Middle 69 take revenge alone. Discharge and fire. Vіdnіmannya u stovpchik
To record numbers, people guessed ten signs, which are called numbers. Tse: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
After an additional ten digits, you can write down any natural number.
There are a number of characters (digits) in the number that contain its name.
A number that consists of one sign (digit) is called single-digit. The smallest unambiguous natural number is “1”, the largest is “9”.
A number that is made up of two characters (digits) is called two-digit. The smallest two-digit number is “10”, the largest is “99”.
Numbers written with two, three, four or more digits are called double-digit, triple-digit, four-digit or multi-digit numbers. The smallest three-digit number is “100”, the largest is “999”.
Each digit in the recording of a multi-digit number occupies a central position - a position.
Remember!
Discharge- This is the place (position) on which there is a digit in the record of a number.
The same digit in the number record can have different meanings depending on what rank it is in.
Discharges will be completed from the end of the day.
Discharge one- This is the youngest category, which is how the number will end.
The number “5” means “5” ones, since the five is in the remaining place in the number record (in the ones category).
Tens rank- This is the category that stands before the category of one.
The number “5” means “5” tens, as it stands in the leading place (at the tens place).
Hundred discharge- This is the rank that stands before the rank of tens. The number 5 means 5 hundreds, as it comes in third place from the end of the number (in the hundreds place).
Remember!
Since there is no place in the number, then in the record of the number the number “0” (zero) is placed in its place.
butt. The number “807” has 8 hundreds, 0 tens and 7 ones - this entry is called digit warehouse numbers.
807 = 8 hundreds 0 tens 7 onesEvery 10 units of any category will create a new unit of a greater category. For example, 10 ones make 1 ten, and 10 tens make 1 hundred.
Thus, the value of the number from digit to digit (from ones to tens, from tens to hundreds) increases 10 times. Therefore, the rahunku (number) system, as we know it, is called the tenth number system.
Class and discharge
When recording numbers, the ranks, starting with the right-handed person, are grouped into classes of three ranks each.
Class one but the first class is the class that the first three ranks create (right-handed at the end of the number): rank of ones, rank of tens and rank of hundreds.
Class thousand and the other class is the class that these three categories create: units of thousands, tens of thousands and hundreds of thousands.
| Numbers | Class thousand (other class) | Class one (first class) | ||||
|---|---|---|---|---|---|---|
| hundreds of thousands | tens of thousands | one thousand | hundreds | tens | units | |
| 5 234 | - | - | 5 | 2 | 3 | 4 |
| 12 803 | - | 1 | 2 | 8 | 0 | 3 |
| 356 149 | 3 | 5 | 6 | 1 | 4 | 9 |
We guess that 10 units in the hundred category (in the class of one) equal one thousand (one in the offensive category: one thousand in the class of thousand).
10 hundred = 1 thousandMillion class and the third class is the class that these three categories create: units of millions, tens of millions and hundreds of millions.
One in the category of million is one million and one thousand thousand (1,000 thousand). One million can be written as the number "1,000,000".
Ten such units create a new rank unit – ten million “10,000,000”
Ten tens of millions create a new digit unit - one hundred million and written in numbers “100,000,000”.
| Numbers | Class thousand (other class) | Class one (first class) | |||||||
|---|---|---|---|---|---|---|---|---|---|
| hundreds of millions | tens of millions | one million | hundreds of thousands | tens of thousands | one thousand | hundreds | tens | units | |
| 8 345 216 | - | - | 8 | 3 | 4 | 5 | 2 | 1 | 6 |
| 93 785 342 | - | 9 | 3 | 7 | 8 | 5 | 3 | 4 | 2 |
| 134 590 720 | 1 | 3 | 4 | 5 | 9 | 0 | 7 | 2 | 0 |
| Numbers | Million class (third class) | Class thousand (other class) | Class one (first class) | ||||||
|---|---|---|---|---|---|---|---|---|---|
| hundreds of millions | tens of millions | one million | hundreds of thousands | tens of thousands | one thousand | hundreds | tens | units | |
| 8 345 216 | - | - | 8 | 3 | 4 | 5 | 2 | 1 | 6 |
| 93 785 342 | - | 9 | 3 | 7 | 8 | 5 | 3 | 4 | 2 |
| 134 590 720 | 1 | 3 | 4 | 5 | 9 | 0 | 7 | 2 | 0 |
How to read a rich number
Remember!
Do not call the name of the class one, but also the name of the class, all three digits and zeros.
For example, the number “134590720” is read: one hundred thirty four million five hundred ninety thousand seven hundred twenty.
The number “418 000 547” is read: four hundred and eighteen million five hundred and forty seven.
On our website, to check your results, you can quickly use the calculator for dividing numbers into online ranks.
