In this article we will look at the topic of multiplying numbers in more detail.
When multiplying numbers, there are several methods or techniques. I'll try to describe them. To begin with, we will divide into two sections and describe these cases.
1) Multiplication of two-digit numbers. Depending on the type of numbers, several methods can be distinguished here. In general, for multiplying two-digit numbers, it is very useful to know the multiplication table for numbers up to 20 (usually in school they teach up to 10 and stop). I recommend learning the table up to 20. Then, if you wish, continue memorizing the multiplication table up to 100. This will help with multiplying three- and four-digit numbers.
2) Under specific in different sources you can find different numbers. Starting from banal multiplication by 10 to multiplication by 75. Some sources give multiplication by some specific three digit numbers. This will also include multiplication by single digit numbers.
Depending on the numbers I choose the method. Don’t rush to multiply, first decide on the method, then rush to multiply using the chosen method. Selecting a method takes a fraction of a second, but choosing the most simple method saves significantly more time and effort.
I’m not at all claiming that I’m a super-calculator, I just got a calculator in the 11th grade, and before I bought it I could easily calculate in my head - and if I had paper at hand, then... Now for me it’s like a rediscovery - I decided to share it with you methods, and remember long-forgotten things.
1) Multiplication of two-digit numbers.
A) The cross method is suitable for multiplying two-digit numbers. This is the most common method. I'll show you on specific examples. Then we will derive a general rule.
Example 1. You need 27*96.
Imagine 27*96=2*9*100+(2*6+7*9)*10+7*6=1800+750+42=2550+42=2592
Example 2. You need 39*78. 39*78=3*7*100+(3*8+9*7)*10+9*8=2100+870+72=2970+72=3042
I think that's enough. With normal multiplication (in a column), you do the same thing - just in a different order: “You multiply 27*6, that is, multiply 6*7+20*6=6*7+2*6*10, write it down in one line and multiply 27 *90=(9*7*10+20*9)*10=(9*7*10+2*9*10)*10 - due to the fact that the digit is 1 more (multiply by 10) You write with offset. Now you can even paint
27*96=(20+7)*(90+6)=20*90+7*90+20*6+7*6=2*9*100+7*9*10+2*6*10+7*6=2*9*100+(7*9+2*6)*10+7*6 ".
This method is rarely shown in schools because it is difficult to explain and not all children will understand it. But as you can see, it is simpler for oral multiplication. Here you can see that the formula (a+b)*(c+d) and the peculiarity of the decimal number system are used. Practice and you will get used to it.
So the rule: To multiply one two-digit number by another two-digit number:
1) multiply the tens numbers among themselves, multiplying by 100,
2) multiply the “outer” digits of the numbers with each other in pairs (right and left), and multiply the internal digits with each other when writing in a line. Add the result and multiply by 10. (When writing in a column, they are multiplied by a cross: units of one number by tens of another and vice versa. The result is added and multiplied by 10.)
3) multiply the digits of the units.
4) Add 3 results: 1)+2)+3).
Actually, there are no other combinations of pairwise multiplication (there are only 4 of them) for two-digit numbers. But you can sum it up in different ways. This is why the ways of writing multiplication methods change. Let me remind you that at school they teach only one method (let’s call it the “tick” method), when numbers are multiplied in sequence. In the proposed “cross” method, multiplication and addition also alternate, but “easier” numbers are added. The “tick the box” method, which is taught in school, is simply the most convenient for “learning”. Whether children multiply quickly and conveniently or not is of no concern to anyone. Agree, few people understood the above method the first time. Many read it quickly, did not understand anything, and... continue to multiply as they were taught. Why I call one method the “cross” method, and the other “tick” method will be clear from the figures.
b) Multiplication of numbers of the form ( 10x+a)*(10x+b), where x is the same number of tens and a+b=10 (1) For example, 51*59; 42*48; 83*87; 94*96, 65*65, 115*115. That is, you see that their tens are the same, and the sum of their ones gives 10.
Rule: In order to multiply two numbers of the form (1), it is necessary to multiply the number of tens X by a number greater than 1 - this is (X+1), and to the right assign the result of multiplying units in the form of a two-digit number.
We remember that form (1), the numbers satisfy the following condition: the number of tens is the same, the digits of the ones of two numbers add up to 10.
Example 3. 51*59=? We see that the numbers satisfy (1). 5*6 (after all, 5+1=6), 5*6=30. To 30 on the right we write 09=1*9 (we assign not 9, but 09) Result 3009=51*59.
