multiplication.
Vidminno How to quickly multiply large numbers, how to drain such brown beginnings? Most people find it difficult to remember how to multiply double-digit numbers by single-digit numbers.
And there’s not much to say about complex arithmetic calculations.
But for the sake of vitality, problems in every person’s skin can be developed.
Regular training, not a lot of grinding and stagnation, broken up by centuries,
effective techniques
allow you to achieve stunning results.
- We choose traditional methods (30+8)*(50+7) ;
- 30*50 = 1500 Methods of multiplying two-digit numbers have been tested for decades and have not lost their relevance.
- 30*7 + 50*8 = 210 + 400 = 610 The simplest methods help millions of primary school students, specialized high school students and lyceums, as well as people who are engaged in self-development, to improve their calculus.
- (1500 + 610) + 8*7 = 2110 + 56 = 2166
The easiest way to quickly learn how to multiply large numbers in your mind is to multiply tens and ones.
First, tens and two numbers multiply, then through ones and tens.
- 47*1 = 47 The simplest methods help millions of primary school students, specialized high school students and lyceums, as well as people who are engaged in self-development, to improve their calculus.
- 47*8 = 376 Several numbers are removed and summed up.
- 376*10 + 47 = 3807.
For example, to multiply 38 by 57 you need:
break down the number into
- Memorize the result;
- Memory;
13*11 = 1(1+3)3 = 143
If the arms have a number greater than 10, then one is added to the first digit, and 10 is added from the sum of the arms.
28*11 = 2 (2+8) 8 = 308
Multiplication of great numbers
It’s easy to multiply numbers close to 100 as they are laid out in the warehouse.
- For example, you need to multiply 87 by 91.
(100 - 13)*(100 - 9)
Each number must be paid as a difference of 100 and one more number:
87 – 9 = 78
91 – 13 = 78 - The answer consists of four numbers, the first two of which are the difference of the first multiplier and appears from the other arm, or, for the same reason, the difference of the other multiplier and appears from the first arm. 13*9 = 144
- The other two digits are confirmed - the result of the multiplication appears from two arms. 87*91 = 7944 .
simple ways
multiplied. After the calculation has been brought to automaticity many times, it is possible to master more advanced techniques..
And after about an hour, the problem is that quickly multiplying two-digit numbers will stop bothering you, and your memory and logic will deteriorate dramatically.
Math trainer
Program - a mathematics simulator for strengthening skills
multiplying two-digit numbers by stacking
20 butts are presented for vigour.
Two double-digit numbers need to be multiplied with a stopper.
To start the butts, press the “START” button
At the top left side of the mathematics simulator page, the number of butts that have lost their value is indicated.
On the right side of the side there is a butt that needs to be adjusted.
The left side has a whole stock of recordings made by a stopper. Use the cursor keys to move up/down/right/left-handed. Press buttons 0-9 on the keyboard and enter the intermediate and sub-bag inputs.
If the butt is positioned correctly, 5 points are added.
How to quickly multiply large numbers, how to drain such brown beginnings?
And there’s not much to say about complex arithmetic calculations.
But for the sake of vitality, problems in every person’s skin can be developed.
Regular training, not a lot of grinding and stagnation, broken up by centuries,
effective techniques
allow you to achieve stunning results.
- We choose traditional methods (30+8)*(50+7) ;
- 30*50 = 1500 Methods of multiplying two-digit numbers have been tested for decades and have not lost their relevance.
- 30*7 + 50*8 = 210 + 400 = 610 The simplest methods help millions of primary school students, specialized high school students and lyceums, as well as people who are engaged in self-development, to improve their calculus.
- (1500 + 610) + 8*7 = 2110 + 56 = 2166
Most people find it difficult to remember how to multiply double-digit numbers by single-digit numbers.
The easiest way to quickly learn how to multiply large numbers in your mind is to multiply tens and ones.
First, tens and two numbers multiply, then through ones and tens.
- 47*1 = 47 The simplest methods help millions of primary school students, specialized high school students and lyceums, as well as people who are engaged in self-development, to improve their calculus.
- 47*8 = 376 Several numbers are removed and summed up.
