It is useful for you to be able to multiply and divide without using a calculator. Learn how to do this using short division and short multiplication.

To divide a large number by a -digit number you can set it out like this:

- goes into once with remaining (remainder ), so put above the hundreds column and carry the to the tens column.
- goes into five times, remainder , so put above the tens column and carry the to the units column.
- goes into exactly three times, so put above the units column.

So,

Sometimes, a number does not divide into another number exactly.

In this case, we can either give the answer as a whole number along with a remainder, or we can give the answer as a decimal. The decimal answer may be a terminating decimal or a recurring decimal. Often, decimal answers may be rounded to a required number of decimal places.

For example:

**Method 1** - answer as a whole number with a remainder.

- goes into once with remaining (remainder ), so put above the hundreds column and carry the to the tens column.
- goes into three times, remainder , so put above the tens column and carry the to the units column.
- goes into seven times, remainder , so put above the units column and have a remainder of .

So, remainder .

We write this with an for 'remainder', so it looks like this:

**Method 2** - decimal answer, rounded to decimal place.

- goes into once with remaining (remainder ), so put above the hundreds column and carry the to the tens column.
- goes into three times, remainder , so put above the tens column and carry the to the units column.
- goes into seven times, remainder , so put above the units column and carry the to the tenths column (writing the as as does not divide into it exactly).
- goes into seven times, remainder , so put above the tenths column and carry the to the hundredths column.
- goes into once, remainder , etc

So,

(correct to decimal place).

**This method is called short division.**