Using the Partial Products Method
The Partial Products Method helps simplify long multiplication. It is a very accessible method because it breaks down complex numbers into simpler, more easilymultiplied, ones. To use the Partial Products method, you need to decompose  that means "break apart" each number into its smaller forms. For example, the number 77 is actually seven tens plus seven ones. Start by writing out your decomposed number for each place value present. For example, in multiplication problem 12 times 47, 12 is actually:
and the number 47 is actually:
Then, multiply each of the decomposed ("broken apart") numbers in the multiplicand (upper number) by each of the decomposed numbers in the lower number (multiplier). The result is:
Finally, add together each partial product to discover the answer, and remember, when adding, to carry those tens! 

Here's a short video that explains how to use the Multiplication Tool to multiply using the partial products method. You may also view a schematic of how the tool works. 