In our public education system we are unfortunately only taught that there are only two ways to multiply.
One is "long multiplication", and the other is a calculator. Long multiplication is the process of starting with the ones column and multiplying and if the number is greater then 9 you carry the value over to the tens column then you multiply and add and so on... It is a very lengthy process depending on the numbers you are multiplying. How ever there are many ways to multiply numbers together and there are many of them that do not test your ability to memorize a multiplication table. Which , in most public school systems that is all we are truly learning, is how to memorize and regurgitate facts. In the real world, there is much more to life than memorizing. Don't get me wrong a strong memory can be a beneficial talent to posses. However, the truth is that everyone is different. Some people have strong memories and some do not. So to address the fact that everyone is different and not every one has strong memories I will go over some alternate forms of multiplication. I will skip over long multiplication as most people are already familiar with it.
Lets start with the alternate long multiplication. So rather than starting on the right hand side and carrying over to the other columns we start on the right. I will demonstrate by example.
WE will multiply 47 X 32 = ?
47 we started with the left hand side which is 4 X 3 which is 12. but if you notice I
x32 a zero after the 12. The left most column is actually the tens column, which means
1200 that we are not multiplying 4 and 3 we are actually multiplying 40 and 30 so we
need put 1200 in here.
47 in this step we cross multiply the 4 and the 2 which is 8, and once again we see
x 32 that we are actually multiplying 40 and 2 which is 80.
47 here we multiply the3 and the 7 which s 21, and again we note that it is actually
x32 30 and 7 we are multiplying.so we add the zero to the end to get 210
47 In this step we multiply the two numbers in the ones column 7 and 2 and we
x32 get 14, and in this step there is no need to add a zero because we are
1200 multiplying only 7 and 2.
47 in this final step we simply add up the rows at the bottom and we
x32 get the final answer which is 1504
This method may not be the best for everyone. I personally prefer this method. However, the point I am trying to make is that everyone learns and understands things differently. So it is best to evaluate all the options and choose what works best for you.