Multiplication – Other Methods

We will now some other strategies for multiplication which would be useful to students.

Multiplication of numbers by Array method (Lattice??)

This method presents the distributive method easier by presenting it in a matrix form. This is an extension of getting multiplication facts of 2-digit numbers using the multiplication table.

Let us do 32 x 28

This method first converts the problem into (30 + 2) X (20 + 8) and makes the multiplication by opening the brackets easier to visualise. Each cell is the product of the top Row and the left Column numbers. 8 X 30 = 240, 20 X 30 = 600, 20 X 2 = 40 & 8 X 2 =16.

Splitting each number into its “tens” & “units”, ensures that only multiplication facts of single digit numbers are needed.

Egyptian Method for Multiplication

The Egyptians used a method which today we can recognise as being related to the "binary" system of writing numbers. It uses the fact that the multiplier (in fact any whole number) can be written as a sum of powers of two.'

Let us do 6 x 7

We prepare a table where the multiplicant is repeatedly doubled, starting from 1.( 1, 2, 4 , 8 etc)

Against each the respective subtotal are written (5, 12, 24, 48 etc)

Only such multiples of the multiplicant are added which correspond to the corresponding multiples of the multiplier. 7 = 1 + 2 + 4. The product is the sum of the corresponding sub-products 6 + 12 + 24 = 42.

So any multiplication is reduced to doubling and adding.

2-digit multiplications using the 1-digit Multiplication Table

The single digit multiplication table can also be used to find multiplication facts of 2 digit numbers, where each of which can be expressed as a sum of 2 single digit numbers. For example, it can be used to find 12 X 13, since both 12 & 13 can be expressed as 8 + 4 & 7 + 6.

The method uses the idea of array multiplication which will be described in the next chapter.

The procedure is locating cells which indicate the 4 products of 8 X 7, 8X6, 4X7 & 4X6 which are 56, 48, 28 & 24 and add them. The answer is 156. So, 12 X 13 = 156.

Visually it would look like this.

With such methods, all children can become proficient with multiplication tables, without developing anxiety or phobia.

Constructing multiplication table for any 2-digit number

Long division is considered a difficult skill to learn. There are actually 2 separate processes, each of which is difficult.

One is the algorithm, as taught in schools, is not very logical and hence can confuse students.

Second is the computation of multiplication facts involving multi-digit numbers, which has to be performed several times, during the algorithm. This compounds the problem faced by students.

This process can be made simpler by constructing the table for the 2-digit number, before starting the division algorithm.

Chapter 12.16 gives a detailed explanation of the procedure for quickly writing down the multiplication table for any 2-digit number.

With a little experience, this procedure can be extended even to a 3-digit number.