I think I invented this method of multiplying; but, sometimes, I doubt it. The method is so obvious, it must be that many others have thought of it. However, until someone convinces me that this scheme is so apparent that it really does not have any inventor, I’ll continue to think that I was the inventor.

The objective of this method is to multiply a two-digit number by a two-digit number and/or a three-digit number by three-digit number easily and quickly with reduced chances for error. However, in order to use this system, *a person needs to know the multiplication table cold.*

Let’s consider an example of how my system works. Suppose we wish to multiply 34 x 85. First, write the numbers on a piece of paper this way:

..34

..85

——-

Now, multiply 3 x 8 and 4 x 5 write the products under the problem this way:

..34

..85

——–

2420

Next, multiply 8 x 4 and 3 x 5 and place the products under the problem this way:

..34

..85

——–

2420

..32

..15

Note carefully where the four products were placed. (The indentations are important.) Every product must be a two-digit number. If necessary, you need to place a zero ahead of a one-digit number. For example, if a product is 6, write 06 in its required place.

Now, draw another horizontal line, and sum the 8 digits above the line. This way:

..34

..85

——–

2420

..32

..15

——–

2890

The problem is solved. The product of 34 x 85 is 2890. You’ll observe that this method of multiplying does not require that you carry any numbers in your head. Accuracy is improved this way.

Now, let’s do a problem involving a three-digit number multiplied by a three-digit number. Let’s consider this problem:

…246

…385

Start the solution this way:

…246

…385

———–

063230

Note where the products of 2 x 3, 4 x 8, and 6 x 5 are placed. You now need to install four more products. They are 3 x 4, 2 x 8, 4 x 5, and 8 x 6. Continue this way:

..246

..385

———–

063230

..1220

..1648

Note where the products of 3 x 4, 2 x 8, 4 x 5, and 8 x 6 are placed. (The indentation is important). There are two more products to place. They are 3 x 6 and 2 x 5. Here they are:

..246

..385

———–

063230

..1220

..1648

….18

….10

———–

94710

(The indentation is important.) The problem has now been solved. The product of 246 x 385 is 94710. Note where the products of 3 x 8 and 2 x 5 are placed. The last step is to draw a summation line and sum the 18 digits.

When one multiplies a two-digit number by a two-digit number, four multiplications are required. If the four products are carefully placed in a matrix, then summed, the result of the problem will be available without any carries having been necessary. The chances of making errors are reduced.

When one multiples a three-digit number by a three-digit number, nine multiplications are required. If the nine products are carefully placed in a matrix, then summed, the result of the problem will be available without any carries having been necessary. As with the smaller problem, the chances of making errors are reduced.

The question might arise as to whether this method of multiplying can be carried forward with larger problems. The answer is *yes*. We’ll leave this as a problem for the student as to what needs to be done.