## Triple Digit Mental Arithmetic

maartens — Tue, 12/28/2010 - 15:37

After the piece on double digit mental arithmetic I wrote not long ago, I wondered if the method could be extended to 3 digit multiplication. However, as I found out while trying, it's all too easy to create temporary numbers beyond all practicality, clogging short term memory and pushing the brain onto a rollercoaster of calculation and recalculation to recover numbers from earlier phases!

Nevertheless, it turns out there is indeed a way to build on the 2 digit method that yields results, and requires only a bit more from short term memory than the 2 digit method. (Remember, the goal is to do the calculation without the aid of a pen and paper!).

Without further ado, let's use for our example

569

x 378:

The first stage is a repeat of the method we employed in the previous article. We take the two rightmost digits and multiply them (have a look at the previous article to see how this is done).

69

x 78

____

111

72

42

5382

This forms the foundation. Our mind has been primed by these numbers, making the subsequent calculations slightly easier to do.

In the second stage we multiply the (thus far unused) number in the top left corner with the (already used) bottom two right digits: 5 x 78. That gives 390. Likewise, we then multiply the (unused) number in the bottom left corner with the top right two digits: 3 x 69. That gives 207, and added to 390 gives **597**.

The final step in stage two is to multiply the number in the top left with the bottom left: 3 x 5 gives **15**.

Now 597 actually represents 59700, and 15 represents 150000, so to calculate the addition we can invoke them visually as follows:

597

15

2097

Note: 15+5=20 followed by 97 gives 2097.

The final calculation we do is to add the earlier result (5382) to the latest (2097). Remember that they represent different multiples of 10, so to add them we follow the same kind of visual method as above:

5382

2097

215082

And that is the answer!

Seems easy? Actually, it does take more twice longer than the 2 digit method, but that is largely down to the number of steps involved, and not due to the intrinsic difficulty of any individual step.

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*This article and its contents is made available freely under the Creative Commons License v3. If you find it useful and want to share, please mention me or link back. Thanks :-)*

*- Maartens Lourens, 2010*