Multiplication of Large Numbers

We know what multiplication is, and hopefully we memorized our times tables.

Well let’s first learn how to do this rigorously on paper, but then let’s learn some easy tricks that will help us do this in our heads much more efficiently.

The distributive property tells us that this is the same as fourteen times ten plus fourteen times one, and these products are easy to get in our heads.

Really, these two methods are doing exactly the same thing, it’s just that one follows a rigid algorithm, while the other involves a little more creativity,

Let’s try another one, four hundred twenty-five times twelve.

If you like using pen and paper and are very diligent, there is no problem with this approach, but it opens up a lot of opportunities for error,

Instead of four hundred twenty-five times twelve, let’s do four hundred twenty-five times ten plus two.

When multiplying by ten we just add a zero, so that’s four thousand two hundred and fifty.

Add them together, and we get our answer.

Let’s take a moment to notice that these numbers are the same as the ones we added together when using the other approach.

When we multiply through the units place, we are multiplying by two. When we multiply through the tens place, we are multiplying by ten.

But while the first method requires many small computations, the second method requires comparatively fewer.

Still, through practice, you may find your own method that works for you,

Being able to do mental math is a great life skill to have,

try not to write anything down, and let’s check comprehension.