Easy way to multiply by 9. Finger multiplication
Then, with the ease of a magician, we "click" multiplication examples: 2 3, 3 5, 4 6 and so on. With age, however, we increasingly forget about factors closer to 9, especially if we haven’t known counting practice for a long time, why we surrender to the power of a calculator or hope for the freshness of a friend’s knowledge. However, having mastered one simple technique of "manual" multiplication, we can easily refuse the services of a calculator. But let's clarify right away that we are talking only about the school multiplication table, that is, for numbers from 2 to 9, multiplied by numbers from 1 to 10.
Multiplication for the number 9 - 9 1, 9 2 ... 9 10 - is easier to fade from memory and more difficult to manually recalculate by addition, but it is for the number 9 that multiplication is easily reproduced "on the fingers". Spread your fingers on both hands and turn your palms away from you. Mentally assign the fingers sequentially from 1 to 10, starting with the little finger of the left hand and ending with the little finger of the right hand (this is shown in the figure).
Let's say we want to multiply 9 by 6. We bend a finger with a number equal to the number by which we will multiply the nine. In our example, you need to bend the finger with number 6. The number of fingers to the left of the bent finger shows us the number of tens in the answer, the number of fingers to the right - the number of units. On the left, we have 5 fingers not bent, on the right - 4 fingers. Thus, 9 6=54. The figure below shows the whole "computation" principle in detail.
Another example: you need to calculate 9 8=?. Along the way, we will say that fingers may not necessarily act as a "calculating machine". Take, for example, 10 cells in a notebook. We cross out the 8th cell. There are 7 cells on the left, 2 cells on the right. So 9 8=72. Everything is very simple.
Now a few words to those inquisitive children who, in addition to the mechanical application of what has been said, want to understand why it works. Everything here is based on the observation that the number 9 is only one missing from the round number 10, in which the units place contains the number 0. Multiplication can be written as the sum of the same terms. For example, 9 3=9+9+9. Each time we add the next nine, we know that one more one in the answer will not reach the round number. Therefore, how many times a nine was added (or, in other words, what number x was multiplied by), the same number of ones will be missing in the answer. Since the unit digit calculates no more than 10 numbers (from 0 to 9), and when multiplying 9 x =? there are exactly x ones missing in the ones place, then the number in the ones place will be equal to 10-x. This is reflected in the example with hands: we bent the finger with number x and counted the remaining fingers on the right to place ones, but in fact, from 10 fingers, we simply excluded fingers with numbers from 1 to x, thus performing the operation 10-x.
At the same time, with each added nine, the number in the tens digit increases by 1, and initially this digit was empty (equal to zero). That is, for the first nine, the tens digit is zero, adding the second nine increases it by 1, the third nine - by another 1, and so on. This means that the number of tens is equal to x-1, since the tens count started from zero. In the hands example, we folded the finger numbered x, thus providing the "minus one" action, and counted the number of fingers to the left of the folded one, and there are exactly x-1 of them. This is the secret of this simple technique.
From this follow additional considerations. Not only that, the example 9 x=? it is easy to calculate through the number x (the tens digit is x-1, the units digit is 10-x), so another example can be calculated as x 10-x. In other words, we add one zero to the right of the number x and subtract the number x from the resulting number. For example, 9 5=50-5=45 or 9 6=60-6=54 or 9 7=70-7=63 or 9 8=80-8=72 or 9 9= 90-9=81. With this unusual step, we turn the multiplication example into a subtraction example, which is much easier to solve.
Multiplication for the number 8 - 8 1, 8 2 ... 8 10 - the actions here are similar to the multiplication for the number 9 with some changes. First, since the number 8 is already missing two to the round number 10, we need to bend two fingers at once each time - with the number x and the next finger with the number x + 1. Secondly, immediately after the bent fingers, we must bend as many more fingers as there are left unbent fingers on the left. Thirdly, this works directly when multiplying by a number from 1 to 5, and when multiplying by a number from 6 to 10, you need to subtract five from the number x and perform the calculation as for the number from 1 to 5, and then add the number 40 to the answer, because otherwise you will have to perform the transition through a dozen, which is not very convenient "on the fingers", although in principle it is not so difficult. In general, it should be noted that multiplication for numbers below 9 is the more inconvenient to perform "on the fingers", the lower the number is located from 9.
