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Division of natural numbers

division

Division of natural numbers

Division is one of the four basic arithmetic operations in mathematics. It is the opposite operation of multiplication and means splitting something into equal groups. The symbols for division are “$/$”, “$÷$” and “$:$” .

The division of two numbers has the following form:

dividend $:$ divisor = quotient”.

The first number is called the dividend, the second is the divisor and result is called the quotient.
We can divide any number by any number except zero. The division by zero is undefined. To be good at dividing numbers you need to have a good knowledge about the division table. The division table is something like an inverse multiplication table.

table of division

Image credit: math-refresher.com

 

Dividing natural numbers

Now, we are going to cover division of natural numbers. If you stick to the principles described in the next part of this lesson, you will have no problem dividing any number by any number. The best way to learn something is by looking at examples of the problem.


Examine 1.

We are going to divide number $117$ by number $9$:

 

division of two whole numbers

The division in the example above is done in the following steps:
-> We start by dividing the most significant digit with the divisor. In our example the most significant digit is $1$. Digit $1$ can not be divided by digit $9$. If we can’t divide the digit by the divisor, we combine that digit with the next significant digit and get a two digit number. In our case, it is the digit $1$ so we get number $11$. We divide number  $11$ by number $9$. The result is number $1$. Write down number $1$ in the result.
-> In this step, we multiply number $1$ by number $9$ and write under number $11$. After that we must subtract those numbers.

->Number $11$ minus number $9$ is number $2$. Write number $2$ as a result of subtraction. Now, we need to add the next digit from the dividend next to number $2$. That is number $7$. Now we have $27$.
-> Now, we need to divide number $27$ by number $9$ to get the next digit in the resulting number. Number $27$ divided by $9$ is number  $3$. Write number $3$ in the result.
-> After that, $3 \cdot 9 = 27$. We write number $27$ under the $27$ and subtract that numbers. The result is equal to $0$. Subtraction is done when number remainder of division can not divide with divisor.
-> The final result is number $13$. That means that $13 \cdot 9 = 117$.


Examine 2.

The next example is going to be more complex. We are going to divide number $1736$ by number  $14$.

division of two complex numbers

The division should look like this:
-> Once again, digit $1$ is lower than number $14$ so we can’t divide. Take the next digit and form $17$. Number $17$ divided by number $14$ is number $1$. Write nuber $1$ in the result.
->Now, we have $1 \cdot 14 = 14$. Write down number $14$ under number $17$ and subtract those numbers. After that,we have $17 \cdot 14 = 3$. Write number  $3$ as the result of subtraction.
-> Add one digit from the dividend. The next digit is $3$. Now we have number $33$. Number $33$ divided by numnber $14$ is number $2$.
->Now, we have $2 \cdot 14 = 28$. Write number $28$ under number $33$ and subtract that. The result is number $5$.
-> Add one digit from the dividend. That digit is digit $6$. Now we have number $56$.Number $56$ divided by number $14$ is number $4$.
-> We have $4 \cdot 14 = 56$. Write number $56$ under number $56$ and subtract. The result of subtract is number $0$.