modulus of a positive number, which is more important to the number itself: | a | = A, where a> 0;
In another way, modules, which are stored from other numbers, equal: | and | = | -A |. So it’s the power to tell us about those opposite numbers, depending on the number of modules, such as on the coordinate line, if you want to smell and to say the opposite numbers, or to smell like the same appearance from the point of view. The third vipliv, which is the modulus of the other numbers equal.
Thirdly, the modulus of zero is equal to zero in the same way, if the number is zero: | 0 | = 0, if a = 0. Here it is possible to say that the module is zero є zero for the value, so that the ear will appear along the coordinate line.
The fourth power of the module is those who create two numbers for the module before the addition of modules of these numbers. Now the report is understandable, which means. If we go for the value, then we know that the module of create numbers a and b will be ab, or - (ab), if, at ≥ 0, or at - (a at), if, and in greater than 0. The record tse bude viglyadati is like this: | a b | = | A | | B |.
Let us take the authorities for those who have the module of the private form of the distribution of numbers to the address of the modules of the number of numbers: | a: b | = | A | : | B |.
The first are the powers of the modulus of the number:
Decision of indignities and inconsistencies, such as revealing the module of the number
Proceeding to the finalization of the building, like the module of the number, next to the memory, when it’s up to date, it is necessary to open the sign of the module, because of the knowledge of the authorities, which is the task of seeing.
Zavdannya 1
So, for example, if you see the sign of the varto viraz module, if you lay it down from the winter, then open the module next to the value:
Surely, when tasks are violated, they will pop up, if the module is open unambiguously. Yaksho, for example, take
Here, it’s bachimo that such a hanging under the sign of the modulus is non-negative for any values x and y.
Abo, for the butt I take
, Mi bachimo, it is not positive for any z-values.
zavdannya 2
In front of you is a coordinate line. On a straight line, it is necessary to refer to a number, the module of which will be available is 2.
Decision
In the first place, I am guilty of crossing the coordinate line. You already see, for the whole, from the chat on the straight, you need to vibrate the ear to the front, directly and to the single one. Dal, we need to put the specks from the ear to the ear, as they go to the two single views.
Yak bachimo, there are such points on the coordinate straight line two, one of which resembles the number -2, and the number 2.
Historical tip about the module of a number
The term “module” is like the Latin name modulus, which in the transcription means the word “world”. Introducing the term English mathematician Roger Cotes. And the axis is the sign of the modulus of the introductions of the Nimetsian mathematician Karl Weierstraß. When written, the module is referred to as the following symbol: | |.
Food for consolidation of knowledge of material
At today's lesson, you have learned about such understandings, like the module of the number, and now let's be revisited, as you have mastered the topic, taking on the power supply:
1. What is the name of a number, as opposed to a positive number?
2. What is the name of the yaku to wear a number, yaku against a negative number?
3. Give a number, like є opposed to zero. Chi isnuє also a number?
4. Name the number that cannot be the modulus of the number.
5. Give the value to the modulo the numbers.
Home zavdannya
1. In front of you are the images of the numbers, as you need to roztashuvati in the order of the modules. As soon as you correctly identify the project, then you know the nickname of the people, which for the first time introduced the term "module" into mathematics.
2. Attach the coordinate line and know the view from M (-5) and K (8) to the cob.
Instructions
In the same rank, use the same rank, in which you can take the place at once, with a module, or without a module. Move all parts without the module to the right part and open the module, reworking one part into the system of two. Here, there is a general requirement to vkazuvati ODZ, so as soon as you will take part in the joke of the decision.
If you want to take revenge on two modules, equal to yourself, do that rank. Open another module so that it is not the same number. With such a rank, you will see a system of two rivnyans, look for skin conditions and find a solution. For example, given an equal Iх + 3I = Iх-7I. If you want to open the module, you need to remove two lines: x + 3 = x-7 and x + 3 = - (x-7). The first solution is not ma (3 = -7), but the other can be trimmed to x = 2. Thus, the solution to one is x = 2.
As soon as there are two modules in the same number, the solution is to speed up. Schob virishity is also equal, break the area of permissible values into intervals. For whom to know the meaning of x, for which modules reset to zero (privnyati modules to zero). In such a rank, you deny the number of intervals, for which modules rozkrivayutsya with small signs. Then look at the window of the skin, open the module with this sign, which is used when setting one value to the interval. As a result, you will remove the decal of the solution, as it is necessary to be used. For example, given an equal Iх + 2I + Iх-1I = 5. modules to zero, cut off the intervals between -2 and 1. Look at the first interval: x
The addition of a new module or a copy of the existing one on site not presenting special folding for the Joomla coristas, the managers of the administrative panels. Vaughn will take care of the simplicity of storage and automation of vibration operations.
