Mental Multiplication

There are many people who have difficulties solving math problems in their head. While most can do simple addition or subtraction, multiplication tends to be rather difficult. This is especially true as you get into multi-digit numbers, or scenarios which go outside of the most commonly remembered multiplication tables. It can sometimes be difficult to transfer the logic you've learned on paper into something paper-free, so I hope to aid you there. You may have learned this long ago in school, but a refresher never hurts.

Starting simple

While most people know the multiplication tables from 1 to 6, there's usually an difficult increase around 7, due to the way the human brain is wired (you'll notice this when counting objects, too; you have to count when there are 7 or more). Because of this common difficulty spike, this is where I'll start.

Now, you might remember that 8*8=64 or 7*7=49, but what about 7*6?

Intuitively, you might recount the 7 sequence in your mind to reach it. That would go a little something like this:

  1. 7+7=14
  2. 14+7=21
  3. 21+7=28
  4. 28+7=35
  5. 35+7=42

This 5-step process is rather tiresome, as I'm sure you'll agree, but there is another, quite obvious - yet likely underused - method. It goes like so:

  1. You know that 7*7=49, so start at 49.
  2. 49-7=42

I have here used 7*7, but you may just as well have used 6*6=36 and added another 6. My intention is not to teach each and every combination, and where to start from, but to explain how the concept can be used no matter the knowledge that you have. Even if you did not remember 7*7=49 or 6*6=36, it is not a problem, because you certainly remember another multiple, which you can go off of instead.

But of course, you might already remember 7*6=42, in which case this might appear pointless. I assure you that it is not.

That is because this concept and the logic surrounding it can be used with problems of much higher complexity.

Extra digits on one side

FOr a slightly more complicated illustration of this concept, please review the problem: 210*8.

I think we can agree that you do not know the solution to this, though you may be able to find it after a bit of thought.

A solution applying the earlier concept might look something like this:

  1. Instead of 210*8, expand to numbers that you know better. (210*10)-(210*2), for example. Multiples of 10 and 2 are extremely fast for the brain.
  2. 210*10=2100
  3. 210*2=420
  4. 2100-420=1680

Thus, 210*8=1680. To some, this may seem obvious. Hopefully, however, you see the benefits of this method, and the ways in which it it can be applied.

Final thoughts

Note that not all math problems can take advantage of this method, but it can nevertheless be a good jumping-off point for even more complex problems.

For practice, consider the below problems.

  • 7*78
  • 9*91
  • 420*6

All three of these problems benefit from the previously described method, but some may be less obvious than others. They should all be solvable in less than a minute.