Last time I talked about memory and memorization I discussed how I learned the Braille alphabet. We reduced the number of symbols to memorize from 64 down to 5, plus a few rules to transform those symbols. I mentioned I wanted to show how I skipped learning the multiplication tables.

In elementary school, I hated having to memorize the multiplication table. Teachers always tried to tell me different ways to memorize it, but I could never shove that knowledge in my head.

In university, I took a computer hardware course. We learned how computer processors work on an electrical level. We built individual components and tested them. As part of this we learned how a computer does multiplication: it adds over and over again.

Suddenly I didn’t need to memorize the multiplication table. I knew I could add repeatedly no problem. All I needed to do was remember the starting number and add something to it.

Let’s go through an example together. Let’s do 12×8.

Brute Force Example

The easiest way I multiply this number is to do the following:

Start = 0. Loop = 1. Add 12. Result: 12. Is loop < 8? Yes: continue.

Start: 12. Loop = 2. Add 12. Result: 24. Is loop < 8? Yes: continue.

Start: 24. Loop = 3. Add 12. Result: 36. Is loop < 8? Yes: continue.

Start: 36. Loop = 4. Add 12. Result: 48. Is loop < 8? Yes: continue.

Start: 48. Loop = 5. Add 12. Result: 60. Is loop < 8? Yes: continue.

Start: 60. Loop = 6. Add 12. Result: 72. Is loop < 8? Yes: continue.

Start: 72. Loop = 7. Add 12. Result: 84. Is loop < 8? Yes: continue.

Start: 84. Loop = 8. Add 12. Result: 96. Is loop < 8? No, stop.

I love knowing this technique because it means as long as I can do addition over and over, I’m guaranteed to get the right answer.

There’s another way to do this problem though!

Decomposition into Easier Problems Example

This is where I apply another shortcut that I learned in math class: multiplication is commutative. What does that mean? It means the following are the same problem:

8×12 = 12×8

In other words, I could run 8×12 or 12×8 and get the same answer. It also means I can apply another mental shortcut I take when multiplying.

If 12×8 = 8×12, I can decompose this problem.

I know that 8×10 = 80. Since multiplication is repeated addition, I can decompose 8×12 into (8×10) + (8×2), or 80 + 16. I can compute these problems in my head much faster than trying to multiply 12 by 8 (or add 12 to itself 8 times).

Transformation into Easier Problems Example

Another trick I use is to find a problem that is close to the one I want to solve and see if there’s a way to work backward.

For example, let’s take 8×9. You could add 8 to itself 9 times, but there’s an easier way to solve this one. 8×9 is close to 8×10. In fact, it’s one step before 8×10. I can decompose this into (8×10) – (8×1). My problem is now an easy one to compute: 80 – 8: 72.

I often find it easier to do a multiply and subtract when I’m dealing with a multiplication problem that’s close to 10.

Another example: 6×8. This is close to 6×10. It’s also equivalent to (6×10) – (6×2). These two problems are way easier for me to compute.

  • (6×10) – (6×2)
  • 60 – (6×2)
  • 60 – 12
  • 60 – 10 – 2 [Because 12 is 10 and 2, and to remove 12 from a number, we can remove 10 and then remove 2]
  • 50 – 2
  • 48

Let me be clear: I hate memorization for the sake of memorization. It annoys me. If you don’t give a piece of information context it will not be remembered by your learners. Humans are great at remembering rules. We suck at memorization for the sake of.

Published by Elias

Elias Puurunen is a versatile entrepreneur and President of Northern HCI Solutions Inc., an IT consulting firm which has worked with Fortune 500 companies, governments, and startups. He has spoken at conferences in Canada and the United States and has been published around the world. Part of his work led to an agreement between the Canadian Government and Siemens Canada, creating jobs and investment into green infrastructure. His company's event management app, the Tractus Event Passport connects people at conferences, seminars and symposiums across Canada. Today he is a consultant and advisor to technology firms and government organizations. He lectures at the University of Waterloo on Coding for Policy Analysis for the School of Public Policy. He is the author of Beyond Passwords: Secure Your Business, a cyber-security book for small business owners.

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