Example 4. 42*48=? 4*5=20 and 2*8=16. Result 2016=42*48
Example 5. 25*25=? 2*3=6 and 5*5=25 Result 625 As you can see, the vaunted methods of multiplying 15*15,25*25, etc. (or squaring numbers of the form a5*a5) this is just a special case of the above-described method - 1b), which in turn is an even more special case.
Note, I first wrote that a=1...9, but this is not entirely correct; you can also multiply 372*378 (the number of tens is 37). The method will also be valid for such cases. 37*38=1406 and 2*8=16 Total result 140616=37*38. Check it out. Of course, the multiplication rule under b) can be proven strictly mathematically, but I don’t have time for that right now. Take my word for now or prove it to yourself. Better instead, for now I’ll write down other rules that are sitting in my head.
Found the time to write down the proof
Let the first factor be 10x+a, the second factor be 10x+b, where a+b=10 x the number of tens, then
(10x+a)*(10x+b)=100x*x+10xa+10xb+ab=10x*(10x+a+b)+ab= =10x*(10x+10)+ab=10x*10(x +1)+ab=x*(x+1)*100+ab From here we see that the rule is written mathematically, which is written in words.
c) Multiplication of numbers of the form 48 * 52; 37*43, 64*56. Those. multiplication of those numbers that are spaced from the “base” by the same number of units. For such numbers, a simple formula is applicable (a+b)*(a-b)=(a-b)*(a+b)= a 2 -b 2
Example 6. 48*52=(50-2)(50+2)=2500-4=2496
Example 7. 37*43=(40-3)*(40+3)=1600-9=1591
d) Multiplication identical numbers- squaring. For some numbers it is convenient to use Newton’s binomial formula: (a±b) 2 =a 2 ±2*a*b+b 2
Example 8. 38*38=(40-2)*(40-2)=1600-2*40*2+4=1600-160+4=1444
Example 9. 41*41=(40+1)*(40+1)=1600+2*40*1+1=1681
d) Multiplying two numbers ending in 5. (the number of tens of the two factors differs by 1)
Let's look at a few examples: 15*25=375; 25*35=875; 35*45=1575; 45*55=2475 As you can see, the result of such a multiplication always ends in 75. The calculation is done in a similar way -1b) with the addition of 75 to the right of the result: the smaller number of tens is multiplied by the number resulting from the number of tens of the second factor with the addition of 1, to the right of this We add 75 works.
Example 10. 25*35 - - - 3+1=4 (to the larger number we add 1 to the number of tens); 2*4=8 add 75. The result is 875. Similarly 15*25=? 2+1=3; 1*3=3 15*25=375.
The ability to instantly count in your head can become an invaluable aid in work and in the fast paced life of a modern person. Accurate calculations without the use of special devices significantly save time, allow you to constantly train your memory and, to hide it, cause admiration among people who are not endowed with such abilities.
How to multiply quickly big numbers How to master such useful skills? Most people find it difficult to verbally multiply two-digit numbers by single-digit numbers. And there is nothing to say about complex arithmetic calculations. But if desired, the abilities inherent in each person can be developed. Regular training, a little effort and the use of effective techniques developed by scientists will allow you to achieve amazing results.
What will help you learn quickly?
Reaching the heights of child prodigies is quite possible. Especially if you use the abilities given by nature wisely.
- Not bad if you're blessed logical thinking, concentration and ability to identify important factors.
- A good start is knowledge effective ways addition and subtraction, understanding of algorithms.
- The quality of learning is influenced by the ability to daily train memory and attention, making tasks more complex.
What are the most effective ways to learn how to multiply two-digit numbers in your head as quickly as possible?
Choosing traditional methods
Methods of multiplying two-digit numbers that have been proven for decades do not lose their relevance. The simplest techniques help millions of ordinary schoolchildren, students of specialized universities and lyceums, as well as people engaged in self-development, improve their computing skills.
Multiplication using number expansion
The easiest way to quickly learn to multiply large numbers in your head is to multiply tens and units. First, the tens of two numbers are multiplied, then the ones and tens alternately. The four numbers received are summed up.
To use this method, it is important to be able to remember the results of multiplication and add them in your head.
