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Division of natural numbers

division

Division is one of the four basic arithmetic operations in mathematics. It is the opposite 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

 

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. So let’s do that. We are going to divide 117 by 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. 1 can not be divided by 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 11 by 9. The result is 1. Write 1 in the result.
-> In this step, we multiply 1 by 9 and write under number 11. Subtract them. 11 minus 9 is 2. Write 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.
-> We need to divide 27 by 9 to get the next digit in the resulting number. 27 divided by 9 is 3. Write 3 in the result.
-> 3 times 9 is 27. We write 27 under the 27 and subtract. The result is 0. Subtraction is done until we have 0 as the result and don’t have any digits to write from the dividend.
-> The final result is 13. That means that 13 times 9 is 117.

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

division of two complex numbers

The division should look like this:
-> 1 is lower than 14 so we can’t divide. Take the next digit and form 17. 17 divided by 14 is 1. Write 1 in the result.
-> 1 times 14 is 14. Write 14 under 17 and subtract. 17 minus 14 is 3. Write 3 as the result of subtraction.
-> Add one digit from the dividend. The next digit is 3. Now we have 33. 33 divided by 14 is 2.
-> 2 times 14 is 28. Write 28 under 33 and subtract. The result is 5.
-> Add one digit from the dividend. That digit is 6. Now we have 56. 56 divided by 14 is 4.
-> 4 times 14 is 56. Write 56 under 56 and subtract. The result is 0. The result is 0 and we don’t have any digit left in the dividend so the subtraction is over.

Division of natural numbers worksheets

Integers

  Two positive integers (72.3 KiB, 510 hits)

  Two integers (120.4 KiB, 439 hits)

Decimals

  Two positive decimals (77.4 KiB, 446 hits)

  Two decimals (130.0 KiB, 427 hits)

Fractions

  Two positive fractions (160.7 KiB, 410 hits)

  Two fractions (297.7 KiB, 395 hits)

Improper fractions

  Two positive improper fractions (146.7 KiB, 416 hits)

  Two improper fractions (268.6 KiB, 414 hits)

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