Дії з modules of numbers. Modulus of number (absolute value of a number), value, butt, power

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 with the coordinate of turning the crochet to the back side, then you will end up at the point with 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 on the coordinate up to the point of the cob of coordinates.
So, the modulus of the number will be. The module of the number is also expensive, 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 it is less than zero, then the blame of the z-pid sign of the module, zmіnuyuchi at the tsyom 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 zychano,! 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 add additional modules to the number of numbers.

for example:

Well, why do we need to distribute two numbers (rotation) under the sign of the module? So then, well, for many people! 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 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 soon as we have such a hang in front of us:

What can we do with tsim viraz? The meaning of x is unacceptable to us, but then it is already known, well, but to mean. The number is greater than zero, but you can simply write down:

Axes mi i came to the іnsh power, yak in Zagalom viglyadі can be stated like this:

And why should this hang:

Otzhe, we need to add a sign pіd module. And why is the need for a sign here? Svychayno, dumb, as a memory, be it a number in a square, be 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 door?

3. Know the meaning of the virus:

If not everything is clear and difficult in the solutions, then let's get it right:

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.

Also, the value of the first viraz under the sign of the module is negative, the other is positive:

Tse means, open the sign of the module of the first viraz, we are guilty of taking the hangs from the sign "-". The axis is like this:

For another, the symbol of the module is simply visible.

In tsіy statti mi detailed analysis the absolute value of a number... Mi damo value of the value of the module of the number, introduced value and given graphical illustrations. With a great deal of development, add the value of the modulus of the number for the value. Writing about the basic power of the module. In the statistics, we will talk about those, how to start and to find the module of a complex number.

Navigation on the side.

Modulus of number - value, value and butt

a selection of modulus of number... The modulus of the number a will be written yak, tobto, lіvoruch і right-handed from the number we will put vertical lines, so that the sign of the modulus is validated. Guided by the butt. For example, module -7 you can write yak; the module 4.125 is written in yak, and the module is written in the form.

The beginning of the value of the module is carried to, and from the same, і to, і to the whole, і to rational, and to the іrrational numbers, like up to folding numbers. We will talk about the moduli of a complex number in.

Viznachennya.

Modulus of number a- the number a itself, if a is a positive number, or the number -a, which is opposite to the number a, if a is a negative number, if not 0, if a = 0.

The sound of the value of the module is often written in the offensive viglyadі , Tsei notation means,,,,,,,,,,,,,,,,,,<0 .

The recording can be displayed in a larger compact form ... Tsei notation means,, (a more or 0), і, a<0 .

Also maє mіsce i record ... Here okremo slid explain the vipadok, if a = 0. In general, vipadku maєmo, ale -0 = 0, so as zero vvazhayut number, as opposed to itself.

Hopefully add the knowledge of the modulus of the number for the help of the voiced viznachennya. For the butt, we know the modulus of numbers 15 i. It’s almost znakhozhennya. So as the number 15 is positive, then the module for the value of the most expensive number, tobto ,. And why do you need a number module? So yak is a negative number, then its module is suitable for a number that is opposite to a number, tobto, a number ... In such a rank,.

At the end of the point, one visnovok is brought up, which can be manually fixed in practice when the number module is known. The value of the module of the number of slid, modulus of the number to the number by the sign of the modulus without the urahuvannya of the sign And from the viscera the butt is even more clearly visible. I’ll explain what the module of the number is for. absolute value of the number... So the modulus of the number і is the absolute value of the number - at least one і the same.

Modulus of the number yak vidstan

Geometrically, the modulus of a number can be interpreted as see... Hopefully the value of the module of the number through the appearance.

Viznachennya.

Modulus of number a- the price is seen from the cob along the coordinate straight line to the point where the number is a.

The given value is used for the value of the modulus of the number given in the first item. Let us explain the moment. View from the ear to the point where the number is positive, so the number itself. If the ear appears to be zero, then the ear appears to be from 0 to the point from the coordinate 0 to zero View from the cob to the point with the negative coordinate of the previous number, opposite the coordinate of the central point, as well as the road from the cob of coordinates to the point with the coordinate of the opposite number.

For example, the modulus of the number 9 is on the way to 9, so how will it appear from the cob to the point z coordinate 9 on the way to nine. Guided by the butt. The point z coordinate -3.25 is located from point O at 3.25, that is .

The sounding of the value of the module of the number є will be surrounded by the drop of the value of the module of the difference of two numbers.

Viznachennya.

Two numbers difference module a and b roads are located between points of a coordinate straight line with coordinates a and b.

So, if a point is given on the coordinate line A (a) and B (b), then there is one from point A to point B to the modulus of difference of numbers a and b. Whereas in the position of the point In taking the point O (the ear of the ear), then we can see the value of the module of the number, aiming at the ear of the point.

The value of the modulus of a number through the arithmetic square root

іnodі develop the value of the module through the arithmetic square root.

For the butt, the modulus of numbers is numbered -30 and at the given value. Maєmo. Similarly, the two-third module is calculated: .

The value of the modulus of the number through the arithmetic square root can also be used for the values ​​given in the first paragraph of the statistics. Shown tse. Let a - a positive number, with a number -a - negative. Todi і , If a = 0, then .

module power

The module is attracted by a number of characteristic results - module power... Infections caused by the main and most often vicarious from them. When the authorities are grounded, we will spiral to the value of the modulus of the number through the appearance.

Almost from the most obvious power of the module - modulus of a number cannot be a negative number... In the letter viglyadіtse, the power can be written in the form for any number a. The price of power is even easier to obruntuvati: the modulus of the number є appears, but you cannot appear as a negative number.

