The Secrets of Mental Math

There is a book dedicated to mental arithmetic, Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks, commonly translated into Chinese as 《心算秘密》. It was co-written by mathematician Arthur Benjamin and writer Michael Shermer, providing an in-depth explanation of mental math techniques along with numerous tricks and memory aids.

1. Addition and Subtraction from Left to Right:

For example, in calculating 412 + 379, start by adding 400 + 300 to get 700, then 10 + 70 to get 80, and 2 + 9 to get 11. Finally, add 700 + 80 + 11 to reach 791. Some might think this approach isn’t much faster than the traditional method (which adds from right to left, starting with the units digit and moving to the left). However, this method is actually more aligned with how the human brain processes numbers. With extensive practice, one can develop rapid calculation skills. This ability is similar to learning to type: beginners need to look at the keyboard constantly, while proficient typists type effortlessly without looking. Likewise, once you become familiar with left-to-right addition, the intermediate steps become mentally compressed, allowing you to speak the answer instantly.

2. Decomposed Multiplication:

Multiplication works on the same principle. For example, 36 × 7 can be broken down as 30 × 7 = 210 and 6 × 7 = 42, then adding 210 + 42 to get 252. This approach is also more brain-friendly than multiplying directly. With regular practice, it’s possible to say the result of any multiplication problem within seconds.

The examples above are the simplest methods featured in the book, which also includes many advanced techniques. In fact, any ordinary person can, by following the book’s methods and committing to long-term practice, develop mental math skills that feel almost magical.