Important!
Numbers greater than 1,000 Numbering
Select the correct type
KHALITOVA I.M., teacher of cob classes
MOBU "ZOSH No. 48" R. ORENBURG
2. In which series of numbers is the order of increase written?
a) 67490, 67940, 67094, 67049
b) 64079, 67094, 67049, 64094
c) 69074, 69407, 69047, 69704
d) 69047, 69407, 69704, 69740
3. In the number 75394, the number 5 indicates quantity:
b) tens of thousands
c) tens
d) one thousand
4. Who has 400 first class units?
5. Until what date do you need to add 1 in order to subtract 160,000?
6. If the number 14390 is changed to 3 hundred, you get:
7. How many units of the other category are included in the number 84026?
8. Whose number is 7 d.t. 9 od.t. 3 s. 4 days?
9. Which number must be written before the number of unevenness so that it becomes correct?
b) c) = "width = "640" 10. What sign is required to put in order for the record to be correct?
"width="640" Believe yourself!
2. d) 69047, 69407,
3. d) one thousand
Rate your job!
There are no reprieves - “5” (Excellent!)
1 – 2 reprieves – “4” (Good!)
3 – 4 strikes – “3”
5 favors and more – “2”
Literature:
- Mathematics: Test: 4th grade.
Educational method. Pos_bnik \ S. I. Volkova, I. S. Ordinkina. -
M: TOV "Vidavnitstvo Astrel", 2005
1. What is the number in which there are 1 hundred and 2 tens?
2. How many tens does this number have?
3. Show the number 120 in units.
Decision: 1. The number in which there is one hundred and two tens is 120.
2. One hundred is not ten tens. There are also two tens in this number. We have twelve dozen.
3. 120 - 100 units and 20 units. Enter 120 units.
To determine the number of units (tens, hundreds), it is necessary to transfer all the digit units from the required unit to the rank and remove the results of the categorization.
1. How many tens are there in the number 150?
2. How many tens are there in the number 270?
3. How many tens are there in the number 400?
4. How many hundred are there in the number 300?
5. How many hundred are there in the number 900?
Decision: 1. The number 150 has one hundred. 1 cell = 10 des. Also mid 5th dec. The total number of dozens is 15.
2. Middle 270 two hundred. 2 cells = 20 des. Also mid 7th dec. The total number of dozens is 27.
3. Between 400 and hundreds. 4 cells. = 40 des. Ushogo 40 tens.
4. Middle 300 three hundred. Usyogo 3 hundred.
5. Middle 900 nine hundred.
1. How many ones make 25 tens?
2. How many units make 5 hundreds?
Decision: 1. 1 ten has 10 ones. 25 tens have 250 ones.
2. 1 hundred = 100 ones. Then five hundred have more than 500 units.
The height of the boy (Fig. 2) is 1 m 27 cm. How many centimeters?
Small 2. Growth of the boy ()
Decision: 1. To give information about food, you need to guess that 1 m = 100 div. Add up to 100 divs, add 27 and subtract 127 divs.
The width of the window is 150 cm. Help Mikki (Fig. 3) to calculate how many decimeters?
Small 3. Mikki and vikno ()
Decision: 1. 1 dm = 10 cm
2. Between 150 ten and five tens, subtract 15 dm.
Write down five numbers (Fig. 4), each containing 37 tens. How many such numbers can you write down?
Decision: 1 37 tens - the number is 370. If you change a lot of ones, then a lot of tens will not change, then we write 370, 371, 372, 373, 374.
2. You can write down ten such numbers: 370, 371, 372, 373, 374, 375, 376, 378, 379.
List of references
- Mathematics. 3rd grade Navch. for backlighting. install from add. to electron. noses. About 2 years. Part 1/[M.I. Moreau, M.A. Bantova, G.V. Beltyukova and in.] - 2nd view. – K.: Education, 2012. – 112 pp.: ill. - (School of Russia).
- Rudnitska V.M., Yudacheva T.V. Mathematics, 3rd grade. - M: VENTANA-COUNT.
- Peterson L.G. Mathematics, 3rd grade. - M: Yuventa.
- Uchu24.ru ().
- Myshared.ru ().
- Math-ukr.ru ().
Home improvement
- Mathematics. 3rd grade Navch. for backlighting. install from add. to electron. noses. About 2 years. Part 2/[M.I. Moreau, M.A. Bantova, G.V. Beltyukova and in.] - 2nd view. - M: Prosvitnitstvo, 2012, Art. 51 No. 1-5.
- Name the rule by which you can calculate the number of ones, tens, and hundreds in a number.
- How many three-digit numbers can you write, such as 52 tens?
- * How many units become one hundred? How many ones are there in 70 tens? Match the numbers.
