Dividing large numbers (long division)
We are going to divide 426 by 25.
The number that we dividing is called the dividend.
In our example 426 is the dividend. Dividend comes from a Latin word dividendum which meant something to be divided.
The number that we are dividing by is called the divisor. We divide the dividend by the divisor. In our example, 25 is the divisor.
We want to calculate 426 ÷ 25. This is the same as 426/25. It is also the same as
This symbol means divide the number inside the symbol by the number to the left of it.
In other words, we place the dividend inside the symbol and the divisor outside it, to the left.
This is read as four hundred and twenty six divided by twenty five.
We are going to work out how many complete \times 25 will go into 426 and how much is left over. For example 2 will go into 3 one time with one left over.
This is how it is done:
First we see how many \times the divisor will go into the first number of the dividend
It is clear that 25 doesn’t go into 4 any \times, so we see how many \times the whole of 25 goes into the first and second digits which is 42
25 goes into 42 one time so we write a 1 above the 2 of 42 like so
Then we multiply this 1 by the divisor and write the result under the first digit of the dividend
Then we subtract this number from the 42.
42 – 25 = 17. We draw a line and write 17.
Next we ‘bring down’ the next digit in the dividend. This is the 6. We write it beside the 17 to create the number 176.
25 goes into 176 seven \times with one left over.
We write 7 on top beside the 1
Then we multiply the 7 by the 25 and write it below the 176. 7 x 25 = 175
Then we subtract the 175 from the 176 to find the remainder
The remainder is 1
The answer to 
This is the same as saying
We can prove this by rearranging this to 