Now consider an example of multiplication for the number 8. Let's say we want to multiply 8 by 4. We bend the finger with number 4 and after it the finger with number 5 (4 + 1). On the left we have 3 unbent fingers, so we need to bend 3 more fingers after the finger with number 5 (these will be fingers with numbers 6, 7 and 8). There are 3 fingers not bent on the left and 2 fingers on the right. Therefore, 8 4=32.
Another example: calculate 8·7=?. As mentioned above, when multiplying by a number from 6 to 10, you need to subtract five from the number x, perform the calculation with the new number x-5, and then add the number 40 to the answer. We have x \u003d 7, which means we bend the finger with number 2 ( 7-5=2) and the next finger number 3 (2+1). On the left, one finger was not bent, so we bend another finger (with number 4). We get: 1 finger is not bent on the left and 6 fingers on the right, which means the number 16. But 40 must also be added to this number: 16+40=56. As a result, 8 7=56.
And just in case, let's look at an example with a transition through a dozen, where no fives need to be subtracted beforehand and no 40s need to be added after either. Suddenly it will be easier for you. Let's try to calculate 8·8=?. We bend two fingers with numbers 8 and 9 (8 + 1). On the left, there are 7 uncurved fingers. Remember that we already have 7 tens. Now we begin to bend 7 fingers on the right. Since there is only one unbent finger left, we bend it (6 more to bend), then go through a dozen (this means that we unbend all the fingers), and bend 6 unbent fingers from left to right. On the right, there are 4 fingers left not bent, which means that the answer will have the number 4 in the unit category. Earlier, we remembered that there were 7 tens, but since we had to go through a dozen, one ten must be discarded (7-1 \u003d 6 tens). As a result, 8 8=64.
Additional considerations: here it is also possible to calculate examples simply through the number x in the form of a subtraction expression x·10-x-x. That is, we add one zero to the right of the number x and subtract the number x twice from the resulting number. For example, 8 5=50-5-5=40, or 8 6=60-6-6=48, or 8 7=70-7-7=56, or 8 8=80-8-8 =64, or 8 9=90-9-9=72.
Multiplication for the number 7 - 7 1, 7 2 ... 7 10. Here you can not do without transitions through a dozen. The number 7 is enough for the triple to the round number 10, therefore, you will have to bend 3 fingers at once. We immediately remember the resulting number of tens by the number of fingers not bent on the left. Next, as many fingers are bent on the right as there are dozens. If during the bending of the fingers a transition through a dozen is required, we do it. Then the same number of fingers are bent a second time, that is, one operation is performed twice. And now the number of uncurved fingers remaining on the right is recorded in the category of units, the number of previously counted tens (minus the number of transitions through a dozen) - in the category of tens.
You see how it is already becoming more difficult to count "on the fingers" than to get this information out of memory. And then, for the numbers 7, 8 and 9, the forgetfulness of the elements of the multiplication table is somehow justified, but for the numbers below it is a sin not to remember. Therefore, at this point we will stop the story in the hope that you have grasped the very thread of "calculations" and, if it is absolutely necessary, you will be able to independently descend to numbers below 7, although a person who counts "on his fingers" something in the spirit of "five five "must look really stupid.
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Many parents whose children graduated from the first grade ask themselves the question: how can you help your child quickly learn the multiplication table. For the summer, children are asked to learn this table, and the child does not always show a desire to engage in cramming in the summer. Moreover, if you just memorize mechanically and do not consolidate the result, then you can later forget some examples.
In this article, read the ways how to quickly learn the multiplication table. Of course, this cannot be done in 5 minutes, but in a few sessions it is quite possible to achieve a good result.
Also read the article
At the very beginning, you need to explain to the child what multiplication is (if he does not already know). Show the meaning of multiplication simple example. For example, 3 * 2 - this means that the number 3 needs to be added 2 times. That is 3*2=3+3. And 3 * 3 means that the number 3 must be added 3 times. That is 3*3=3+3+3. And so on. Understanding the essence of the multiplication table, it will be easier for a child to learn it.
