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Division of natural numbers


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

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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 \codt 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.