Mental math is fundamental to understanding concepts and solving problems in your head. However, some problems can seem really challenging, which forces us to rely on calculators and computers. As a result, in this 4-part series for mental math, we will go over: Multiplication, Division, Addition & Subtraction, and my personal favourite- Percentages. Now, let’s get into multiplication!

The problems above might be simple and easy to solve in your head. Multiplying by 10 or 2 isn’t really that difficult, but what happens when you increase the size and complexity of these problems?

Before you pull out your calculators, let’s think about how we can solve these problems entirely mentally. One great strategy for multiplication, is breaking one number into a sum or difference of two numbers. The reason being, x10 and x5 are easy to perform so if you have something like 12×16, you could make it 16x(10+2) or 12x(10+5+1) or 12x(20-4). If we use these approaches, we would get: a) 160 + 32 = 192, b) 120 + 60 + 12 = 192, and c) 240 – 48 = 192. Hence, using a couple of different approaches, we were able to arrive at 192. There is also another interesting approach to consider when you have an even difference between your values. For example, if you have 21 and 27, the difference is 6, so it would work there. In particular, this approach uses the logic behind a difference of squares:

Similarly, let’s apply this to our earlier example of 27×21:

Overall, let’s apply these concepts to our first 4 questions and see how we can quickly and efficiently solve these problems:

Thus, there are many different approaches we can take to get to the answer. The important part is breaking down the problem into smaller pieces. Also, if you liked this post, be sure to check out the rest of the series, where we go over division, addition, subtraction, and percentages!

Lastly, if you enjoyed reading this post, then please share it with your friends! Also, let me know in the comments below what you would like to see a post about next…