For example, to multiply 38 by 57 you need:
- factor the number into (30+8)*(50+7) ;
- 30*50 = 1500 – remember the result;
- 30*7 + 50*8 = 210 + 400 = 610 – remember;
- (1500 + 610) + 8*7 = 2110 + 56 = 2166
Naturally, it is necessary to have excellent knowledge of the multiplication table, since it will not be possible to quickly multiply in your head in this way without the appropriate skills.
Multiplication by column in the mind
Many people use a visual representation of the usual columnar multiplication in calculations. This method is suitable for those who can memorize auxiliary numbers for a long time and perform arithmetic operations with them. But the process becomes much easier if you learn how to quickly multiply two-digit numbers by single-digit numbers. To multiply, for example, 47*81 you need:
- 47*1 = 47 – remember;
- 47*8 = 376 – remember;
- 376*10 + 47 = 3807.
Speaking them out loud while simultaneously summing them up in your head will help you remember intermediate results. Despite the difficulty of mental calculations, after some training this method will become your favorite.
The above multiplication methods are universal. But knowing more efficient algorithms for some numbers will greatly reduce the number of calculations.
Multiply by 11
This is perhaps the simplest method that is used to multiply any two-digit numbers by 11.
It is enough to insert their sum between the digits of the multiplier:
13*11 = 1(1+3)3 = 143
If the number in brackets is greater than 10, then one is added to the first digit, and 10 is subtracted from the amount in brackets.
28*11 = 2 (2+8) 8 = 308
Multiplying large numbers
It is very convenient to multiply numbers close to 100 by decomposing them into their components. For example, you need to multiply 87 by 91.
- Each number must be represented as the difference between 100 and one more number:
(100 — 13)*(100 — 9)
The answer will consist of four digits, the first two of which are the difference between the first factor and the subtracted from the second bracket, or vice versa - the difference between the second factor and the subtracted from the first bracket.
87 – 9 = 78
91 – 13 = 78 - The second two digits of the answer are the result of multiplying those subtracted from two parentheses.
13*9 = 144
- The result is the numbers 78 and 144. If, when writing down the final result, a number of 5 digits is obtained, the second and third digits are summed.
Result: 87*91 = 7944 .
These are the most simple ways multiplication. After using them multiple times, bringing the calculations to automation, you can master more complex techniques. And after a while, the problem of how to quickly multiply two-digit numbers will no longer worry you, and your memory and logic will improve significantly.
Found a mistake? Select it and click left Ctrl + Enter.
Difficulty level: Easy
1 step
The simplest case is when you have to multiply a single-digit number by a two-digit number. For example, 8 and 23. Let's decompose the number 23 into its constituent tens and units, namely 20 and 3. Multiply each of the numbers by 8. As a result, 8*20=160, 8*3=24. Now let's add these two results: 160+24=184. It's very simple. You just need to practice.
Step 2
Now let's complicate the task. We will multiply two two-digit numbers. For example, we multiply 21 by 47. We also use the method of decomposing numbers. You just need to decide which number is more convenient to decompose. It is always more convenient to multiply numbers by a small number. Therefore, let's decompose 21 into 20 and 1. Multiply 47*20 and 47*1. As a result, 47*20=940, and 47*1=47. Add 940+47=987.
Step 3
To reinforce this, let’s multiply at first glance complex numbers 99*63. What number should be expanded in this case? It’s better to decompose the smaller 63 into 60 and 3. Multiply 99*60 and 99*3. But multiplying 99 by 60 and 99 by 3 is also not easy. Let's see that 60 is 20+20+20. Let's multiply 99*20. In your head it's just 99*20=1980. That is, 99*60=1980+1980+1980. And adding these three numbers is also not easy. And if so 99*60=(2000-20) + (2000-20) + (2000-20)=6000-60=5940. I replaced the number 1980 with (2000-20). Remember the number 5940. Now let's multiply 99 by 3. We see that 99*3=99+99+99. And if so, 99*3=(100-1)(100-1)=300-3=297. That is, we now have two numbers: 5940 and 297, which must be added. Let's get started, 5940+297=5940+(300-3)=6240-3=6237
Thus, 99*63=6237.
- The most important thing is practice. Train and apply your skills in life.
Additional materials
Dear users, do not forget to leave your comments, reviews, wishes. All materials have been checked by an anti-virus program.