We pass to the offensive power of the module. Modulus of the number of doors to zero tody and only to those, if the number is zero... Zero modulus є zero based on values. The ear is shown to zero, no point on the coordinate straight line to zero is not shown, so as the skin effective number is set at the viewpoint of one point on the coordinate straight line. The reason for any number, as seen from zero, as a point, as seen as a cob. And the view from the ear to the point, from the point O, is not zero, so as it appears between two points, it is zero and only one, if the number of points match. To bring up the world, bring it to zero if the module is zero.

Ydemo dal. Other numbers may be equal to modules, so, for any number a. Surely, two points on the coordinate straight lines, the coordinates of which є opposite numbers, are located on the same side of the line from the ear to the side, mean the modules of the opposite numbers.

The power of the module is as follows: module create two numbers add additional modules in qix numbers, tobto,. For the value of the module, create numbers a і b dorіvny either a b, which, or - (ab), which There are three rules for the multiplicity of valid numbers, so that the moduli of the numbers a and b are correct either a · b, or - (a · b), as if to bring the analyzed authority.

The module of the part from the spaced a to b, tobto,. Determination of the power of the module. So, if you are private, dobutku, then. Due to the forward power of maєmo ... If it’s too late, it’s faster to be equal, as it’s fair due to the value of the modulus of the number.

The onset of the power of the module will be registered in the eyes of the indigence: , A, b і c - most valid numbers. Writing down the inconsistency є nі scho іnshe yak inertia of a tricycle... As a matter of fact, it became zoomed, at the points A (a), B (b), C (c) on the coordinate straight, and the viral tricycle ABC was easily visible, at which top to lie on the same straight line. According to the designation of the module, the increase in the output of the AV, - the increase in the output of the AS, and - of the increase in the output of the SV. So, as if I don’t change the bag of the two sides, it’s fair to say that , Otzhe, rightly and inept.

Tilki scho brought the irregularity on the road more often to see at the viglyad ... Record the inconsistency of the formulas: “ The modulus of a sum of two numbers does not interchange the sum of moduli of qix numbers". Allegedly, the inertia of the non-middle vaping is due to the inaccuracy, as in the new substitution b in favor of -b, and accept c = 0.

Complex number module

damo the value of the modulus of a complex number... Let it be given to us complex number, Written in an algebraic form, de x and y are the actions of the design numbers, which are obviously the parts of the given complex number z, and are clearly one.

The modulus of the number n is the number of single views from the cob of coordinates up to point n. Moreover, it is not important, in which bik there will be a yak - to the right or to the left of zero.

Sponsor of the distribution of P & G Statistics on the topic "How to know the module of a number"

Instructions

The absolute value of a number is also taken to be called the absolute value of a number. Win is signified by short vertical lines, carrying out the right hand on the date. For example, the module of the number 15 can be written in the following way: | 15 |.

Remember that a module can only be a positive number or a zero. The module of a positive number is important to the number itself. Zero modulus to zero. So for any number n, which is larger than or equal to zero, if the formula | n | = N. For example, | 15 | = 15, so the modulus of the number 15 is 15.

The modulus of a large number will be the same number, but with the opposite sign. So for any number n, less than zero, the formula | n | = -N. For example, | -28 | = 28. The module of the number -28 is the 28th.

You may know modules not only for numbers, but for other numbers. Moreover, there are also rules for other numbers. For example, | 0.25 | = 25, so that the modulus of the number is 0.25 and is equal to 0.25. A | -? | = ?, Tobto the modulus of the number -? will be available?.

When there are robots with modules, the nobility is corianne, and the modules of other numbers must be supplied one to one, so that | n | = | -N |. The main power of the modules. For example, | 10 | = | -10 |. The modulus of the number 10 is 10, in the same way, the modulus of the number is -10. Besides, | a - b | = | B - a |, so you go from point a to point b and go from b to a go one to one. For example, | 25 - 5 | = | 5 - 25 |, tobto | 20 | = | - 20 |.

yak just

Інші news on topics:

The word "module" resembles the Latin modulus, yake, in one's own heart, є changes in the form of the word modus - world. With such a rank, modulus, it is roughly transformed into "little world", "detail". Sponsor of the distribution of P & G Statistics on the topic "Scho also module" Yak multiply the vector by the number Yak

A complex number is a number of the form z = x + i * y, de x і y are numbers, and i = is a clear one (that’s a number, the square of which is 1). In order to understand the argument of a complex number, it is necessary to look at the complex number on a complex area in a polar coordinate system.

The modulus of the number x or the absolute value is called the construction of the form | x |. In the common sense, the module is the norm of the element of a large-scale vector space and it means yak || x ||. The modulus of a number cannot be negative, for one and the same number taken with opposite signs,

Arithmetic works with negative numbers of people are often brought to visonuvati. The most widespread variety of dressings with vimir of high-street temperature. For example, you need to know that the temperature has risen by a few degrees or dropped in the previous day. Zі folded that

In the course of school mathematics, there is a lot of memory, where the root is the solution of the ryvnyannya, that is, the meaning of X, at which the parity of its parts can be reached. As a rule, the zakhodzhennya znakhozhennya module of growth of roots is placed only on square roots, and even the smell itself may be two roots, growth

Complex numbers are called numbers of the form z = a + bi, de a is a valid part, which means Re z, b is an explicit part, which means Im z, i is an explicit unit. Without complex numbers, the extension of the set of arbitrary numbers is denoted by the symbol C. Above complex numbers, one can

Absolutely significant numbers - the module - shows how many times the number is displayed as zero. Brothers in modulus are possible, whether values ​​are not inconsistent in the negative part of the scale, until inconsistencies in positive, or the result of the whole operation will always be positive, as if the meaning appears to be