Multiplying by a positive whole number that’s less than is easy. The result is simply repeated. For example,
and so on.
Most people know this, but what’s less wellknown is that there’s also a neat trick to multiply larger numbers by Suppose is a whole number with two digits. To work out simply work out the sum of the digits of and drop that sum inbetween the digits. For example, let The sum of its digits is Dropping that sum between the digits gives which is indeed equal to
There’s just one little caveat. If the sum of the digits of is or larger, you need to carry a digit. In other words, you stick the rightmost digit of the sum between the original digits and add the leftmost digit of the sum to the original leftmost digit. For example, if then the sum of the digits is We therefore stick a between the original digits and and add a to the to get which again is the correct result.
You can convince yourself that this trick always works using long multiplication. Suppose the digits of are and so Long multiplication now tells us that








from which our result easily follows.
Can you work out the trick for numbers with more than two digits? As a hint, here is the long multiplication when the digits of are up to :







= 







+ 