Educational aids and simulators in the Integral online store for grade 4
Simulator for the textbook by L.G. Peterson Simulator for the textbook M.I. Moro
Multiplying multi-digit numbers by single-digit numbers
1. Write the given sentences in the form of numerical expressions and solve them.
1.1. Multiply the number 67 by the number 4.
1.2. Multiply the number 248 by the number 9.
1.3. Multiply the numbers 482 and 7.
2. Solve examples.
Solving word problems involving multiplying a single-digit number by a multi-digit number
1. Dad harvested potatoes and put them in bags. Each bag contained 35 kg of potatoes. How many kg of potatoes did dad harvest if the crop fit into 9 bags?
2. The electricity tariff is 4 rubles 10 kopecks per kilowatt. How much should you pay if a total of 8 kilowatts are used?
3. For the new school year, 9 were purchased simple pencils 2 rubles 10 kopecks per pencil, 18 notebooks at 5 rubles per notebook and 12 books at 80 rubles per book. How much money was spent on all purchases?
4. To participate in the school mathematics Olympiad, all schoolchildren were divided into equal groups. Second grade schoolchildren were divided into 4 groups of 17 people, third grade students were divided into 6 groups of 12 people, and fourth grade students were divided into 5 groups of 15 people. How many students were there in the second, third, and fourth grades? How many students in total took part in the Olympiad?
5. Soldiers took part in the parade in honor of May 9th. They lined up in 5 groups of 12 ranks in each group. How many soldiers are there in the group if there are 8 soldiers in the line? How many soldiers took part in the parade?
Multiplying a multi-digit number by a two-digit number
1. Solve examples.
| 470 * 53 = | 357 * 49 = | 214 * 22 = | 693 * 24 = |
| 453 * 33 = | 285 * 73 = | 204 * 76 = | 349 * 35 = |
| 517 * 44 = | 614 * 28 = | 854 * 25 = | 949 * 15 = |
2.1. Multiply the number 675 by the number 46.
2.2. Multiply the number 688 by the number 95
2.3. Multiply the numbers 832 and 48.
Solving word problems involving multiplying a multi-digit number by a two-digit number
1. The factory sews children's clothes. Over the course of a month, she sends 26 containers of children's socks, 53 containers of shirts and 28 containers of children's hats to the store. How many total socks, shirts and hats does the factory sew during a month, if it is known that one container contains 258 pairs of socks or 67 shirts or 58 hats?
2. Children come to summer camp on a special bus. The bus brings 45 children in one trip. How many children were brought to the camp if 24 trips were made?
3. 140 boxes of books were brought to the city library. Of these, 15 boxes are large, 58 are medium, and the rest are small. IN big box holds 180 books, the medium one - 148, and the small one - 86 books. How many books were brought to the city library?
Multiplying a multi-digit number by a multi-digit number
2. Write down the given sentences in the form of numerical expressions and solve them.
2.1. Multiply the number 675 by the number 746.
2.2. Multiply the number 253 by the number 632.
2.3. Multiply the numbers 811 and 496.
3. Solve examples.
| 533 * 215 = | 521 * 384 = | 439 * 922 = | 523 * 612 = |
| 723 * 318 = | 269 * 942 = | 468 * 754 = | 431 * 521 = |
| 237 * 522 = | 322 * 363 = | 325 * 522 = | 966 * 247 = |
Of all the sciences, mathematics enjoys special respect because its theorems are absolutely true and indisputable, while the laws of other sciences are to a certain extent controversial and there is always the danger of their refutation by new discoveries.
Schoolchildren primary classes must be able to perform simple arithmetic calculations in their heads. For example, children should be able to add and subtract two- and three-digit numbers mentally.
For adults, adding and subtracting two-digit and three-digit numbers does not cause difficulties, since an adult has independently developed for himself methods of basic mental calculation.
80 - 67 = 80 - 60 - 7 = 20 - 7 = 13 (separate the ones place when subtracting)
Combinations of different methods
79 - 50 (adding one to the numbers)
70 - 50 + 9 = 20 + 9 = 29 (units division)
80 + 67 (transfer of one from the number 68 to the number 79)
80 + 67 = 80 + 20 + 47 = 100 + 47 = 147
In similar ways, three-digit numbers can be easily added and subtracted in the mind.
300 + 57 (+3) + 38(-3) (transfer of three from 38 to 57)
287 (+1) - 29 (+1) (adding one to the minuend and to the subtrahend)
419-297(400-200), 219 (+3) - 97 (+3) (adding three to the minuend and to the subtrahend).