2nd grade for pouches ІІІ quarter
1. Tell me how many tens there are in the number 69.
1) 9 2) 69 3) 6 4) 96
2. Enter the number that corresponds to the value of 17 – (8+2)
1) 10 2)11 3) 7 4) 9
3. The value of the virazu is correctly found: 94 – (89 + 1) = 4
1) so 2) neither
4. Zaznach, the record is divided correctly.
From the number 13 you need to calculate the difference between 7 and 5. Petya says this:
13 – 7 – 5
- so 2) no
5. This means how much 60 is greater than 5.
1) at 55 2) at 65 3) at 45 4) at 51
6. Meaning of confirmation.
There are 86 lugs on one pasik, and 12 lugs less on the other. How many tracks are there on the other side?
- 92 2) 74 3) 68 4) 62
7. Indicate which of the entries is for your peers.
1) 16 - a 2) x
8. Why is it equal to 70 dm.
1) 7 cm 2) 70 mm 3) 7 m 4) 70 cm
9. This means that the value is more than 50 dm.
1) 90 cm 2) 3 m 3) 60 mm 4) 5 m 1 dm
10. So, any kind of cutthroat is not a straight cutter.
1) 2) 3) 4)
11 .Show how many numbers are called in the order between the numbers 38 and 48.
1) 8 2) 10 3) 9 4) 12
12 . Think about the number in a series of numbers: 79, 69, 59, 49,
1) 39 2) 48 3) 50 4) 29
13 . This is the number that needs to be written down so that jealousy is true.
1 = 30 + 5
Our first lesson is called numbers. We looked at just a small part of it. In fact, the topic of numbers is great. She has a lot of subtle and nuances, a lot of cunning and useful tricks.
Today we continue the topic of numbers, but again we don’t look at it all, so as not to complicate the beginning with information that is not particularly needed at the beginning. Let's talk about discharging.
Lesson replacementWhat is a discharge?
As they say in simple terms, the rank is the position of the digit in the number of places, and the digit is expanded. For example, take the number 635. This number is made up of three digits: 6, 3 and 5.
The position containing the number 5 is called discharge one
The position containing the number 3 is called in the order of tens
The position containing the number 6 is called in the order of a hundred
Every one of us in our schools has heard such speeches as “units”, “tens”, “hundreds”. Places, in addition to playing the role of the position of a digit in a number, provide us with information about the number. Zokrema discharges tell us the number of dates. The stinks represent how many units, how many tens and how many hundreds.
Let's go back to our number 635. The one's rank contains a five. What can I say? And what about those that discharge one to avenge five units. It looks like this:
The tens rank is replaced by a three. We're talking about those that have tens and three tens. It looks like this:
The category of hundreds is replaced by a six. It should be noted that the category of hundreds is expanded to six hundred. It looks like this:
When we add up the number of ones, the number of tens and the number of hundreds, we get our cob number 635.
There are also senior categories such as the category of thousands, the category of tens of thousands, the category of hundreds of thousands, the category of millions and so on. Such large numbers are rarely seen by us, but it is important to know about them.
For example, in the number of 1645832, the category of ones contains 2 units, the category of tens - 3 tens, the category of hundreds - 8 hundreds, the category of thousands - 5 thousand, the category of tens of thousands - 4 tens of thousands, the category of hundreds of thousands - 6 hundred thousand, the category of millions - 1 million .
At the first stages of changing the ranks, it is important to figure out how many ones, tens, hundreds, and any other number. For example, the number 9 avenges nine units. The number 12 contains two ones and one ten. The number 123 contains three ones, two tens and one hundred.
Grouping of objects
After cleaning up some items, you can select a different grouping of those items. For example, if we have found 35 targets at the yard, we can select discharges to group this target. When objects are grouped, the categories can be read from left to right. So, the number 3 in the number 35 means that there are three tens in the number 35. And this means that 35 tseglins can be grouped into three ten pieces.
Well, let’s group three groups of ten pieces each:
There were thirty tseglins. Ale lost five more targets. I'll call you yak "five one"
There were three tens and five ones.
If we didn’t group things into tens and ones, then we could say that the number 35 is equal to 35 ones. The following grouping would be acceptable:
You can similarly size other numbers. For example, about the number 123. Earlier we were told that this number has three ones, two tens and one hundred. You can also say that this number is 123 units. Moreover, you can group this number in another order, saying that there are 12 tens and 3 ones.
