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How to Do Long Division


Here, you are going to learn how to divide numbers that are not in the times table.

Division is the opposite of multiplication. The link between division and multiplication is the same as the link between addition and subtraction. One of them makes up for the other one.

It is also important to notice that fractional calculation and division are identical operations. The numbers in a division are called the dividend and the divisor. The dividend is the number before the division symbol ( :), and the divisor is the number after the division symbol. The answer you get when executing the division is called a quotient.

By now, you may have noticed that the dividend is the same as a numerator and that the divisor is the same as a denominator. The terms are used interchangeably, but numerator and denominator are used when we’re working with fractions, and dividend and divisor are often used when we’re dividing.

Formula

Dividend ÷divisor = quotient

Rule

You cannot divide by zero!

You can never have 0 as divisor or denominator. It makes no sense dividing a number by something that does not exist!

Example 1

4 ÷ 0 = IMPOSSIBLE4 0 = IMPOSSIBLE

4 ÷ 0 = IMPOSSIBLE4 0 = IMPOSSIBLE

Rule

The Division Method

1.
Write the division like this:
“Divisor”)“Dividend”¯
2.
How many times does the divisor go into the leftmost digit in the dividend? Write the number on the line above the dividend unless the answer is 0. If it’s 0, you have to add another digit from the dividend.
3.
How many times does the divisor go into this new number? Write the answer on the line above the dividend.
4.
Multiply the number on top of the dividend with the divisor, and write the product under the leftmost digits of the dividend with a minus in front of it.
5.
Subtract the numbers from each other and write the answer below them.
6.
Now, grab the next digit in the dividend and write it next to the answer in Item 5. Repeat the method from Item 3.
7.
Continue until there are no more digits left in the dividend.

Note! What do you do if the number below the line is less than the divisor? You’re allowed to multiply with 0. Multiply the divisor with 0 and put 0 on top of the dividend. You need to write 0 below the number underneath the line as well. Move another digit down from the dividend.

Continue calculating.

What do you do if the dividend is already used up and you haven’t gotten 0 below the line? Put a comma-sign behind the numbers on top of the dividend and a 0 next to the residual value. Continue calculating.

Below are some examples.

Example 2

Calculate 243 ÷ 9 and 625 ÷ 25

243 divided by 9 = 27 solved using long division.     624 divided by 25 = 25 solved using long division.

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Examples of Long Division