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How Do You Multiply?

In Japan, elementary school students are expected to memorize multiplication from 1×1 through 9×9. It is called kuku (九九). We repeat the tables rhythmically until answers such as 7×8=56 come almost automatically.

 

In some countries, students memorize even further. In India, for example, it is common for some students to learn multiplication tables beyond 10, sometimes to 20 or higher. I have even heard claims about memorizing much larger tables, although 99×99 does not appear to be a general educational standard.

 

But how do you calculate something you haven't memorized?

 

For 17×8, I would think:

 

10×8 = 80
7×8 = 56
80+56 = 136

 

For 99×9, I might think:

 

100×9 − 9 = 891

 

Today we always have calculators and smartphones nearby. But mental arithmetic is still useful.

 

The interesting question is not just how much did you memorize?

 

It is: How do you multiply in your head?