Words units, tens, hundreds, Replace the multiplicities of 1, 10 and 100. For example, in the unit place of the number 123, the number 3 is expanded. With the addition of the multiplier 1, you can write that this unit is placed in the unit place three times:
100 × 1 = 100
If we subtract the results 3, 20 and 100, then we subtract the number 123
3 + 20 + 100 = 123
As we say, the number 123 contains 12 tens and 3 ones. In other words, tens will be grouped 12 times:
10 × 12 = 120
And the units are trichy:
1 × 3 = 3
This can be seen in the example. If there are 123 apples, you can group the first 120 apples 12 times, 10 pieces each:
There were one hundred and twenty apples. Alya lost three more apples. I'll call you yak "three ones"
If we subtract the results 120 and 3, we subtract the number 123 again
120 + 3 = 123
You can also group 123 apples into one hundred, two tens and three ones.
Group of a hundred:
We group two tens:
We group three units:
If we subtract the results 100, 20 and 3, we subtract the number 123 again
100 + 20 + 3 = 123
Well, let’s look at the remaining possible grouping, where the apples will not be divided into tens and hundreds, but will be collected at once. In this case the number 123 is read as "one hundred twenty-three ones" . The following grouping would be acceptable:
1 × 123 = 123
The number 523 can be read as 3 ones, 2 tens and 5 hundreds:
1 × 3 = 3 (three ones)
10 × 2 = 20 (two tens)
100 × 5 = 500 (five hundred)
3 + 20 + 500 = 523
You can also read as 3 ones 52 tens:
1 × 3 = 3 (three ones)
10 × 52 = 520 (fifty-two tens)
3 + 520 = 523
Another number 523 can be read as 523 units:
1 × 523 = 523 (five hundred twenty-three ones)
Why zastosuvati discharge?
It will significantly reduce the cost of calculation. Realize that you and your daughters are in danger. You may have finished your work, it is no longer possible to calculate the remaining amount and cancel the confirmation. Viraz, which needs to be counted, looks like this:
I don’t have a calculator at hand, but I want to quickly write down the evidence and calculate all my calculations. It’s simple, just like we’ve added up units, we’ve added up tens and hundreds. It is necessary to start from the category of one. In the first place, after the sign one (=), it is necessary to put three dots in your thoughts. Replacing these points with a new number (our version):
Now we start folding. The one place of the number 632 has a digit 2, and the one place of the number 264 has a 4. This means that the one place of the number 632 contains two ones, and the one place of the number 264 contains four ones. We add 2 and 4 units - we subtract 6 units. We write the number 6 in the ones place of the new number (our version):
Then there are dozens. The tens place of the number 632 has the number 3, and the tens place of the number 264 has the number 6. This means that the tens place of the number 632 has three tens, and the tens place of the number 264 has six tens. Add 3 and 6 tens - subtract 9 tens. We write the number 9 in the tens place of the new number (our version):
Well, by the end of the day there will be around a hundred. The hundreds place of the number 632 has a digit 6, and the hundreds place of the number 264 has a 2. This means that the hundreds place of the number 632 has six hundreds, and the hundreds place of the number 264 has two hundred. Add 6 and 2 hundreds, subtract 8 hundreds. We write the number 8 in the hundreds place of the new number (our version):
In this way, if you add 264 to 632, you get 896. Of course, you will calculate this type of expression sooner and will begin to despair at your richness. They think that you quickly calculate large numbers, but in reality you calculated small ones. Wait, it’s easier to calculate small numbers than big ones.
Renewal of rank
The digit is characterized by one digit ranging from 0 to 9. Otherwise, when calculating the numerical value in the middle of the solution, the digit may be overdone.
For example, when adding the numbers 32 and 14, there is no re-addition. Adding one more number will give 6 units to the new number. And adding tens of these numbers will give 4 tens to the new number. You'll see 46 or more six ones and four tens .
And the axis, when adding the numbers 29 and 13, will be renamed. Adding ones to these numbers gives 12 ones, and adding tens gives 3 tens. If in a new number, in the units category, write down 12 ones, and in the tens category, write down 3 tens, then the result is:
The value of the virus 29 + 13 is equal to 42, but not 312. How do you fix the track when it is resurfaced? In our case, there was a change in the number of units of the new number. When we added up nine and three units, we got 12 units. And in the unit of one you can write numbers in the range from 0 to 9.
On the right, 12 ones are not easy "twelve one" . Otherwise, this number can be read as "two ones and one ten" . The range of one assignments is less than one. There is no place for dozens there. Here is our mercy. Having added 9 units and 3 ones, they subtracted 12 units, which in another way can be called two ones and one ten. Having written two ones and one ten in one place, we started making mistakes, which resulted in an incorrect type.
To correct the situation, two ones need to be written down in the one place of the new number, and the ten that is missing must be transferred to the next tens place. After adding tens at the butt 29 + 13, we will add to the resulting result the ten that was lost when adding ones.