One of the techniques for accelerated multiplication is the technique of cross multiplication, which is very convenient when working with two-digit numbers. The method is not new; it goes back to the Greeks and Hindus and in ancient times was called the “lightning method” or “cross multiplication.”
"Multiplying with a cross."
Let’s say we need to multiply 2432. Mentally arrange the numbers according to the following scheme, one below the other:
Now we perform the following steps sequentially:
1) 42=8 is the last digit of the result;
2) 22=4; 43=12; 4+12=16; 6 is the average number of the result; we remember the unit;
3) 23 = 6 and also a unit retained in the mind, we have 7 - this is the first digit of the result.
We get all the digits of the product: 7, 6, 8=768
Another method, which consists in the use of so-called “supplements,” is conveniently used in those cases. when the numbers being multiplied are close to 100. The obtained result is correct, as can be clearly seen from the following transformations;
8896=88(100-4)=88100-884
496= 4(88+8)= 48+884
929 =8832+0
Multiplication table for "9".
There are a huge variety of techniques for speeding up the execution of arithmetic operations, techniques intended for everyday calculations.
Squaring numbers ending in "5".
To square a number, for example 65, you need to add 1 to the tens place (i.e. 6+1=7) and multiply 6*7=42, and 5*5=25. So =4225
| 35*35 | =1225 3*4=12 |
all answers end with the number 25. But how do you get the first two digits of the answer? They are obtained by multiplying the tens digit by the following natural number. To square a number, for example 65, you need to add 1 to the tens place (i.e. 6+1=7) and multiply 6*7=42, and 5*5=25. So =4225.
Memorizing a table of Sin, Cos, tg values for acute angles.
You see, the fingers of the left hand form angles:
little finger-0 (zero finger)
ring-30 (first finger)
middle-45 (second finger)
index - 60 (third finger)
thumb-90 (fourth finger)
Knowing the sines, you can fill in the cosines (vice versa), tangents and cotangents of acute angles.
Method for multiplying numbers close to 100
Example: 95 * 93
To get the last 2 digits of the answer (tens and ones), you need
To get the first 2 digits of the answer (thousands and hundreds), you need
4) 93 - 5 = 88 or (95 - 7 = 88)
We get 8835
Example 2: 98 * 92
We get 9016
Let's assume that you need to multiply 92 * 96. The addition for 92 to 100 will be 8, and for 86 - 4. The action is carried out according to the following scheme:
Multipliers: 92 and 96.
Additions: 8 and 4.
The first two digits of the result are obtained by simply subtracting the multiplicand from the “complement” factor, or vice versa: i.e. 4 is subtracted from 92 or from 96-8. In both cases we have 88; the product of “additions” is added to this number: 8?4 = 32. We get the result 8832.
Another example - you need to multiply 78 by 77:
Multipliers: 78 and 77.
Additions: 22 and 23.
Numbers 1, 5 and 6
Probably everyone knows that multiplying a series of numbers ending in 1, 5 or 6 produces a number ending with the same digit.
46 = 2116; 46 = 97 336
Extraction from under the root
1). To extract a number from the root, for example, divide this number by two digits from right to left like this: = 568
1. Divide the number (5963364) into pairs from right to left (5`96`33`64)
2. Take the square root of the first group on the left (number 2). This is how we get the first digit of the number.
3. Find the square of the first digit (2 2 =4).
4. Find the difference between the first group and the square of the first digit (5-4=1).
5. We take down the next two digits (we get the number 196).
6. Double the first digit we found and write it on the left behind the line (2*2=4).
7. Now we need to find the second digit of the number: double the first digit we found becomes the tens digit of the number, which when multiplied by the number of units, you need to get a number less than 196 (this is the number 4, 44*4=176). 4 is the second digit of the number.
8. Find the difference (196-176=20).
9. We demolish the next group (we get the number 2033).
10. Double the number 24, we get 48.
11. There are 48 tens in a number, when multiplied by the number of ones, we should get a number less than 2033 (484*4=1936). The units digit we found (4) is the third digit of the number.
The numbers 10, 11, 12, 13 and 14 have an amazing feature. Who would have thought that
10 2 + 11 2 + 12 2 = 13 2 + 14 2. Let's prove it: 100 + 121 +144 = 169 + 196
Addition of numbers close to each other in magnitude.
In the practice of technical and trading calculations, there are often cases when it is necessary to add columns of numbers that are close to each other in size. For example;
To add such numbers, the following technique is used
40*7=280, 3-2-1+5+1-1+2=7, 280+7=287.