It will be easier for children to perceive the multiplication table not in the form of columns, but in the form of a Pythagorean table. She looks like this:
Explain that the numbers at the intersection of the column and row are the result of multiplication. It is much more interesting for a child to study such a table, because here you can find certain patterns. And, when you look closely at this table, you can see that the numbers highlighted in one color are repeated.
From this, the child will even be able to draw the conclusion himself (and this will already be the development of the brain) that when multiplying when changing factors, the product does not change in places. That is, he will understand that 6*4=24 and 4*6=24 and so on. That is, it is necessary to learn not the whole table, but half! Believe me, when you see the whole table for the first time (wow, how much you need to learn!), the child will become sad. But, realizing that you need to learn half, he will noticeably cheer up.
Print out the Pythagorean table and hang it in a conspicuous place. Each time, looking at it, the child will memorize and repeat some examples. This moment is very important.
You need to start studying the table from simple to complex: first learn multiplication by 2, 3, and then by other numbers.
For easy memorization, tables use various tools: poems, cards, online simulators, small secrets of multiplication.
Flashcards are one of the best ways to quickly learn the multiplication table.
The multiplication table must be learned gradually: one column can be taken per day for memorization. When multiplication by any number is learned, you need to fix the result with the help of cards.
You can make cards yourself, or you can print ready-made ones. You can download the cards from the link below.
Download flashcards for learning multiplication tables.
The numbers to be multiplied are written on one side of the card, and the answer on the other. All cards are stacked face down. The student draws cards from the deck one by one, answering the given example. If the answer is correct, the card is put aside, if the student made a mistake, the card is returned to the general deck.
Thus, memory is trained, and the multiplication table learns faster. After all, playing is always more interesting to learn. In the game with cards, both visual memory and auditory memory work (you need to voice the equation). And also the student wants to quickly “deal with” all the cards.
When they learned a little multiplication by 2, they played cards multiplied by 2. They learned multiplication by 3, played cards multiplied by 2 and 3. And so on.
Multiplication by 1 and 10
These are the easiest examples. Here you don’t even need to memorize anything, just understand how numbers are multiplied by 1 and 10. Start studying the table by multiplying by these numbers. Explain to the child that when multiplied by 1, the same multiplied number will be obtained. To multiply by one means to take some number once. There should be no difficulty here.
Multiply by 10 means to add the number 10 times. And you will always get a number 10 times larger than the multiplied. That is, to get an answer, you just need to add zero to the multiplied number! A child can easily turn units into tens by adding zero. Play flashcards with the student so that he remembers all the answers better.
Multiply by 2
A child can learn multiplication by 2 in 5 minutes. After all, at school he had already learned to add units. And multiplication by 2 is nothing but the addition of two identical numbers. When a child knows that 2*2 = 2+2, and 5*2 = 5+5 and so on, this column will never become a stumbling block for him.
Multiply by 4
After you have learned multiplication by 2, move on to multiplying by 4. This column will be easier for the child to remember than multiplying by 3. To easily learn multiplication by 4, write to the child that multiplying by 4 is multiplying by 2, only twice . That is, first multiply by two, and then the result by another 2.
For example, 5 * 4 = 5 * 2 * 2 = 5 + 5 (as when multiplying by 2, you need to add the same numbers, we get 10) + 10 = 20.
Multiply by 3
If there are difficulties with the study of this column, you can turn to verses for help. Poems can be taken ready-made, or you can come up with your own. Children have a well-developed associative memory. If a child is shown a clear example of multiplication on any objects from his environment, then he will more easily remember the answer that he will associate with any object.
For example, arrange pencils in 3 piles of 4 (or 5, 6, 7, 8, 9 - depending on which example the child forgets) pieces. Think of a problem: you have 4 pencils, dad has 4 pencils and mom has 4 pencils. How many pencils are there? Count the pencils and conclude that 3 * 4 = 12. Sometimes this visualization is very helpful in remembering a “complex” example.
Multiply by 5
I remember that for me this column was the easiest to remember. Because each successive product increases by 5. If you multiply an even number by 5, the answer will also be an even number ending in 0. Children easily remember this: 5*2 = 10, 5*4 = 20, 5*6 = 30 and etc. If you multiply an odd number, then the answer will be an odd number ending in 5: 5*3 = 15, 5*5 = 25, etc.