Now, from 12 ones, two ones are written in the one place of the new number, and one ten is transferred to the offensive place
As you can see from the little one, 12 ones were represented as 1 ten and 2 ones. Two ones are written in the units category of the new number. And the ten was transferred to the ranks of tens. We added these tens to the result of adding tens of numbers 29 and 13. So as not to forget about this, we wrote the number 29 above the tens.
Now we add up dozens. Two tens plus one ten will be three tens plus one ten, which was lost as a result of the previous addition. The result has several tens in the tens order:
Butt 2. List the numbers 862 and 372 behind the ranks.
We start with the category of one. The one digit of the number 862 has a digit 2, the one digit of the number 372 has the same digit 2. This means that the one digit of the number 862 contains two 1s, and the one digit of the number 372 also contains two ones. Add 2 units plus 2 units – subtract 4 units. We write the number 4 in the ones place of the new number:
Then there are dozens. The tens place of the number 862 has the number 6, and the tens place of the number 372 has the number 7. This means that the tens place of the number 862 has six tens, and the tens place of the number 372 has seven tens. Add 6 tens and 7 tens - subtract 13 tens. The rank was increased. 13 tens This ten is repeated 13 times. And if you repeat the ten 13 times, you will get the number 130
10 × 13 = 130
The number 130 is made up of three tens and one hundred. We will write three tens in the tens place of the new number, and one hundred will be added to the next place:
As you can see from the little one, 13 tens (the number 130) was represented as 1 hundred and 3 tens. Three tens were written down from the tens place of the new number. And one hundred was transferred to hundreds. We added hundreds of numbers to the result of adding hundreds of numbers 862 and 372. So as not to forget about it, we wrote 862 above the hundreds.
Now we have hundreds. All hundred plus three hundred will be eleven hundred plus one hundred, which was lost as a result of the previous addition. The result in the hundreds category is subtracted to twelve hundred:
Here, too, it is necessary to renew the order of hundreds, but do not proceed until the decision is completed. For 12 hundreds, you can do the same things you did for 13 in tens.
12 hundred and one hundred, repeated 12 times. And if you repeat a hundred 12 times, you get 1200
100 × 12 = 1200
The number 1200 has two hundred and one thousand. Two hundred are written to the hundreds of the new number, and one thousand is transferred to the thousand place.
Now let's take a look at the butt on display. For starters, we can guess what this is all about. This is an operation that allows one number to be taken out of another. The result consists of three parameters: change, difference and difference. It is also necessary to watch for discharges.
Butt 3. Raise the number 12 from 65.
We start with the category of one. In the place of one of the number 65 there is a digit 5, and in the place of one of the number 12 there is a digit 2. This means that the place of one of the number 65 has five units, and the place of one of the number 12 has two units. From five one there are two units, and three ones are subtracted. We write the number 3 in the ones place of the new number:
Now we are counting dozens. The tens place of the number 65 has the number 6, and the tens place of the number 12 has the number 1. This means that the tens place of the number 65 has six tens, and the tens place of the number 12 has one ten. From six tens we take one ten, subtract five tens. We write the number 5 in the tens place of the new number:
Butt 4. Take the number 15 from the number 32
The unit of number 32 has two units, and the unit of number 15 has five units. Between two units, there are five units, but two units are less, and there are five units.
We group 32 apples so that the first group has three dozen apples, and the other has two apples that are missing:
Well, we need to pick up 15 apples from these 32 apples, so we can pick up five one and one dozen apples. Moreover, pay attention to the discharges.
You can't get five apples from two apples. To vindicate the day, two guilty parties took a bunch of apples from a group of judges (about tens). Alas, you can’t get too distracted, there are dozens of fragments strictly ordered in groups of ten. The order of tens can be assigned to two units or even tens.
So, let’s take one ten from the tens category and give it to two ones:
Up to two apples now there are a dozen apples. There are 12 single apples. And from twelve you can raise five, then come out. We write the number 7 in the ones place of the new number:
Now we are counting dozens. The fragments of tens have given one ten to one, and now there are not three, but two tens. So from two tens we take one ten. Lose one ten. We write the number 1 in the tens place of the new number:
Just so you don’t forget that in each category there is one ten (or a hundred or a thousand), it is customary to put a dot above this category.
