How to learn how to multiply a column by unambiguous, two -digit, three -digit numbers: rules and an algorithm for multiplication in a column. How to explain the child multiplication with a column? Examples of multiplying multi -valued numbers into a column

If you have already forgotten how to multiply the numbers in the column, then read the article. Here you will find all the information about this mathematical action.

The content of the article

Even some adults did not master at school, as you can multiply the numbers in a column. But this skill can come in handy in life if it does not go at hand of a calculator or mobile phone.

Moreover, this is not at all difficult if you know the multiplication table and realized how to properly have numbers in this process. Multiplication in a column always begins to study with multiplication of a multi -valued number by an unambiguous one in order to understand the rules of this action. Further in more detail.

Rules and algorithm for multiplication in a column

Mathematical classes are not given to many children the first time. This is a difficult science that requires special attention, understanding. And the students in elementary grades are required to help mom and dad in solving complex examples, tasks. In particular, it is impossible to leave everything on a gear if your child did not understand what multiplication, division of numbers, etc. It is necessary to help understand the topic and learn the multiplication table, so as not to get bad grades, and not be upset.

It will be easy to master multiplication in a column if:

The student knows the multiplication table perfectly. Not confused in the values \u200b\u200bof the work.
I understood in what sequence the numbers of a multi -digit number should be changed.
The child realized where to write them correctly. And he knows how to add polynomials in a column.

You need to know, the rule that the work does not change from the change of places of the multipliers. More precisely, if you multiply 56 ⋅ 2 \u003d 112 and 2 ⋅ 56 \u003d 112 - the work will be 112.

Recommendations for multiplication in a column

IMPORTANT: When the numbers are shifted to the column. Under the bottom, they write the number that has fewer numbers in its composition.

How to multiply in a column of three -digit numbers by unambiguous, two -digit, three -digit

Any multiplication is the addition of the same numbers to the required number of times. More precisely, 725 ⋅ 2 \u003d 725 + 725 \u003d 1450. But such an example can be made orally if the second number is 2.3.4. And if it is 8, then it is already better to change in a column. For this:

You need to write a number at the top 725, and below under the number - 5 Write the number - 8.
Now you need one by one starting with 5, all values \u200b\u200bof a three -digit number change by 8.
More precisely: 5 ⋅ 8 \u003d 40 ( we write zero below for eight and five, and - 4 remember).
Next, multiply: 2 ⋅ 8 \u003d 16 ( by 16 we add - 4 \u003d 20, again we write 0, only under a deuce, and - 2 remember).
It remains to multiply: 7 ⋅ 8 \u003d 56 ( by 56, add - 2 \u003d 58, we write an eight under the seven, and five in front).
As a result of such multiplication ( 725 ⋅ 8) it will turn out - 5800. And this calculation was obtained manually, without any cars, calculators.

Multiplication in a column - three -digit by three -digit

Multiply a polynomial by polynomial is somewhat more difficult. However, if you already in the first example understand how the process takes place, then it will not be difficult for you to change three -digit numbers, and then put in a column, the resulting values.

Consider in detail how to multiply 125 by 32

At the top on the sheet write a three -digit number 125, under it 32, and arrange it as follows: troika under a deuce of the first day, A two of the second under the five of the first day - it is very important.
Start changing from the end. That is: change All numbers of a three -digit number (125) at first on two.
You it turns out 250, zero write under a deuce, the rest of the numbers in front.
Further change 125 to three. And place the value of the work on the leaf ( 375), starting with the number - 3.
Now it remains to fold 250 and 375 (0), it turns out 250 + 3750 = 4000.

IMPORTANT: How to change three -digit numbers can clearly be seen in the figure above. The numbers change in a strict sequence, starting from the end, and then all the resulting values \u200b\u200bare folded.

How to multiply in a column of numbers with zeros?

Already from elementary grades mathematics, any student knows that if you multiply any number by zero, then the work will also be 0. That is why, when it is multiplied in a column, then no multiplication is carried out by the figure, it is taken beyond the scope, and they are attributed to the work Zero or several zeros - look at the image below.

Multiplication with zeros

How to explain the child multiplication with a column?

If you decide to hold a lesson in mathematics at home, study how to multiply into a column, then turn your lesson into a game.
Gradually, patiently explaining how this is done. Answer all the questions of the student so that he understands what and what to do for.
Give it first for examples simple examples, and then choose more difficult tasks.

Multiplication for children

IMPORTANT: Devote more time to your children, do not ignore their requests for help. At school, the teacher complies with program requirements. The consolidation of the material is not given much time. Therefore, not all schoolchildren manage to master the program, especially in such a complex business as multiplication, division into a column.