Multiply by 9
I write immediately after 5 9, because in multiplying by 9 there is a little secret that will help you quickly learn this column. You can learn multiplication by 9 with your fingers!
To do this, place your hands palms up, straighten your fingers. Mentally number your fingers from left to right from 1 to 10. Bend the finger by which number you need to multiply 9. For example, you need 9 * 5. Bend your 5th finger. All fingers on the left (there are 4 of them are tens), fingers on the right (there are 5 of them) are ones. We connect tens and ones, we get - 45.
One more example. How much will 9*7 be? We bend the seventh finger. 6 fingers remain on the left, 3 on the right. We connect, we get - 63!
To better understand this easy way to learn multiplication by 9, watch the video.
Another interesting fact about multiplying by 9. Look at the picture below. If you write down the multiplication by 9 from 1 to 10 in a column, you will notice that the products will have a certain pattern. The first digits will be from 0 to 9 from top to bottom, the second digits will be from 0 to 9 from bottom to top.
Also, if you look closely at the resulting column, you will notice that the sum of the numbers in the product is 9. For example, 18 is 1+8=9, 27 is 2+7=9, 36 is 3+6=9 and etc.
The second interesting observation is this: the first digit of the answer is always 1 less than the number by which 9 is multiplied. That is, 9 × 5 \u003d 4 5 - 4 is one less than 5; 9 × 9 \u003d 8 1 - 8 is one less than 9. Knowing this, it is easy to remember which digit the answer begins with when multiplied by 9. If you forgot the second digit, then you can easily calculate it, knowing that the sum of the numbers in the answer is 9.
For example, how much is 9×6? We immediately understand that the answer will begin with the number 5 (one less than 6). Second digit: 9-5=4 (because the sum of the numbers is 4+5=9). It turns out 54!
Multiply by 6,7,8
When you and your child start learning how to multiply by these numbers, he will already know how to multiply by 2, 3, 4, 5, 9. From the very beginning, you explained to him that 5 × 6 is the same as 6 × 5. This means that he already knows some answers, they do not need to be taught first.
The rest of the equations need to be learned. Use the Pythagorean table and the flashcard game for better memorization.
There is one way how to calculate the answer when multiplying by 6, 7, 8 on the fingers. But it is more complicated than when multiplying by 9, it will take time to calculate. But, if some example does not want to be remembered in any way, try counting on your fingers with your child, perhaps it will be easier for him to learn these most difficult columns.
To make it easier to remember the most complex examples from the multiplication table, solve simple problems with the necessary numbers with your child, give an example from life. All children love to go shopping with their parents. Think of a problem for him on this topic. For example, a student cannot remember how much 7 × 8 will be. Then simulate the situation: he has a birthday. He invited 7 friends to visit. Each friend needs to be treated with 8 sweets. How many candies will he buy at the store for his friends? Answer 56 he will remember much faster, knowing that this is the number of treats for friends.
You can memorize the multiplication table not only at home. If you are with a child on the street, then you can solve problems based on what you see. For example, 4 dogs ran past you. Ask the child how many paws, ears, tails do dogs have?
Children also love to play on the computer. So let them play well. Turn on the online simulator for the student to memorize the multiplication table.
Engage in the study of the multiplication table when the child has good mood. If he is tired, began to act up, then it is better to leave further training for another time.
Use the methods that work best for your child and you'll be fine!
I wish you easy and quick memorization of the multiplication table!
In real life, people who can calculate in their minds look like "super smarts", although there is nothing complicated about this. A calculator is a calculator, but counting in your mind is useful!
How to help your child learn the multiplication table
Below are some simple tricks
Multiply by 2 or doubling. Doubling is pretty easy, just add something to yourself. At first, I showed on my left and right hand at the same time one, two, three, four, five fingers - so we got 2, 4, 6, 8, 10. Together with the fingers of my student, we reached twenty, and then I pointed to different things in the room, and offered to count and double - the number of letters in the poster, the number of symbols on the clock face, count the number of spokes on one side of the bicycle wheel, and see if total number with double and so on.
