A student I know came up with a way of checking multiplication that has knocked my socks off!
Here are a few web pages to show you how it's done.  If you are a mathematician and can explain how this works, I'd love to hear from you.
 
 
 

You may be doing a multiplication problem and you want to do a quick check for errors.
Here's what you do.
 

After you multiply, draw a large X next to the problem.

Add the digits in the first factor  and write the one-digit sum in the top space of the X.

 
 

Add the digits in the second factor.  If they do not add up to a one digit number, add those digits until you get a one-digit sum.  Write the one-digit sum in the bottom space of the X.

 
 
 

Multiply the one-digit number in the top of the x byt the one-digit number in the bottom of the x. Add the digits of the product until you get a one-digit number. Write that number on the left side of the X.

 
 
 

Add the digits in the product until you get a one-digit number. Write that digit in the right side of the X.

 
 
 

Compare the left and right one-digit number in the X. If they are different, you have definitely made a mistake. If they are the same, you probably have not made a mistake. (But you are not 100% sure.)

Before you try to use this, and just to be sure you have the hang of it, go through another example.
Click on this X.