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 are numbers left over. These are called 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.)

divide step 1 4 ÷ 25 = 0 remainder 4 The first number of the dividend is divided by the divisor.
divide step 2   The whole number result is placed at the top. Any remainders are ignored at this point.
divide step 3 25 × 0 = 0 The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into.
divide step 4 4 – 0 = 4 Now we take away the bottom number from the top number.
divide step 5   Bring down the next number of the dividend.
divide step 6 43 ÷ 25 = 1 remainder 18 Divide this number by the divisor.
divide step 7   The whole number result is placed at the top. Any remainders are ignored at this point.
divide step 8 25 × 1 = 25 The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into.
divide step 9 43 – 25 = 18 Now we take away the bottom number from the top number.
divide step 10   Bring down the next number of the dividend.
divide step 11 185 ÷ 25 = 7 remainder 10 Divide this number by the divisor.
divide step 12   The whole number result is placed at the top. Any remainders are ignored at this point.
divide step 13 25 × 7 = 175 The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
divide step 14 185 – 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.
divide step 15  

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