Long Division with Remainders

When we are given a long division to do it will not always work out to a whole number.

Sometimes there will be numbers left over. These are known as remainders.

Taking an example similar to that on the Long Division page it becomes more clear:

435 ÷ 25

(If you feel happy with the process on the Long Division page you can skip the first bit.)

4 ÷ 25 = 0 remainder 4 The first number of the dividend is divided by the divisor.
  The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 0 = 0 The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into.
4 – 0 = 4 Now we take away the bottom number from the top number.
  Bring down the next number of the dividend.
43 ÷ 25 = 1 remainder 18 Divide this number by the divisor.
  The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 1 = 25 The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into.
43 – 25 = 18 Now we take away the bottom number from the top number.
  Bring down the next number of the dividend.
185 ÷ 25 = 7 remainder 10 Divide this number by the divisor.
  The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 7 = 175 The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
185 – 175 = 10 Now we take away the bottom number from the top number.
    There is still 10 left over but no more numbers to bring down.
 

With a long division with remainders the answer is expressed as 17 remainder 10 as shown in the diagram

 

Answer: 435 ÷ 25 = 17 R 10