- 376*10 + 47 = 3807.
And there’s not much to say about complex arithmetic calculations.
For example, to multiply 38 by 57 you need:
break down the number into
- Memorize the result;
- Memory;
13*11 = 1(1+3)3 = 143
If the arms have a number greater than 10, then one is added to the first digit, and 10 is added from the sum of the arms.
28*11 = 2 (2+8) 8 = 308
Multiplication of great numbers
It’s easy to multiply numbers close to 100 as they are laid out in the warehouse.
- For example, you need to multiply 87 by 91.
(100 - 13)*(100 - 9)
Each number must be paid as a difference of 100 and one more number:
87 – 9 = 78
91 – 13 = 78 - The answer consists of four numbers, the first two of which are the difference of the first multiplier and appears from the other arm, or, for the same reason, the difference of the other multiplier and appears from the first arm. 13*9 = 144
- The other two digits are confirmed - the result of the multiplication appears from two arms. 87*91 = 7944 .
But for the sake of vitality, problems in every person’s skin can be developed.
Regular training, little effort and stagnation, combined with knowledge, effective methods can achieve impressive results.
Naturally, you need to be familiar with the multiplication table; you can’t quickly multiply the fragments in the Duma using this method without the necessary knowledge.
Memorize intermediate results to help you speak them out loud in your immediate thoughts.
Regardless of the complexity of obvious calculations, after constant training, this method will become your farmer.
These are the simplest ways of multiplying.
- After the calculation has been brought to automaticity many times, it is possible to master more advanced techniques.
- And after about an hour, the problem is that quickly multiplying two-digit numbers will stop bothering you, and your memory and logic will deteriorate dramatically.
- Lesson 3. Traditional multiplication in the Duma
For the most effective effect, you need a good knowledge of the table of multiplication of numbers up to 10, the ability to add numbers (up to three digits), as well as the ability to quickly switch between one action and another, keeping the first result in mind.
As a beginner, it is important to learn how to visualize the arithmetic operations that will take place once you have a picture of your decision, as well as the intermediate results. Visnovok. It is not important to worry about the fact that this method is not the most effective, since it allows you to eliminate correct result
.
Follow other methods.
Another method is arithmetic addition
Bringing the butt up to a handy appearance means finishing the rack on the Duma in a wider way.
Adjust the butt by hand if you need to quickly know the approximate or exact match.
As a beginner, it is important to learn how to visualize the arithmetic operations that will take place once you have a picture of your decision, as well as the intermediate results. The need to practice mathematical patterns is often taught in mathematics departments, universities and schools in mathematics classes.
People now know simple and manual algorithms for solving various tasks.
The axis of the butt stock is:
Butt 49*49 can be configured like this: (49*100)/2-49.
The first factor is 49 per hundred - 4900. Then 4900 is divided by 2, which equals 2450, then 49 is added. At the same time 2401. The addition of 56*92 is calculated as follows: 56*100-56*2*2*2.
Input: 56 * 2 = 112 * 2 = 224 * 2 = 448. For 5600, 448 is entered, 5152 is subtracted. 56 * 6 = 300 + 36 = 336 (or 392-56)
Third action: 336 * 10 + 392 = 3360 + 392 = 3 752 - it’s more complicated here, but you can start calling the first number, in which it is said - “three thousand ...”, and while you say it, add 360 and 392.
Visnovok: The frame of the stack is directly folding, but you can, for obvious knowledge, quickly multiply two-digit numbers into single-digit numbers, ask him.
Add this method to your arsenal.
In a simplified way, the method of operation is a slight modification of the first method.
What’s better is food for amateurs.
As you may note, the methods described above do not allow you to fully understand all the applications of multiplying two-digit numbers.
It is necessary to understand that the use of traditional methods of multiplying for calculations is not always rational, which allows you to achieve the maximum result with the least effort.
Lesson 6. Multiplication in the Duma of any numbers up to 100
- To multiply any numbers up to 100 in the Duma, it is important to quickly select the required algorithm.
