Multiplication Algorithm Using Squares with Diagonals


Aside from the standard multiplication algorithm (algorithm really means steps or methods) that we already know, there is another method to do multiplication. That is, to place the numbers in squares. This method can be used for multiplying 2-digit numbers. We will call this method the Square Diagonal Multiplication Algorithm

Steps in Multiplication Algorithm

1. Create a 2 by 2 square and place the numbers on top and on the right side. Each digit should be assigned to one row and one column. The example is shown below for 63 × 17.

multiplication algorithm 0

2. In each square, draw a diagonal slanting to the right. 

3. To multiply, the product of the digits is assigned to the square corresponding to the columns and rows where they are placed. For example, the product of 3 which is on the right and 7 which is on the bottom should be assigned to the bottom-right square.

multiplication algorithm 5

4. Place the digits of each product such that the tens digit is on the triangle on the left and the ones digit is in the triangle on the right.  For example, if we multiply 3 x 7, in the product which is 21, 2 goes to the triangle on the left and 1 goes to the triangle  on the right.

multiplication algorithm

5. If the product is a 1-digit number, put 0 on the left. For example, if we multiply 3 and 1, the product becomes 03.

multiplicaiton algorithm 2

6. Fill out all the triangles.

multiplication algorithm 3

6. To get the product, add the digits diagonally to get the product as shown in the color codes shown below.


Ones digit: 1

Tens digit: 2 + 2 + 3 = 7

Hundreds digit: 4 + 6 + 0 = 10.

Thousands digit: 0

Since the hundreds digit is 10, 0 goes to the hundreds digit and 1 is carried over to the thousands digit. So, the product of 63 x 17 = 1071.

2 thoughts on “Multiplication Algorithm Using Squares with Diagonals

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  2. Pingback: How to Multiply Using Intersecting Lines

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