Multiply by 4 and 8, 3 and 6
When you know how to multiply by two, it's mere trifles. Multiplying by four is the same as doubling the answer for something that has already been doubled, for example, 7 × 4 is 7 × 2x2, and that 7 × 2 is 14, we already remembered well on previous lesson about doubling, so turning 14 into 28 itself is not difficult. When you figured out the four, it's not so difficult to deal with the large numbers of the eight. Along the way, we noticed that, for example, 16 is both 2x8 and 4x4. So we learned that there are numbers consisting entirely of twos: 2, 4, 8, 16, 32, 64.
By multiplying by 3 and 6, we learned the old pirate method of "dividing by three". If you add the digits in a number multiplied by 3, 6, or any other that is divisible by three, then the result of adding the digits of the answer is always a multiple of three. For example, 3x5 = 15, 1+5 = 6. Or 6x8 = 48, and 4+8 = 12, a multiple of three. And you can add the numbers to 12, you get 3 too, so if you reach the end like this, you always get one of three numbers: 3, 6 or 9.
So we turned it into another game. I would give a number, even a three or four digit number, and ask if it was divisible by 3. To answer, just add the numbers, which is quite simple. If the number was divisible by 3, then I asked - "what about 6?" – and then you just had to see if it was even. And then (in the special case of small numbers from the table) sometimes I also wanted to know what would happen with such a division by 3 or 6. It was a very fun activity.
Multiplication by 5 and 7, prime numbers
And now we have multiplication by five, seven, and nine. And this means that we learned how to multiply them by many other numbers - by 1, 2, 3, 4, 6, 8 and 10. We dealt with the five very quickly - it is easy to remember: at the end there is either a zero or five, just the same as a multiplying number: either even or odd. As a subject on which it is convenient to deal with fives, the watch face is great, you can come up with many tasks about traveling in time and space. At the same time, I told why there are sixty minutes in an hour, and we understood how convenient it is.
We saw that it is convenient to divide 60 by 1, 2, 3, 4, 5, 6, and it is inconvenient to divide by 7. So it was time to take a closer look at this number. Of the multiplication by the seven, it remained to remember only 7 × 7 and 7 × 9. Now we knew almost everything we needed. I explained that seven is just a very proud number - such numbers are called prime, they are divisible only by 1 and by themselves.
Math can be fun and easy. Check out this cute table.
If you study it thoughtfully, then there is not much to learn. There are 36 positions in total. The rest are either simple (1 x 10) or reversible (2 x 4 = 4 x 2). Minus 10 positions from the multiplication table by 9. It can be learned in 5 minutes. There is a focus:
So let's go.
To begin with, let's put our hands on the table and mentally number the fingers from left to right from 1 to 10. To perform the multiplication operation, let's say 9 x 3 = ?, bend the third finger from the left. All! The answer is ready: the fingers remaining not bent on the left form the number of tens in the answer, and not bent on the right - the number of units. We count and say the answer: 27!
This way you can get the answer for any number. Here, for example, an example 9 x 7 = 63
watch multiplication by 9 in the video:
In modern primary school they start learning the multiplication table in the second grade and finish in the third, and often learn the multiplication table for the summer. If you didn’t study in the summer, and the child is still “floating” in multiplication examples, we will tell you how to learn the multiplication table quickly and fun - with the help of drawings, games and even fingers.
Problems that often arise in children in connection with the multiplication table:
- Children don't know what 7 × 8 is.
- They do not see that the problem must be solved by multiplication (because it does not say directly: "What is 8 times 4?")
- They do not understand that if you know that 4 × 9 = 36, then you also know what 9 × 4, 36: 4 and 36: 9 is equal to.
- They do not know how to use their knowledge and restore a forgotten piece of the table from it.
How to quickly learn the multiplication table: the language of multiplication
Before you start learning the multiplication table with your child, it’s worth stepping back a little and realizing that a simple multiplication example can be described in a surprising number of different ways. Take the 3 × 4 example. You can read it as:
- three times four (or four times three);
- three times four;
- three times four;
- the product of three and four.
At first, it is far from obvious to the child that all these phrases mean multiplication. You can help your son or daughter if, instead of repeating yourself, you casually use different language when talking about multiplication. For example: "So how much is three times four? What happens if you take three times four?"
