# 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

**method.**

*short division*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:

- 72 ÷ 4 =
- 78 ÷ 6 =
- 102 ÷ 3 =
- 224 ÷ 4 =
- 222 ÷ 6 =
- 245 ÷ 7 =
- 4311 ÷ 3 =
- 5624 ÷ 4 =
- 5634 ÷ 6 =
- 8638 ÷ 7 =