For the manual selection, this lesson shows the most manual variations of the skin multiplication technique. Descriptions of most techniques can be divided into universal (additional to any numbers) and private (manual specific types). - Universal methods
For the manual selection, this lesson shows the most manual variations of the skin multiplication technique. The validity of universal methods for multiplying numbers up to 100 taka:
One reference number wiki (Lesson 5):
- All numbers in the ranges up to 30, 40-60, 85-100 – are used as a basis for multipliers.
For the manual selection, this lesson shows the most manual variations of the skin multiplication technique. 98*24, 12*44, 43*103, 23*62
For example:
13 * 17, 18 * 23, 29 * 22, 53 * 61, 88 * 97 etc.
If one number is very close to the manual reference (+/- 3 in 10, 20, 50, 100), another may be the same.
21*67 (21 is close to 20), 48*33 (48 is close to 50), 98*32 (98 is close to 100)
- For the manual selection, this lesson shows the most manual variations of the skin multiplication technique. Vykoristanny of two reference numbers (Lesson 5):
If one reference number is a multiple of another and if one of the reference numbers is manual (10, 20, 50, 100)
Other numbers can be manually multiplied using the traditional methods of Lesson 3, if the tens and ones places are not very large (Lesson 3).
In addition, the traditional method is easy if you don’t know which other method you should use.
- For the manual selection, this lesson shows the most manual variations of the skin multiplication technique. 69*69 = (70-1) 2 = 70 2 – 70*2*1 + 1 2 = 4 900-140+1 = 4 761
Now, you have a serious algorithmic device for multiplying applications by multiplying numbers up to 100. In addition, you can now multiply many applications with multipliers greater than 100. The main factor that affects your multiplication in total is That's the proof of the training.
You can go through the training lower.
Training
If you want to improve your memory on the topic of this lesson, you can use the next step.
The correctness of your inputs and spending on the hour that passes is reflected in the score you take.
Please note that the numbers are very different.
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Rule for multiplying two-digit numbers by two-digit numbers
32 * 45 =
1. 32 — 55 = — 13
2. 68 * 55 = .
However, how many people didn’t realize that this is the same stopper they started with in grades 3-4, without any other records.
can you be more detailed?
de same tse “that same stovpchik”?
Take and multiply 64 * 38 in both ways, resulting in the same results - multiply and add the numbers together.
Well, it’s okay that this method is only suitable for options where one of the numbers is from 90 to 99. Otherwise:
And the story 1440 Remember the method for options, where one of the multipliers in the range of 10 numbers... well, not seriously, tell Kondrashev A.A. Hello, do you know the name of this book?
I offer a lot of thanks for your time.
I’ll ask for a confession for such a story - planning to joke about it at the saint’s new night.
Unfortunately, I don’t know the book itself.
Trying to find out about it
from the outside looking in
There is still nothing on the Internet.
I didn’t take out the insurance for confirmation.
Thank you for spending an hour looking for a book!
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- Large number of two-digit numbers |
- Online trainer
You have the right to be respected by Wikon after 7 correct answers
Vikonannya norm - 3 hvilini
For successful witchcraft, you have the right to familiarize yourself with the theory and practice previous lessons
Multiplication of two-digit numbers |
Theory
In the literal form, the multiplication in the range of two-digit numbers can be manually added to the offensive order:
4) 1440 + 72 = 1752
for the base (first or left hand) number take the number with the largest other digit;
1) 47 x 52 (the number 47 is taken as the base (first) number, fragments 7>2)
2) 47 x 50 = 2350
4) 2350 + 94 = 2444
If one of the numbers ends in 9, then it is more important to proceed in the offensive order:
- For the other (which is right-handed) number, take the number that ends in 9;
- round the other number down to the nearest ten, adding 1 to the next number;
- multiply the first number by the rounded number;
- Take the first number from the result of point 3.
Zavdannya: 39 x 56
1) 56 x 39 (the number 39 is taken for another (which is on the right) number, so it ends in 9)
2) 56 x 39(40-1)
3) 56 x 40 = (50+6) x 4 x 10
50 x 4 = 200;
4) 2240 - 56 = 2184
6 x 4 = 24;
200 + 24 = 224;
224 x 10 = 2240
Since one of the two-digit numbers is higher than 11, then doing this task will be much simpler if you quickly use the technique laid out in Lesson 1.
