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Multiplication of natural numbers

multiplication table

Multiplication table

The multiplication table includes multiplication results for numbers from 1 to 9.

simple numbers multiplication on number line

The multiplication is a lot easier if you know the multiplication table.

multiplication table

 

The result of a multiplication of two numbers is called a product.

The numbers we multiply are called the factors.

The first factor is called the multiplicand and the second is called multiplier.

The multiplication of one-digit numbers is the easiest form of multiplication and must be learned using the multiplication table before moving on to more complex examples.

Now, we are going to look at multiplication of one-digit numbers with two-digit numbers.


Two-digit numbers are composed of numerals  ones and tens.

For example, number 45 we can write down like:

\ 45 = 4 \cdot 10 + 5 \cdot 1


Multiplication of natural numbers

We are going to start with an example of multiplication of number 8 with 53:

simple multiplication

We started by aligning the multiplier, number 8, with the number 3. Then we multiplied each digit of the multiplicand.
We wrote the “ones” digit of each product in the result. If the number has “tens” digit then it will be carried and added to the next product.

The process should look like this:
-> 3 \cdot 8 =24. Write number 4 and carry the number  2.
-> 5 \cdot 8 = 40. We adding carried number 2 to number 40. The result is number 42.
-> The final result is number 424.


Now, we will move on to the multiplication of two-digit numbers.
Let’s take a look at the next example. We will multiply number 71 with number  56:

multiplying two whole numbers

First we multiplied the “ones” digit, number 6, with number 71 using the method shown before. The result is number 426.

Now we multiply number 5 with  number 71. The result is number 355. Note that we shifted the result (355) one digit to the left, and a number 0 is added at the end. The result is shifted because we multiplied the “tens” digit, number 5, with 71.

The process should look like this:
-> 6 \cdot 1= 6. Write number  6.
-> 6 \cdot 7 = 42. Write number 42. Now we get number 426.
-> 5 \cdot 1 = 5. Write number 5.
-> 5 \cdot 7 =35. Write number 35. Now we got the number 355, and it is shifted by one digit to the left.

That means that the last digit is 0.
-> Now we need to add number 426 to 3550 and the result is number 3976.

 

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