Long multiplication: Using a placeholder

A very common mistake in long multiplication is for a pupil to forget to use a place holder when multiplying by the tens digit, because they don’t understand its purpose and importance.

Place value needs to be reinforced, so that when pupils multiply by the 1, they understand that they are actually multiplying by a ten. Multiplying a whole number by 10 always gives an answer which ends in zero, so we know there will be no units in the answer and can simply use a placeholder. Forgetting to use a place holder means that they have multiplied by 1 instead of 10 and pupils should be prompted to look at their answer to realise this mistake.

A simple way to illustrate this place value is to multiply by 11. If the place holder is forgotten, both rows in the multiplication are identical and it is easy to see that each answer is a result of multiplying by 1. This means overall, the initial number has only been multiplied by 2.

Similarly, when multiplying by 3 digit numbers, two placeholders are needed to maintain the place value when multiplying by the hundreds digit.