How to learn the multiplication table
The most natural way for children to learn the multiplication table is to start with the easiest and work your way up to the hardest. A reasonable sequence is:
Multiply by ten (10, 20, 30...), which children learn naturally in the process of learning to count.
Multiply by five (after all, we all have five fingers and toes).
Multiplication by two. couples, even numbers and doubling are familiar even to small children.
Multiply by four (after all, this is just a doubling of multiplication by two) and eight (doubling of multiplication by four).
Multiplication by nine (for this there are quite convenient tricks, about them below).
Multiply by three and six.
Why 3x7 equals 7x3
When helping your child memorize the multiplication table, it is very important to explain to him that the order of the numbers does not matter: 3 × 7 gives the same answer as 7 × 3. One of better ways show it clearly use an array. This is a special mathematical word denoting a set of numbers or shapes enclosed in a rectangle. Here, for example, is an array of three rows and seven columns.
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An array is a simple and visual tool to help a child understand how multiplication and fractions work. How many dots are there in a 3 by 7 rectangle? Three lines of seven elements each have 21 elements. In other words, arrays are an easy-to-understand way to visualize multiplication, in this case 3 × 7 = 21.
What if we draw the array in a different way?
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Obviously, both arrays must have the same number of points (they do not have to be counted individually), because if the first array is rotated a quarter of a turn, it will look exactly like the second.
Look around, look nearby, in the house or on the street, for some arrays. Take a look at the cakes in the box, for example. Cakes are stacked in a 4 by 3 array. And if you rotate? Then 3 by 4.
Now take a look at the windows of the high-rise building. Wow, this is also an array, 5 by 4! Or maybe 4 by 5, how to look? As soon as you start paying attention to arrays, it turns out that they are everywhere.
If you have already taught your children the idea that 3 × 7 is the same as 7 × 3, then the number of multiplication facts that you need to remember decreases dramatically. It is worth memorizing 3 × 7 - and as a bonus, you get the answer to 7 × 3.
Knowing the commutative law of multiplication reduces the number of multiplication facts from 100 to 55 (not exactly by half due to cases of squaring, such as 3×3 or 7×7, which do not have a pair).
Each of the numbers above the dotted diagonal (for example, 5 × 8 = 40) is also present below it (8 × 5 = 40).
The table below contains another hint. Children usually begin to learn the multiplication table using counting algorithms. To figure out what 8 × 4 is, they count like this: 4, 8, 12, 16, 20, 24, 28, 32. But if you know that eight times four is the same as four times eight, then 8, 16 , 24, 32 will be faster. In Japan, children are specially taught to "put the lower number first." Seven times 3? Do not do this, count 3 times 7 better.
Learning the squares of numbers
The result of multiplying a number by itself (1×1, 2×2, 3×3, etc.) is known as square number. This is because graphically such a multiplication corresponds to a square array. If you go back to the multiplication table and look at its diagonal, you will see that it is all squares of numbers.
They have interesting feature which you can explore with your child. When listing the squares of numbers, pay attention to how much they increase each time:
Squares of numbers 0 1 4 9 16 25 36 49...
Difference 1 3 5 7 9 11 13
This curious connection between square numbers and odd numbers is a perfect example of how different types numbers are related in mathematics.
Multiplication table for 5 and 10
The first and easiest table to memorize is the 10 multiplication table: 10, 20, 30, 40...
In addition, children memorize the multiplication table for five with relative ease, and their hands and feet, visually representing four fives, help them with this.
It is also convenient that the numbers in the five times table always end in 5 or 0. (So, we know for sure that the number 3,451,254,947,815 is present in the five times table, although we cannot verify this with a calculator: on such a number simply does not fit on the screen of the device).
Children can easily double numbers. This is probably due to the fact that we have two hands with five fingers on each. However, children do not always associate doubling with multiplying by two. The child may know that if you double six, you get 12, but when you ask him what six is equal to two, he has to count: 2, 4, 6, 8, 10, 12. In this case, you should remind him that six is two - the same as twice six, and twice six - this is the doubled six.
Thus, if your child is good at doubling, then he essentially knows the multiplication table by two. At the same time, he is unlikely to immediately realize that with its help you can quickly imagine a multiplication table for four - for this you just need to double and double again.
