Associated Topics || Dr. Math Home || Search Dr. Math

Rapid Multiplication ... Diagonally?

```Date: 02/24/2010 at 07:50:32
From: George
Subject: Alternative multiplication method (fast!)

Some years ago, I saw a system of multiplication demonstrated on
television.

As I recall, the system involved multiplying the top left digit by
the bottom right, and continuing to multiply diagonally in this way,
moving in opposite directions along each term.

How does this high-speed calculation technique work?

```

```
Date: 02/24/2010 at 21:53:10
From: Doctor Vogler
Subject: Re: Alternative multiplication method (fast!)

Hi George,

Thanks for writing to Dr. Math.

Here's what you probably saw:

To find the product of two multi-digit numbers, you have to keep a
borrow a term often used in computers).

Start out your accumulator at zero.  Compute the digits of the
product as follows, starting with the rightmost digit and moving to
the left:  To compute the n'th digit from the right, you have to add
n products to your accumulator, starting with the n'th digit from the
right of the top factor and the rightmost digit of the bottom factor,
and ending with the rightmost digit of the top factor and the n'th
digit from the right of the bottom factor.  After adding all n of
those products to your accumulator, you write down the last digit of
your accumulator and then shift the accumulator to the right by one
digit.

For example, to compute 486 * 197, you start with the accumulator at
0.  Then you add 6*7 = 42, giving 42.  You write down the digit 2 in
the "ones" place (that's the rightmost digit of your product) and
shift your accumulator, which is now waiting at 4 in the "tens" place:

_ _ _   (4) 2

Then you add to that 8*7 + 6*9 = 56 + 54 = 110, giving 114.  You
write down the 4 and shift the accumulator, which is now 11:

_ _ (11)  4  2

Then you add 4*7 + 8*9 + 6*1, giving 117.  You write down the 7, and
shift again, giving 11:

_ (11) 7  4  2

Then you add 4*9 + 8*1, giving 55.  You write down the 5, and shift,
giving 5:

(5) 5  7  4  2

Then you add 4*1, giving 9, which you write down (that's the leftmost

9  5  7  4  2

So your answer is all of the digits you've written down, namely 95742.

back and show me what you have been able to do, and I will try to
offer further suggestions.

- Doctor Vogler, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Multiplication

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search