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Mathematical oral calculation skills of 1.9 (two-digit multiplication)

The formula is about 9:

1 × 9 = 9 2 × 9 = 18 3 × 9 = 27 4 × 9 = 36

5 × 9 = 45 6 × 9 = 54 7 × 9 = 63 8 × 9 = 72

9 × 9 = 8 1

Have the children learned the above formula?

In the first grade of primary school, you may only learn addition, but in the first semester of the second grade, you will learn multiplication formula.

In fact, many parents may have taught the above formula when their children are not in school.

But did the children take a closer look at the characteristics of the formula above?

Do you see from the above formula that any number from 1 to 9 is multiplied by the product of 9, single digits and ten digits?

The sum of is still equal to 9.

Look at the top: 0+9 = 9; 1 + 8 = 9; 2 + 7 = 9; 3 + 6 = 9;

4 + 5 = 9; 5 + 4 = 9; 6 + 3 = 9; 7 + 2 = 9; 8 + 1 = 9

Maybe children will ask, what's the use of discovering this secret?

My answer is very useful. This is the basis for training you to be good at observing, summarizing and finding out the laws of things.

Let's do some more complicated multiplication:

18 × 12 = ? 27 × 12 = ? 36 × 12 = ? 45 × 12 = ?

54 × 12 = ? 63 × 12 = ? 72 × 12 = ? 8 1 × 12 = ?

The multiplication of two digits may not be learned until the third grade, but did the children see that in the above topic, the previous multipliers are all multiples of 9, and the sum of one digit and ten digits is equal to 9?

So can we find a simple algorithm? That is to say, turn the multiplication of two digits into the multiplication of one digit?

Let's change these figures first.

18 = 1 × 10 + 8; 27 = 2 × 10 + 7; 36 = 3 × 10 + 6;

45 = 4 × 10 + 5; 54 = 5 × 10 + 4; 63 = 6 × 10 + 3;

72 = 7 × 10 + 2; 8 1 = 8 × 10 + 1;

Shall we change the numbers on it again?

1 × 10 + 8 = 1 × 9 + 1+8 = 1 × 9 + 9 = 1 × 9 + 9 = 2 × 9

Of course, if you know the formula, you can directly put 18 = 2 × 9.

The main thing here is to let children learn how to disassemble a number.

Similarly, you can break down the following numbers or recite formulas. Go back and practice by yourself.

27 = 3 × 9 ; 36 = 4 × 9 ; 45 = 5 × 9

54 = 6 × 9 ; 63 = 7 × 9 ; 72 = 8 × 9

8 1 = 9 × 9

In order to find a way to calculate the above problems, let's change the above formula again.

18 = 2×( 10- 1); 27 = 3×( 10- 1); 36 = 4×( 10- 1)

45 = 5×( 10- 1); 54 = 6×( 10- 1); 63 = 7×( 10- 1)

72 = 8×( 10- 1); 8 1 = 9×( 10- 1)

Now let's calculate the above question:

18 × 12 = 2×( 10- 1)× 12

= 2 ×( 12 × 10 - 12)

= 2 ×( 120- 12)

The children in brackets should be able to add, right? That was grade one.

120 - 12 = 108;

So you have it.

18 × 12 = 2 × 108 = 2 16

Did you change a two-digit multiplication into a one-digit multiplication?

And you can get the result by oral calculation? Can children try it on their own?

That's how I taught Vivian to multiply. He only needs me to calculate this one, and he will solve the latter problem himself.

It seems that our above calculation is very troublesome. In fact, it is very simple to sum up now.

Look at the next topic:

27 × 12 = 3×( 10- 1)× 12 = 3 ×( 120- 12)

= 3 × 108 = 324

36 × 12 = 4×( 10- 1)× 12 = 4 ×( 120- 12)

= 4 × 108 = 432

Did the children find any patterns? The following questions don't seem to need calculation. They all add 1 to the previous number and then multiply it by 108.