Butt 5. Take the number 286 from the number 653
The unit of number 653 has three units, and the unit of number 286 has six units. From three ones you cannot get six ones, so we take one ten from the tens row. We put a dot over the tens place to remember that we took one ten:
Taking one ten and three ones at once makes thirteen ones. From thirteen units you can get six units, and from this one you can get six units. We write the number 7 in the ones place of the new number:
Now we are counting dozens. Previously, the tens place of the number 653 was replaced by five tens, but then we took one ten from it, and now the tens place has several tens. From several dozens you can’t get all tens, so we take one hundred from the category of hundreds. We put a dot over the hundreds place to remember that we took one hundred:
One hundred is taken and dozens are taken at once to create fourteen dozen. From fourteen tens you can get all tens, from six tens. We write the number 6 in the tens place of the new number:
Now there are hundreds. Previously, the hundreds place of the number 653 was equal to six hundred, but now we took one hundred from it, and now the hundred place is five hundred. For five hundred you can get two hundred and get three hundred. We write the number 3 in the hundreds place of the new number:
It is much easier to understand from numbers like 100, 200, 300, 1000, 10000. These are numbers that seem to have zeros. To conclude, the skin discharge has to borrow tens/hundreds/thousands from the offensive discharge. Let's see how it works.
Butt 6
The units of the number 200 have zero ones, and the ones of the number 84 have four ones. You can’t take any ones from zero, so we take one ten from the tens place. We put a dot over the tens place to remember that we took one ten:
But in the category of tens there are not many tens that we could take, because there is also a zero. If the order of tens gives us one ten, we can take one hundred from the order of hundreds. We put a dot over the hundreds place to remember that we took one hundred for the tens place:
One hundred taken is ten tens. From these ten tens we take one ten and give one to one. This one ten and one extra zero one make ten ones at once. From ten units you can get four units, resulting in six units. We write the number 6 in the ones place of the new number:
Now we are counting dozens. In order to remove the ones, we increased to the rank of tens after one ten, but at that moment this rank was empty. So that the order of tens is equal to one ten, we take one hundred in the order of hundreds. Qiu one hundred mi called "ten tens" . One ten was given to one. This means that at the same time in the category of tens there are not ten, but nine tens. Out of nine tens you can get all tens, out of one ten. We write the number 1 in the tens place of the new number:
Now there are hundreds. For the order of tens, we took from the order of hundreds one hundred. From now on, the discharge of hundreds will consist of not two hundred, but one. There are no fragments in the opened hundreds place, we transfer one hundred tenth to the hundred place of the new number:
Naturally, it is difficult to finish milk using such a traditional method, especially from the beginning. Having understood the principle of visibility itself, you can speed up the process in non-standard ways.
The first way is to change the number from zero to one. Next, from the removed result, it is possible to add one to the removed difference, which was originally removed from the changed one. Let's look at the front butt this way:
The number is changed to 200. The number is changed to one. If from 200 you get 1 from 199. Now in the butt 200-84, instead of the number 200, the number 199 is written and the butt 199-84 is added. And the solution to this butt does not pose any particular difficulties. Ones are taken from ones, tens from tens, and a hundred is simply transferred to a new number, leaving the number 84 without a hundred:
We took out the line 115. Now we add one to this line, which we just picked up from the number 200
Residual 116 was removed.
Butt 7. Take the number 91899 from the number 100000
One is taken from 100,000, 99,999 is subtracted
Now from 99999 we can see 91899
To the final result of 8100 we add one, which we took from 100000
Residual 8101 was removed.
Another way is to look at the number in the category as an independent number. There are probably a lot of butts using this method.
Butt 8. Take number 36 from number 75
Also, in the place of one of the number 75, the number 5 is expanded, and in the place of one of the number 36, the number 6 is expanded. From five to six, we take one one in the offensive number, which is from the place of tens.
In the tens place, the number 7 is expanded. Take one unit from this number and add a thought to the left hand for the number 5
And from the number 7 one unit is taken, this number is changed by one unit and increases to the number 6
Now in the place of one of the number 75 the number 15 is added, and in the place of one of the number 36 the number 6. From 15 you can get 6, out of 9. We write the number 9 in the place of one of the new number:
Let's move on to the date of the day, which is in the tens range. Previously, the number 7 was expanded there, but then we took one one from this number, then the number 6 is then expanded there. And in the tens place of the number 36, the number 3 is expanded. From 6 you can get 3, from there 3. We write the number 3 in the tens place of the new number:
Butt 9. Take the number 84 from the number 200
Also, the unit of the number 200 is expanded by zero, and the unit of the number 84 is expanded by four. You can’t take anything away from zero, so we take one one from the upcoming number, which is in the category of tens. Ale in the tens category is also a zero. Zero cannot give us one. In this case, the number 20 is taken as the offensive.