Instructions
Create a login to the admin panel in a standard way and open the "Expanded" menu of the top toolbar for updating the procedure for adding a new or a copy of an existing module to your site... Enter the dialogue window of the "Module manager" and use the "Create" button to speed up the necessary operation. Create signs for additional moduleі open it with the mouse clicker on the row with the name.
Enter the names of the selected mode in the "Subject" field and place the references in the "Show title" and "Enabled" fields. Enter the component position in the drop-down menu of the "Position" row and remember the parameter to allow the opening of an unsettled value. Viber the need to improve the accessibility of the folded module for the driver site and in the pop-up menu of the "Access" field, you can speed up the automatic configuration for the options by vibrating the "Vibrate all menu items" command.
Once again, open the "Expanded" menu of the top toolbar in the program and click on the "Plugin Manager" tool. Raise the utilization menu and add the Content - Load Module item. Open the folds module Let's click Misha on the row and name the dialogue "Parameters" in the right area of the manager's window. Freeze the forerunner on the field "Turn on plugin" and add the item "Unframed" to the viable catalog of the "Style" row. Save the damage to the onslaught of the "Save" button at the top of the toolbar in the utility window.
Go to the side where you want to add the folded module, and insert the loadposition value of the saved_name_of_created_module in the component folder. Go over to the fact that there is no vikorystovuvalasya posilannya, as there is not an itemid, but the starting point of the menu and do not vikorist the parts, tied in a wicked way - obeying theinshi materials, silania with the category. Possibility of the module attribute on the selected page without the middle is tied to the itemid links!
Video by topic
dzherela:
- How to insert a module on a specific side?
dzherela:
- how to open a module in a module
Basic views about the module
module value may be given by the offensive rank: absolute value numbers a(Module) is called as a point, as the image is given a number a on the coordinate straight line, to the cob of coordinates. The value of the vapingє, scho:
In such a rank, in order to open a module, it is necessary to have a sign of submodular rotation. If it's positive, then you can just clean up the sign of the module. If the modular viraz is negative, then it needs to be multiplied by the "minus", and the sign of the module, again, do not write anymore.
The main powers of the module:
Deyaki Methods of Verification of Rivnyans with Modules
Існує кілька typeів рівнян with a module, for those є shortening ways of displaying. At the same time, we don’t know how to do it. For example, for an equal look:
We will use the method to reduce the transition until the end of the day:
And for the people of the mind:
It is also possible to go to the same level as it is, but as the module accepts only positive values, then the right part of the ryvnyannya is positive. Tsya umova needs to be added in the quality of a zagalny obmezhennya for the whole butt. Todi otrimaєmo system:
The offense of the type of ryvnyan can be done in a different way: by opening the module at the prominence of the de-modular viraz there is a sign. In general, we will have to remove the two systems. Hopefully zagalny viglyad The solution is for both types of guides:
For a new version, there are more than one module available. method of intervals, Yakiy Polyagaє in the offensive:
- A set of points on the numerical axis is known, in which the skin is close to zero, where it stands before the module.
- Dalimo all the numerical values on the intervals between the cut-off points and until the sign of the skin with submodular virazs on the cutaneous interval. Respect, for the sign of virazu, you need to present it in a new meaning x from the interval, except the boundary points. Select the value x It is easy to present.
- Distant to the cutaneous cut-off interval, all modules are open, according to the signs on the given interval, and the top-to-bottom line is shown. At the peddler's view, the vipisuєmo only the root of the ryvnyannya, which they enjoy in the last few minutes. Once again: this procedure is carried out for the cutaneous zatrimanyh intervals.
- Learn all formulas and laws in physics, and formulas and methods in mathematics. As a matter of fact, the list is much simpler, there are about 200 necessary formulas in physics, and there are three fewer in mathematics. For skin objects, there are about a dozen standard methods for establishing the basic level of folding, which can also be fully developed, and in such a rank, absolutely automatically, and without difficulty, at the required moment, a larger part of the CT can be displayed. If you want to think too much about the most sophisticated staff.
- Review all three stages of the rehearsal test from physics and mathematics. Kozhen RT can be introduced two times to resolve the offense option. I know on the Central Television, because it’s smart and clear, it’s clear that it’s necessary to know the formulas and methods. Also, in the course of the RT, it is important to sound before the style of setting nutrition in the tasks, as on the Central Television it is possible for unprepared people to be even unaccounted for.
Successful, diligent and forewarning of these three points to allow you to show on the Central Television an indication of the result, the maximum of that on the basis of the results.
Know the pardon?
Yaksho Vi, how can you be built, knew the mercy in main materials, Then write, be weasel, about her to the post. You can also write about the pardon in the social netting (). At the sheet, add a subject (physics or mathematics), called either the number of those or the test, the number of the test, or the point in the text (side) de on your thought є a pardon. Also describe in what the field is close to a grave. Your sheet will not be overlooked, the pardon will be corrected, otherwise you will need to understand why the pardon is not worth it.