Multiplying large numbers in your head may seem like a daunting task, but it can come in handy if you ever find yourself without paper or a calculator. It will take some practice, but it is not as difficult as it may appear to be; the trickiest part is keeping track of your numbers. Not only will learning to solve large multiplication problems without aid give you an unusual skill to show off, it will help you to become better at math in general, with or without a pencil and paper.
Break down the numbers in your multiplication problem into smaller parts. For example if you are multiplying 320x23, look at the numbers as added-together parts: 300+20 and 20+3.
Multiply one of the numbers in its entirety with the first part of the other broken down number. For example 320x20. If this is too much for you, then break down the numbers even further: 32 and 0, and 2 and 0. Multiply 32x2 which is 64. Add on the two additional zeros, and you get 6400 which is the product of 320x20.
Keep the number 6400 in your memory. Remembering the numbers along the way may be the most difficult part of doing multiplication in your head without any tangible way to keep track of the numbers, but as you practice you will be surprised to find how much your memory can actually hold.
Multiply the same first number with the second part of the second number. For example, multiply 320x3. If, again, it is easier for you to break this down even more, than multiply 32x3 and save that zero to add on to the end result. 32x3 is 96, place the zero on the end and your product is 960.
Add your two products together: 6400+960 and you have your final answer: 7360!
Practice different multiplication problems using this method. Begin with smaller, more simple numbers, and use larger ones as you improve. Check your answers with a calculator until you get a hang of it.