Ordinary Multiplication Method

The multiplication how is teaching in early grades have the below organization.

Example 1......................

Where 12 and 34 are plot.
48 and 360 are multiples of 4 by 12 equal to 48
30 by 12 equal to 360
Then they are summed.

Many mistakes can be made with this form. Like the bad multiplication of each term, or finally error in the sum. In the end, it causes a difficulty to check for errors.

Arab Method of Multiplication or Gelosia

This method had its origins with Arab merchants. In this process we multiply with two digits at a time with a diagonal separating the respective results. Making the arrangement with Example 1.

Example 2...........................

We separated 12x34 in a square of 2x2, with each square with a diagonal.
Remembering the order of unity, tens places.
ascending vertically and to the left horizonally.

After multiplying the two digits of the meeting in the organization, we first complete the right side of the diagonal and if there was an excess in the base-10, we add digits to the left side of the diagonal. The sum is done diagonally starting from the right.

Making another example:

Example 3.................................

In this case, we have 346x67, that is a number with 3 hundreds, being this difference from the previous case.
With this, instead of doing 2x2 in the square, we make a rectangle of 2x3.
We proceed as before.

Adding the diagonals, find 345x67 = 23115. Making a generalization, being two numbers with how many digits are the sum of the number of digits of a number is equal to a part of the rectangle. For example, 4567, being a parcel, we will then have four rows or columns, depending on the position the student places.

The learning curve of this multiplication method is not so great, but the benefits are much greater. Facilitating the arrival of multiplication, and the visualization of possible errors.