Game: double walker
It is possible to adapt any game in which players roll a die so that all rolls count as doubles. This gives several advantages at once: on the one hand, children like the idea of going twice as far with each throw as the dice shows; on the other hand, they gradually master the multiplication table by two. In addition (which is important for parents busy with other things), the game ends twice as fast.
9 Times Table: Compensation Method
One way to master the nine times table is to take the result of ten times and subtract the excess.
What is nine times seven equal to? Ten times seven is 70, subtract seven, we get 63.
7 x 9 = (7 x 10) - 7 = 63
Perhaps a quick sketch of the appropriate array will help cement this idea in the child's mind.
If you memorized the multiplication table for nine only up to "nine ten", then nine 25 will confuse you. But ten times 25 is 250, subtract 25, we get 225. 9 × 25 = 225.
Test yourself
Can you solve the 9 × 78 example mentally using the compensation method (multiplying by 10 and subtracting 78)?
There is another convenient way to master the nine times table. It uses fingers and kids love it.
Hold your hands in front of you, palms down. Imagine that your fingers (including the thumb) are numbered from 1 to 10. 1 is the little finger on the left hand (the extreme finger on your left), 10 is the little finger on the right (the extreme finger on the right).
To multiply a number by nine, bend the finger with the corresponding number. Let's say you are interested in nine 7. Bend the finger that you mentally labeled as the seventh number.
Now look at your hands: the number of fingers to the left of the curled one will give you the number of tens in the answer; in this case it is 60. The number of fingers on the right will give the number of units: three. Total: 9 × 7 = 63. Give it a try: this method works with all single digit numbers.
Multiplication table for 3 and 6
For children, the multiplication table by three is one of the most difficult. In this case, there are practically no tricks, and the multiplication table by 3 will simply have to be memorized.
The six times table follows directly from the three times table; here, again, it all comes down to doubling. If you can multiply by three, just double the result and you get a multiplication by six. So 3 x 7 = 21, 6 x 7 = 42.
Multiplication table by 7 - dice game
So, all we have left is the multiplication table for seven. There is good news. If your child has successfully mastered the tables described above, there is no need to memorize anything at all: everything is already in the other tables.
But if your child wants to learn the multiplication table for 7 separately, we will introduce you to a game that will help speed up this process.
You will need as many dice as you can find. Ten, for example, is a great number. Tell your son or daughter that you want to see which of you can add the numbers on the dice the fastest. However, let the children decide for themselves how many dice to roll. And to increase the child's chances of winning, you can agree that he must add the numbers indicated on the upper faces of the cubes, and you - those on both the upper and lower ones.
Have each child choose at least two dice and place them in a glass or mug (they are great for shaking the dice for random rolls). You only need to know how many cubes the child took.
As soon as the dice are rolled, you can immediately calculate how much the numbers on the upper and lower faces will give! How? Very simple: multiply the number of dice by 7. Thus, if three dice were drawn, the sum of the top and bottom numbers would be 21. (The reason, of course, is that the numbers on opposite sides of the die always add up to seven.)
The kids will be so amazed at how fast you can calculate that they'll want to learn this method too so they can use it someday with their buddies.
In the era of the so-called British imperial system of measures and "non-decimal" money, everyone needed to own an account up to 12 × 12 (then there were 12 pence in a shilling, and 12 inches in a foot). But even today, 12 pops up every now and then in the calculations: many people still measure and count in inches (in America this is the standard), and eggs are sold by the dozen and half a dozen.
Little of. A child who freely multiplies numbers greater than ten begins to develop an understanding of how to multiply big numbers. Knowing the multiplication tables for 11 and 12 helps to notice interesting patterns. Let's bring complete table multiply up to 12.
Note that the number eight, for example, occurs four times in the table, while 36 occurs five times. If you connect all the cells with the number eight, you get a smooth curve. The same can be said about the cells with the number 36. Indeed, if a certain number appears in the table more than twice, then all places of its occurrence can be connected by a smooth curve of approximately the same shape.
You can encourage your child to explore on their own, which will keep them busy for (maybe) half an hour or more. Print out several copies of the 12 times 12 multiplication table, and then ask him to do the following:
- colorize all cells with even numbers in red, and with odd numbers in blue;
- determine which numbers occur there most often;
- say how many different numbers are found in the table;
- answer the questions: "What is the smallest number not found in this table? What other numbers from 1 to 100 are missing in it?".