In many cases, the complex task of multiplying two-digit numbers in your mind will be much easier if you use the factorization method.
Factorization is the process of converting numbers from the simplest numbers.
For example, the number 24 can be converted into either 8 or 3 (24 = 8 x 3) or 6 or 4 (24 = 6 x 4).
The number 24 can also be used in the form of 12 and 2 (24 = 12 x 2), but in the case of arithmetic operations in the mind of the right hand with single-digit numbers.
Along with two-digit numbers, you can also add three single-digit numbers.
For example, 84 = 7 x 6 x 2 = 7 x 4 x 3.
Let us solve the problem of multiplication by additional factorization. Zavdannya: 34 x 42 Factorization of the number 24 gives 8 and 3 or 6 and 4. For the final task, imagine the number 24 as 6 and 4, or, if you prefer, you can choose the addition 8 and 3.
We multiply the first number by 6, then multiply the result by 4:
34 x 6 = 204
204 x 4 = 816
To know which two-digit numbers can be factorized, you need to carefully read the multiplication table.
You can write down all two-digit numbers that can be factorized from the designated
possible ways
Their factorization.
If you are offended by double-digit numbers that are multiplied and subject to factorization, then in most cases it is easier to factorize a smaller number.
Zavdannya: 36 x 72
Zavdannya: 81 x 44
If the numbers are close to the values of a round number, then when they are multiplied, it is reasonable to manually figure out the following formulas: (C+a)(C+b) = (C+a+b)C+ab;
(C-a)(C-b) = (C-a-b)C+ab;
(C+a)(C-b) = (C+a-b)C-ab**, where “C” is close to two numbers that are multiplied, a round number, and “a” and “b” are the differences between the multiplied numbers and a round number.
Zavdannya: 67 x 64
(60 + 7) x (60 + 4) = (60 + 7 + 4) x 60 + 7 x 4 = 71 x 60 + 28 = 4260 + 28 = 4288
Zavdannya: 39 x 38
(40 - 1) x (40 - 2) = (40 - 1 - 2) x 40 + 1 x 2 = 37 x 40 + 2 = 1480 + 2 = 1482
Zavdannya: 41 x 38
- (40 + 1) x (40 - 2) = (40 + 1 - 2) x 40 + 1 x 2 = 39 x 40 - 2 = 1558
- Multiplying two-digit numbers, the first digits (tens) being equal, and the other digits (ones) giving a total of 10, it is best to work in this order:
- multiply the first digit of two-digit numbers by the digit multiplied by one;
multiply other digits of two-digit numbers;
Place the results in paragraph 1 and paragraph 2 one by one.
Zavdannya: 76 x 74
Don’t get discouraged and don’t give up if you initially find it difficult to multiply double-digit numbers.
For a successful victor, such an operation requires practice, as well as a creative approach.
* To memorize intermediate calculation results, you can use mnemonics based on the association of numbers with images. ** Prove the formulas by means of transformation: (C+a)(C+b) = (C+a)C+(C+a)b = C 2 +Ca+Cb+ab = (C+a+b)C+ab ;(C-a)(C-b) = (C-a)C-(C-a)b = C 2 -Ca-Cb+ab = (C-a-b)C+ab;
(C+a)(C-b) = (C+a)C-(C+a)b = C 2 +Ca-Cb-ab = (C+a-b)C-ab.
*** Proof of the method: together with the formula, which is stagnant in the previous method (C+a)(C+b) = (C+a+b)C+ab;
Watch below the cheat sheet in the full form.