We take one one from the number 20 and add the left hand to the zero, which expands into the ones category. And from the fragments of the number 20 one unit is taken, and this number grows to the number 19
Now the number of units is expanded to 10. Ten minus the original six. Write the number 6 in the ones place of the new number:
Let's move on to the date of the day, which is in the tens range. Previously there was a zero, but this zero together with the leading number 2 created the number 20, from which we took one one. As a result, the number 20 increased to the number 19. It turns out that now the number 9 is expanded in the tens place of the number 200, and the number 8 is expanded in the tens place of the number 84. Nine minus all one to one. We write the number 1 in the tens place of our line:
Let's move on to the date, which goes up to the hundreds. Previously there was the number 2, but this number together with the number 0 was taken to be the number 20, from which we took one. As a result, the number 20 has increased to the number 19. It turns out that now the hundreds place of the number 200 is expanded to the number 1, and in the middle of 84 the hundred place is empty, so we transfer one hundredth to the new number:
This method initially seems complicated and reduces any sense, but it is actually the easiest. Basically, we will be interested in it when adding and identifying numbers in a stacker.
Adding to stovpchik
Adding to the stovpchik is a school operation, so many people remember it, but don’t care to guess it again. Addition to the stacker is added to the ranks - ones are added to ones, tens to tens, hundreds to hundreds, thousands to thousands.
Let's take a look at a bunch of butts.
Butt 1. Sklasti 61 and 23.
First, write down the first number, and below it another number, so that the ones and tens of the other number are written under the ones and tens of the first number. Everything is connected by the addition sign (+) vertically:
Now the units of the first number are added to the units of another number, and the tens of the first number are added to the tens of another number:
We subtracted 61+23=84.
butt 2. Sklasti 108 and 60
Now we add the units of the first number with the units of another number, the tens of the first number with the tens of another number, the hundreds of the first number with the hundreds of another number. Another hundred is only the first number 108. In this case, the number 1 from the hundreds place is added to a new number (our subdivision). As they said at school to “get worn out”:
Apparently, we brought the number 1 to our branch.
When it comes to adding, it makes no difference in what order you write the numbers. Our whole example could be written like this:
The first entry, where the number 108 was on top, is easier for calculation. People have the right to choose any entry, but it is obligatory to remember that units need to be written strictly under ones, tens under tens, hundreds under hundreds. In other words, these entries will be incorrect:
If, when adding up the different digits, a number appears that does not fit into the digit of the new number, then you need to write down one digit from the younger digit, and transfer what was lost to the next digit.
In this case we have to talk about the re-ranking of the category that we talked about earlier. For example, if you add 26 and 98, you get 124. Let's see how it turned out.
We write down the numbers up to the stop. Ones under ones, tens under tens:
We add the units of the first number with the units of the other number: 6+8=14. The number 14 was taken away because it would not fit into the category of one of our species. Since we have a 14th digit, we write one in the category, and we write them down in the category of one of our species. The one digit of the number 14 has the digit 4. We write this digit in the one digit of our type:
Where does the number 1 go from the number 14? This is where things start to get better. Qiu one is transferable to the offensive discharge. It will be added to the category of dozens of our species.
We add tens from tens. 2 plus 9 is equal to 11 plus we add one, which we got from the number 14. Having added our one to 11, we subtract the number 12, which we write in the tens category of our line. Once the decision is over, there is no longer any need to talk about those that fit into the category of dozens. 12 we write down completely, confirming the residual evidence.
Confirmation 124 was withdrawn.
Speaking in the traditional way of addition, when adding 6 and 8 units, 14 units were obtained. 14 ones are 4 ones and 1 ten. Several singles were recorded in the category of ones, and one ten was sent to the next category (up to the category of tens). Then, having added 2 tens and 9 tens, we subtracted 11 tens, plus added 1 ten, which was lost when adding ones. As a result, 12 tens were removed. Twelve dozens of them were recorded in their entirety, establishing the residual evidence124.
This simple butt demonstrates the school situation, so to speak “Whatever we write, one is in our minds” . If you use butts, and after adding up the digits, you will lose a number, so you need to remember, write it down above this digit, where it will then be added. Please don't forget about her:
Butt 2. Sklasti numbers 784 and 548
We write down the numbers up to the stop. Units under ones, tens under tens, hundreds under hundreds:
We add the units of the first number with the units of another number: 4+8=12. The number 12 does not fit into the one category of our type, so from 12 we take the number 2 from the one category and write it into the one category of our type. And the number 1 can be transferred to the offensive discharge:
Now we add up dozens. We add 8 and 4 plus the one that was lost in the previous operation (the one was lost in 12, which is shown in the blue color on the little one). The sum is 8+4+1=13. The number 13 does not fit into the tens place of our type, so we will write the number 3 in the tens place, and move the one to the advancing place:
Now we have hundreds. We add 7 and 5 plus one, which was lost in the previous operation: 7+5+1=13. We write the number 13 to hundreds:
Vіdnіmannya u stovpchik
Butt 1. The number 53 is taken from the number 69.
