Impressing Your Vietnamese Friends with Mental Arithmetic

HCMC2During my travels I spent a week in Ho Chi Minh City, absolutely loving my time there! One day, after visits to museums, temples and little shops, I ended up in a comfortable bubble tea store. While sipping my passion fruit bubble tea, a group of Vietnamese university students came in and started practicing their English. After some time, they asked whether I could help them with their English and I joined their study group. During introductions, I mentioned that I was a mathematician. Immediately I was bombarded by mental arithmetic questions and had to prove my worth. With the help of something I’d read about ages ago and never forgotten, I managed to impress them.

There is an ancient Indian form of mathematics known as Vedic mathematics. (Admittedly, there is some controversy surrounding it.) This type of mathematics involves a ton of tricks for mental arithmetic.

One of my all-time favorite tricks, and the one that came in handy, is a quick way for multiplying two-digit numbers with the same first digit and whose second digits add up to 10. (For example 63·67.)

Method:

  1. Perform the following multiplication: (first digit)·(first digit+1). The result will form the first few digits of the number.
  2. Then do: (second digit of 1st number)·(second digit of 2nd number). This yields the last two digits of the result.
    Note: If you perform 1·9=9, then write 09, as we need the product to take up the last two digits of the answer.
  3. Write the results next to one another and you end up with the answer.

Example: Let us take a look at 63·67:

  1. The first digit of 63 and 67 is 6. Hence we do 6·(6+1)=6·7=42.
  2. The second digits of 63 and 67 are 3 and 7 respectively. We do 3·7=21.
  3. Putting these answers together gives 4221.

 

Why does this work?Multiplication Trick copy

If, after performing the calculations on the right hand side, we were forced to express 100a(a+1)+b(10-b) in words, we would get:

x·y=the product of (first digit of x & y) and ((first digit of x & y) + 1), followed by the two digits given by the product of (last digit of x) and (last digit of y)

This is exactly what our method states.

 

Let me know about your favorite number tricks!

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