Focus with eleven
The multiplication table for 11 is the easiest to build.
1 x 11 = 11
2 x 11 = 22
3 x 11 = 33
4 x 11 = 44
5 x 11 = 55
6 x 11 = 66
7 x 11 = 77
8 x 11 = 88
9 x 11 = 99
- Take any number from ten to 99 - let's say 26.
- Break it into two numbers and push them apart so that there is a gap in the middle: 2 _ 6.
- Add together the two digits of your number. 2 + 6 = 8 and paste what you got in the middle: 2 8 6
This is the answer! 26 x 11 = 286.
But be careful. What happens when you multiply 75 × 11?
- Splitting the number: 7 _ 5
- Add up: 7 + 5 = 12
- We insert the result in the middle and we get 7125, which is obviously wrong!
What's the matter? There is a little trick to this example that needs to be applied when the digits used to represent the number add up to ten or more (7 + 5 = 12). We add one to the first of our numbers. Therefore, 75 × 11 will not be 7125, but (7 + 1)25, or 825. So the trick is actually not as simple as it might seem.
Game: beat the calculator
The purpose of this game is to develop the skill of quickly using the multiplication table. You will need a deck of playing cards without pictures and a calculator. Decide which player will use the calculator first.
- The player with the calculator must multiply the two numbers drawn on the cards; however, he must use a calculator, even if he knows the answer (yes, this can be very difficult).
- Another player must multiply the same two numbers in their mind.
- The one who gets the answer first gets a point.
- After ten attempts, the players change places.
In today's reality, people who are able to calculate in their minds look like some kind of "super smart", although there is nothing complicated about this. A calculator is a calculator, but counting in your mind is useful!
Today I suggest you teach your favorite children the multiplication table for "9" on your fingers.
I have already shown this to many kids, and this action has always been perceived with great enthusiasm.
Unfortunately this way only good for the multiplication table for "9".
So, we started.
To begin with, let's put our hands on the table and mentally number the fingers from left to right from 1 to 10. To perform the multiplication action, let's say 9 x 3 \u003d?, Bend the third finger from the left. All! The answer is ready: the fingers remaining not bent on the left form the number of tens in the answer, and not bent on the right? number of units. We count and say the answer: 27!
This way you can get the answer for any number. Here, let's say, an example of 9 x 7 = 63.
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The next step, after mastering this multiplication table, you can teach children such a simple trick:
Take a calculator and type on it? 12345679 (all numbers in a row without the eight), press the "x" symbol (multiply) and ask: "What is your favorite number?".
Let's say they said "4", so we multiply by 36 and only fours flaunt on the calculator's display!
How it's done?
It's very simple, you need to multiply your "favorite number" by 9 in your mind, and already multiply this long number by the resulting result. Those. if they call "8", then 12345679 should be multiplied by (8 x 9 =) 72 and get on the screen? 88888888.
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And finally, you want to surprise everyone by accurately naming the day of the week that falls on any date of the year!
It's so simple. Take, for example, the current months. I have a calendar hanging on my wall, which I photographed so as not to bother too much.
pay attention to empty cells before the beginning of the month, i.e. until the 1st. In July? "3", in August? "6", in September? "2". These are the so-called "numbers of the month". That's all we need to know in advance!
Remembering the 12 numbers of the year is not difficult, if you also apply "mnemonics". These three figures form, for example, a very well-known price in the USSR? 3.62. The price of a bottle of vodka.
Now the technology of "guessing" the day of the week. Let's say you are told: "What day of the week is August 5?"
Do you do simple calculations in your mind? Add the "day of the month" to the day (in our case? "6") and divide the resulting amount by 7. The remainder of the division will give us the desired day of the week.
We make calculations: 5 + 6 = 11 / 7 = 1 and 4 in the remainder. So the day of the week? 4 (Thursday).
Accordingly: 1? Monday, 2? Tuesday, etc. If it is divided without a remainder, then the desired day? "Sunday"
Numbers of the month until the end of the year: October? 4, November? 0 December? 2 (straight, "Moskvich-402").
Those. in November, you don’t need to add anything, but immediately start dividing.