We find the sum in the same way:
750*6+1=4501
The arithmetic mean of numbers that are close in magnitude
| Rub. |
| 465 |
| 473 |
| 475 |
| 467 |
| 478 |
| 474 |
| 468 |
| 472 |
They do the same thing when they find the arithmetic mean of numbers that are close in value. Let us find, for example, the average of the following prices:
We eyeball a round price close to the average, i.e. 470 rubles. We write down the deviations of all prices from the average: surpluses with a plus sign, deficiencies with a - sign.
We get: -5+3+5-3+8+4-2+2=12. Dividing the sum of deviations by their number. We have: 12:8 = 1.5.
Hence the required average price is 470 + 1.5 = 471.5 (471 rubles 50 kopecks).
Multiplication by numbers 5, 25, 125
Let's move on to multiplication.
Here, first of all, we point out that multiplication by the numbers 5, 25, 125 is significantly accelerated if we keep in mind the following:
Therefore, for example,
Multiply by 15.
When multiplying by 15, you can use the fact that
Therefore, it is easy to do calculations in your head like this:
36*15=360*1=360+180=540,
Or simpler: 36*1*10=540;
Multiply by 11.
When multiplying by 11 there is no need to write five lines:
It is enough just to sign it again under the multiplied number, moving it one digit:
4213 or 4213 and add.
It is useful to remember the results of multiplying the first nine numbers by 12, 13, 14, 15. Then multiplying multi-digit numbers by such factors is significantly faster. Let it be required to multiply
Let's do it this way. We multiply each digit of the multiplicand in our minds immediately by 13:
7*13=91; 1 we write, 9 we remember;
8*13=104;104+9=113; 3 we write, 11 we remember;
5*13=65;65+11=76; 6 we write; 7 remember;
4*13=52; 52+7=59.
Total 59631.
After several exercises, this technique is easy to remember.
A very convenient technique exists for multiplying two-digit numbers by 11: you need to move the digits of the multiplicand apart and enter their sum between them:
If the sum of digits is two-digit, then the number of its tens is added to the first digit of the multiplicand:
48*11=4(12)8, that is 528.
Division by 5; 25; 125.
Let us indicate some methods of accelerated division.
When dividing by 5, multiply the dividend and the divisor by 2:
3471:5=6942:10=694,2
When dividing by 25, multiply both numbers by 4:
3471;25=13884:100=138.84. Do the same when dividing by 1 (= 1.5) and 2 (= 2.5); 3471: 1=6942:3=2314; 3471: 2.5=13884:10=1388.4
Russian method of humiliation.
Here's an example:
32*13; 16*26; 8*52; 4*104; 2*208; 1*416
Dividing in half continues until the quotient reaches 1, while simultaneously doubling the other number. The last doubled number gives the desired result.
What should you do if you have to divide an odd number in half? If the number is odd, remove one and divide the remainder in half; but to last number in the right column you will need to add all those numbers in this column that stand opposite the odd numbers in the left column: the sum will be the required product. 19 * 17; 9*34; 4*68; 2*136; 1*272. Adding the uncrossed numbers, we get the correct result: 17+34+272=323.
Multiplying numbers ending in 5.
When multiplying a pair of numbers in which the tens digits were even or odd, and the ones digit was 5, you need to multiply the tens digits and add half the sum of these digits to their product. We get the number of hundreds. To the number of hundreds you need to add the product 5*5=25.
For example:
85*45=(8*4+(8+4)/2)hundreds+5*5=38*100+25=3825
35*55=(3*5+(3+5)/2)hundreds+5*5=19*100+25=1925
Let's take an example that is familiar to us from 5th grade.
Find the sum of the first hundred natural numbers:
1+2+3+4+5+6+ : +94+95+96+97+98+99+100=?
How easy is it to calculate the following example:
34*48+18*12+23*24=34*2*24+9*24+23*24=24*(68+9+23)=24*100=2400
You can independently create examples for each rule and practice mental calculations. When creating examples and completing assignments, the children do not experience any difficulties.
Literature:
- Encyclopedia for children. Mathematics. M., Avanta, 2002.
- Ya.I. Perelman, Entertaining arithmetic. M., 1954.
- Magazine "Practical magazine for teachers and school administration". No. 9, 2004.
- J. "Mathematics", No. 4, 1994.