Let's write down the numbers up to the limit. Ones under ones, tens under tens. Then we follow the discharges. The unit of the first number is subsumed by the units of the other number. From the tens of the first number, the tens of another number are added:
They took away confirmation 16.
butt 2. Find out the value of viraza 95 − 26
The units rank of the number 95 is 5 units, and the units rank of the number 26 is 6 units. From five ones you cannot get six ones, so we take a ten from the tens. This ten and obviously five units become 15 units at once. From 15 units you can get 6 units, you will get 9 units. We write the number 9 in the unit category of our line:
Now we are counting dozens. The tens place of the number 95 was previously 9 tens, and then we took one ten from this place and now there are 8 tens. And the tens place of the number 26 is equal to 2 tens. With eight tens you can get two tens, which will give you six tens. We write the number 6 in the tens place of our line:
The speed with which the skin number enters the number is accepted as the number around it. When identifying large numbers, this method is very simple.
The number 5 is added to the digit of one that has been changed. The number 6 is added to the digit of one. The fives do not raise the six. So we take one one from the number 9. The one of the thought is taken and added left-handedly to the heel. The fragments from the number 9 took one unit, and the whole number changed by one unit:
As a result, the five rolls up to the number 15. Now you can remove 6 from 15. Enter 9. Write down the number 9 for the rank of one of our type:
Let's move on to the tens category. Previously, the number 9 was rotated there, but when we took one unit in the new one, it increased to the number 8. In the tens place of another number, the number 2 is expanded. All minus two will be six. We write the number 6 in the tens place of our line:
butt 3. We know the value of the virus 2412 − 2317
Let's write this down in the column:
In the unit of the number 2412, the number 2 is expanded, and in the unit of the number 2317, the number 7 is expanded. If you don’t take out the double, we take the one from the beginning number 1. When you take the unit of thought, add the word to the two:
As a result, the deuce increases to the number 12. Now you can take out 7 from 12. Enter 5. We write down the number 5 in the digit one of our line:
Let's move on to tens. In the tens place of the number 2412, the number 1 was previously expanded, but when we took one unit into the new one, it returned to 0. In the tens place of the number 2317, the number 1 is expanded. You cannot raise a one from zero. Therefore, we take one unit from the advancing number 4. The taken unit of thought is added to zero. The fragments from the number 4 took one unit, and the whole number changed by one unit:
As a result, the zero increases to the number 10. Now you can take 1 from 10. Enter 9. We write the number 9 in the tens place of our line:
In the hundreds place of the number 2412, the number 4 was previously expanded, but now the number 3 is expanded there. In the hundreds place of the number 2317, the number 3 is also expanded. Three minus three is equal to zero. The same with the thousands digits in both numbers. Two minus two is equal to zero. Since the difference in senior ranks is equal to zero, this zero should not be recorded. So the residual evidence will be 95.
Butt 4. Find out the value of the virus 600 − 8
The one digit of the number 600 is replaced by a zero, and the one digit of the number 8 is the same number. You can’t take a value from zero, so we take one from the coming number. Ale such a quantity is zero. Then we take the number 60 as the next number. We take one unit of this number and add it left-handedly to zero. The fragments from the number 60 took one unit, and the whole number changed by one unit:
Now the number 10 is expanded from the one rank. From 10 you can get 8, resulting in 2. We write the number 2 in the one rank of the new number:
Let's move on to the date of the day, which is in the tens range. The tens place previously had a zero in it, but now the number 9 is in the same place as the other number has a tens place. So the number 9 is transferred to a new number:
Let's move on to the date of the day, which is hundreds. The hundreds place previously had the number 6 expanded, but now the number 5 is expanded there, just like the other number has the hundreds per day. So the number 5 is transferred to a new number:
Butt 5. Find out the value of the virus 10000 − 999
Let's write this in stovpchik:
In the rank of one of the number 10000, the number is expanded to 0, and in the rank of one of the number 999, the number is expanded to 9. You can’t take a nine from zero, so we take one one in the upcoming number, which is from the rank of tens. Ale in the offensive discharge is also zero. Then we take 1000 as the next number and take one from this number:
The next number in this series was 1000. Having taken one, we increased it to the number 999. And the taken one was added to zero.
Further, the calculation did not present any special difficulties. Ten minus nine one to one. A collection of numbers in which the tens place of both numbers gives a zero. A combination of numbers in the order of hundreds of both numbers also gave zero. And the nine in the thousand category was moved to a new number:
Butt 6. Find out the value of the virus 12301 − 9046
Let's write this in stovpchik:
The one digit of the number 12301 is expanded to the number 1, and the one digit of the number 9046 is expanded to the number 6. The one does not add up to six, so we take one one in the offensive number from the tens rank. But in the offensive discharge, zero is displayed. Zero can't give us anything. Then for the coming number we take 1230 and take one as the number:
Vantaged...