Reproduction directly on the site (online)
*| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 | 36 | 38 | 40 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 | 39 | 42 | 45 | 48 | 51 | 54 | 57 | 60 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56 | 60 | 64 | 68 | 72 | 76 | 80 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 | 80 | 85 | 90 | 95 | 100 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 | 78 | 84 | 90 | 96 | 102 | 108 | 114 | 120 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 | 91 | 98 | 105 | 112 | 119 | 126 | 133 | 140 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 | 104 | 112 | 120 | 128 | 136 | 144 | 152 | 160 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 | 117 | 126 | 135 | 144 | 153 | 162 | 171 | 180 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | 190 | 200 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 | 143 | 154 | 165 | 176 | 187 | 198 | 209 | 220 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 | 156 | 168 | 180 | 192 | 204 | 216 | 228 | 240 |
| 13 | 13 | 26 | 39 | 52 | 65 | 78 | 91 | 104 | 117 | 130 | 143 | 156 | 169 | 182 | 195 | 208 | 221 | 234 | 247 | 260 |
| 14 | 14 | 28 | 42 | 56 | 70 | 84 | 98 | 112 | 126 | 140 | 154 | 168 | 182 | 196 | 210 | 224 | 238 | 252 | 266 | 280 |
| 15 | 15 | 30 | 45 | 60 | 75 | 90 | 105 | 120 | 135 | 150 | 165 | 180 | 195 | 210 | 225 | 240 | 255 | 270 | 285 | 300 |
| 16 | 16 | 32 | 48 | 64 | 80 | 96 | 112 | 128 | 144 | 160 | 176 | 192 | 208 | 224 | 240 | 256 | 272 | 288 | 304 | 320 |
| 17 | 17 | 34 | 51 | 68 | 85 | 102 | 119 | 136 | 153 | 170 | 187 | 204 | 221 | 238 | 255 | 272 | 289 | 306 | 323 | 340 |
| 18 | 18 | 36 | 54 | 72 | 90 | 108 | 126 | 144 | 162 | 180 | 198 | 216 | 234 | 252 | 270 | 288 | 306 | 324 | 342 | 360 |
| 19 | 19 | 38 | 57 | 76 | 95 | 114 | 133 | 152 | 171 | 190 | 209 | 228 | 247 | 266 | 285 | 304 | 323 | 342 | 361 | 380 |
| 20 | 20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200 | 220 | 240 | 260 | 280 | 300 | 320 | 340 | 360 | 380 | 400 |
How to multiply numbers using a stopper (mathematics video)
To practice and learn fluently, you can try multiplying numbers using a footstool.
There are three zagalny way: direct multiplication, support number method and Trachtenberg method.
Master their skills so that your skin can be damaged in one or another situation.
You can practice removing skills using an additional training table.
Straight multiplying
This method is manual if one of the multipliers is in the range of 12-18 or ends at 1, and the other one significantly increases.
One of the many ideas is divided into tens and ones.
Then multiply the other multiplier by tens, then ones and add.
For example, 62x13 = 62x10 + 62x3 = 620 + 186 = 806.
Sometimes it’s easy to break the larger multiplier into tens and ones: 42×17 = 17×40 + 17×2 = 714.
Reference number method
To master the method, a little practice is required, but it is even easier if the two factors are close numbers.
Zokrema is the main method for multiplying two-digit numbers by square.
The reference number is a round number, close to both multipliers.
It may be less than both multipliers, more than both multipliers, or between them. As a reference number, select numbers that are easy to multiply.
- For example, 50 or 100, since the stench is close to two times.
- It is clear that, as the reference number and multipliers are related, the technique of multiplying slightly varies.
- A. The reference number is less than two factors.
For example, you need to multiply 32 by 36. The reference number is 30. The multipliers greater than the reference number are 2 and 6.
- Add 6 to the first multiplier and multiply the number on the support: 38 × 30 = 1140.
- Add an additional 2 and 6 bottles: 1140 + 2×6 = 1152.
- b.
The reference number is greater than two factors. For example, you need to multiply 43 by 48.
- The reference number is 50. Multipliers less than the reference number are 7 and 2.
- Take 2 from the first multiplier and multiply the number on the support: 41 × 50 = 2050.
- Add an additional 7 and 2: 2050 + 7×2 = 2064.
V. The reference number is between multipliers.
For example, you need to multiply 37 by 42.
After all, Trachtenberg’s method is not entirely original, for which it is better to master multipliers before ochima.
Next, practice without writing down the output numbers.
- Let's use the butt method to multiply 87 by 32.
- Submit the numbers sequentially: 8732. Multiply two inside numbers (7 and 3), two outside numbers (8 and 2) and add.
- Come out 37.