45 × 12 = 5 × 108 = 540

54 × 12 = 6 × 108 = 648

63 × 12 = 7 × 108 = 756

72 × 12 = 8 × 108 = 864

8 1 × 12 = 9 × 108 = 972

Let's take a look at the above calculation results. Did the children find anything?

We changed a two-digit multiplication into a one-digit multiplication. The sum of one digit and ten digits of a multiplier is equal to 9, so that the multiplier of one digit in the changed number is just larger than the previous multiplier 1.

Another feature of the last two digits is that it is a hyphen (12), and 1 and 2 are continuous.

Can you find a simpler calculation method?

In order to find a simpler algorithm. Here I introduce a new term-children's complement.

What is complement? Because this term is simple, even kindergarten children will understand it quickly.

1 + 9 = 10; 2 + 8 = 10; 3 + 7 = 10; 4 + 6 = 10; 5 + 5 = 10;

6 + 4 = 10; 7 + 3 = 10; 8 + 2 = 10; 9 + 1 = 10;

As can be seen from the above addition, if the sum of two numbers is equal to 10, then the two numbers are complementary.

That is to say, 1 and 9 are complements, 2 and 8 are complements, 3 and 7 are complements, and 4 and 6 are complements. You don't need to remember the complement of 5 or 5, just remember 4.

Now let's take a look at the above calculation results:

Take a 63 × 12 = 7 × 108 = 756 as an example.

The first digit of the result is 7 (whatever it is), is it exactly equal to the first digit of the first multiplier (63) plus 1? 6 + 1 = 7

How did the last two figures of the result come out? If this 7 is multiplied by the last complement (8) of the following multiplier (12), what will it be? 7 × 8 = 56

Hehe, there is no need to decompose now. Just add 1 to the first number in the first multiplier (63) to get the first number of the result, and then multiply this number by the last digit's complement (8) of the last multiplier (12) to get the last two digits of the result.

Is this ok? If it works, it's really too fast. It is really a quick calculation.

Try another question:

18 × 12 =

The number before the first multiplier (18) plus 1: 1+ 1 = 2- the first number in the result.

The complement of the number (2) after multiplying 2 by the second multiplier (12) (8): 2× 8 = 16.

The result is 2 16. Take a look at your face?

27 × 12 =

The first number in the result is -2+ 1 = 3.

The last number of the result -3× 8 = 24.

Result 324

36 × 12 =

The first number in the result is -3+ 1 = 4.

The last number of the result -4× 8 = 32.

Result 432

45 × 12 =

The first number in the result is -4+ 1 = 5.

The last number of the result -5× 8 = 40.

Result 540

54 × 12 =

The first number in the result is -5+ 1 = 6.

The last number of the result -6× 8 = 48.

Result 648

63 × 12 =

The first number in the result is -6+ 1 = 7.

The last number of the result -7× 8 = 56.

Result 756

72 × 12 =

The first number in the result is -7+ 1 = 8.

The last number of the result -8× 8 = 64.

Result 864

8 1 × 12 =

The first number in the result is -8+ 1 = 9.

The last number of the result -9× 8 = 72.

Result 972

Is the calculation result the same as the above method?

What else can the child see from the results?

Is it the sum of the three digits of the calculation result or is it equal to 9 or multiple of 9?

Do the math yourself, don't you?

Children who read this article, I will give you a few questions to see if you have mastered the method.

54 × 34 = ? 18 × 78 = ? 36 × 56 = ?

72 × 89 = ? 45 × 67 = ? 27 × 45 = ? 8 1 × 23 = ?

Through this topic, I mainly want my children to draw inferences from one another.

Find a pattern from it. In this way, you can quickly master the addition, subtraction, multiplication, division and Divison of mathematics without doing too many problems.

If the above topic is expanded, the following hyphen will be expanded into multiple digits.

Such as: 123, 234, 345, 2345, 34567, 123456, 23456789 and so on.

Let's see if there are any calculation rules. Maybe you can all find a quick calculation method.

If possible, for example

63 × 2345678 =

Such a topic can be quickly calculated by oral calculation.

I believe that every child is a genius as long as he constantly summarizes scientific methods.