In this publication, we will look at the rules and practical examples of how natural numbers (two-digit, three-digit and multi-digit) can be multiplied by a column.
Column multiplication rules
To find the product of two natural numbers with any number of digits, you can perform multiplication in a column. For this:
- We write the first multiplier (we start with the one with more digits).
- Under it we write down the second multiplier (from a new line). At the same time, it is important that the same digits of both numbers are located strictly under each other (tens under tens, hundreds under hundreds, etc.)
- Under the factors we draw a horizontal line that will separate them from the result.
- Let’s start multiplication:
- The rightmost digit of the second multiplier (digit – units) is alternately multiplied by each digit of the first number (from right to left). Moreover, if the answer turned out to be two-digit, we leave the last digit in the current digit, and transfer the first digit to the next, adding it with the value obtained as a result of multiplication. Sometimes, as a result of such a transfer, a new bit appears in the response.
- Then we move on to the next digit of the second multiplier (tens) and perform similar actions, writing the result with a shift by one digit to the left.
- We add the resulting numbers and get the answer. We examined the rules and examples of adding numbers in a column in a separate.
Column Multiplication Examples
Example 1
Let’s multiply a two-digit number by a one-digit number, for example, 32 by 7.
Explanation:
In this case, the second multiplier consists of only one digit – one. We multiply 7 by each digit of the first multiplier in turn. In this case, the product of the numbers 7 and 2 is equal to 14, therefore, in the answer, the number 4 is left in the current digit (units), and one is added to the result of multiplying 7 by 3 (7⋅3+1=22).
Example 2
Let’s find the product of two-digit and three-digit numbers: 416 and 23.
Explanation:
- We write the multipliers under each other (in the top line – 416).
- We alternately multiply the number 3 of the number 23 by each digit of the number 416, we get – 1248.
- Now we multiply 2 by each digit 416, and the result (832) is written under the number 1248 with a shift of one digit to the left.
- It remains only to add the numbers 832 and 1248 to get the answer, which is 9568.