How do I multiply two numbers

Written multiplication

Written multiplication allows you to multiply larger numbers. How this procedure works is explained below. Examples including exercises with solutions complete the explanations.

First a small note: If you have problems understanding this article, it could be due to your previous knowledge. To brush up on these, you should read through the articles Basics of Multiplication and Written Adding and do the associated exercises. This knowledge is required for the further article.

Important: There are two ways to carry out the written multiplication. We introduce both of you here. Choose the variant that you think is easiest or that is given to you by the teacher.

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Variant 1 of the written multiplication

Now we come to written multiplication: The aim of this article is to Multiplications such as solving 12x30. I will now do the math here first - as well as a second example - and then explain the procedure below the calculation.

And that's how it works. Example 1:

  • The two numbers are written next to each other and a multiplication sign is written between them. A line is drawn underneath.
  • Then the first number is multiplied by the first digit of the second factor, in German: 12 · 3 = 36. The 36 is written under the 3.
  • The same for the last digit: 12 · 2 = 24. This number is written under the 2.
  • And now it is added in writing. Digit by digit, from back to front: 4 + 0 = 4; 6 + 2 = 8 and 3 + 0 = 3.
  • So 12 * 32 = 384.

And the whole thing for example 2:

  • The result of 23 * 14 is searched. The two numbers are written down again and a multiplication symbol is placed between them. Another line drawn underneath.
  • Now the first digit of the second number is again taken into account and multiplied. Say 23 · 1 = 23. This number is written under the 1.
  • The same game for the last digit: 23 · 4 = 92. The number is written underneath, as shown above.
  • Then it is added again in writing. The answer is 322.
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Written multiplication with more digits

Of course, the written multiplication also works for more than two digits. Two examples follow to illustrate this. But first a little tip: Always write the larger number backwards. So do not calculate 322 · 12, but 12 · 322. That simplifies the calculation.

Here, too, the explanations. For example 1:

  • The first digit: 10 3 = 30
  • The second digit: 10 · 2 = 20
  • The third digit = 10 * 1 = 10
  • Now additions are made again in writing. The result is 3210.


And now the explanations for example 2:

  • The first digit: 18 2 = 36
  • The second digit: 18 1 = 18
  • The third digit: 18 0 = 0
  • Now additions are made again in writing. The result is 3780.

Written multiplication variant 2

Let us now look at a second variant of written multiplication. Here, too, we proceed bit by bit to calculate the solution.

Example 1:

Method:

  • 5 · 9 = 45, write the 5 and note the 4
  • 5 · 2 = 10, 10 + 4 = 14, write the 4 and note the 1
  • 5 4 = 20, 20 + 1 = 21, write the 1 and note the 2
  • 5 5 = 25, 25 + 2 = 27, write the 7 and note the 2
  • Write the 2 at the beginning

Example 2:

Method:

  • 8 · 8 = 64, write the 4 and note the 6
  • 8 6 = 48, 48 + 6 = 54, write the 4 and note the 5
  • 8 4 = 32, 32 + 5 = 37, write the 7 and note the 3
  • 8 · 8 = 64, 64 + 3 = 67, write the 7 and note the 6
  • 8 · 2 = 16, 16 + 6 = 22, write the 2 and note the 2
  • Write the noted 2 at the beginning

Example 3:

Method:

  • Calculates 28468 · 1 using the usual calculation method from the previous examples and writes the result down so that the last digit is under 1
  • Calculates 28468 · 6 using the usual arithmetic method from the previous examples and writes the result down so that the last digit is under 6
  • Performs written addition (0 + 8 = 8, 8 + 0 = 8, etc.). So add the places on top of each other.

I recommend that Work on exercises. Written multiplication can only be learned well by practicing tasks.

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