Short Division

I have always wondered why the division algorithm we were taught during our elementary grades is called long division since there was no short division.

In our previous post about dividing by two, we showed how a long number can be easily by halved by decomposing it into several addends. For example,

578 ÷ 2 =  (500 + 70 + 8) ÷ 2 = 250 + 35 + 4 = 289

or 578 ÷ 2 =  (400 +160 + 18) ÷ 2 = 200 + 80 + 9 = 289.

My preference to use the second way of partitioning or decomposing a number, where the initial digit(s) is/are even, led me to write about my one-line division technique in my book 25 Math Short Cuts. However, I found out much, much later that it was, in fact, the short division method.

Here is how it is done: Divide the number starting from the left. Write the remainder, if any, as a prefix to the next digit of the dividend before proceeding with the division.

Let’s take another example: 2892 ÷ 3 =   

Try using the short division method in the following:

1. 72  ÷ 4 =
2. 78  ÷ 6 =
3. 102  ÷ 3 =
4. 224  ÷ 4 =
5. 222  ÷ 6 =
6. 245  ÷ 7 =
7. 4311 ÷ 3 =
8. 5624 ÷ 4 =
9. 5634 ÷ 6 =
10. 8638 ÷ 7 =