A Multiplication Algorithm

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Is your child having difficulty learning the multiplication algorithm or multiplication tables.  Has he mastered addition? If your answer to both questions is yes, place value may be his stumbling block. Good new! A simpler method exists. It’s easy to learn and it will enable him to continue to progress with his classmates while he masters the standard method.

This method is an old method. It uses the 2 – times table and addition – his strong suits. The method can be used to multiply any two numbers. Ancient Egypt used it and it is used in  modern computer arithmetic. However multiplication by large numbers may prove prohibitive due to time constraints.

Let illustrate it by multiplying  11 *  54.

Designate 11 as the multiplier and 54 as the multiplicand.

Construct a table with two columns. The first column contains the powers of two:  1, 2, 4, 8, 16, etc. End the list when  the sum in the list is greater than the multiplier, in this case 11.

1    
2    
4    
8

1+2+4+8 = 15 which is greater than 11.

The second column starts with the multiplicand, 54.  The members of  this column are the double of the previous number. Hence the completed table is

1                    54
2                  108
4                  216
8                  432

Call the numbers in the first column that are addends of the multiplier, chosen. The chosen for 11 are then : 1, 2, 8 since  1+2+8=11.

Strikeout the table rows that are not led by chosen numbers.  4 is not a chose number. So the altered table is

1                    54
2                  108
8                  432

The product, 11 *  54, is the sum of the numbers in the second column of the altered table.   54+108+432 = 594.

11 *  54 = 594.

A deeper look: Using the numbers in the second column, this method gives the answer to each multiplication listed below:
1*54    =     the second column in the 1 row
2*54    =      the second column in the 2 row
3*54,   =      the sum of second column numbers in the 1 and 2 rows
4*54    =      the second column in the 4 row   
5*54    =     the sum of second column numbers in the 1 and 4 rows
6*54    =     the sum of second column numbers in the 2 and 4 rows
7*54    =    the sum of second column numbers in the 1, 2  and 4 rows

etc.  to

15*54.        the sum of second column numbers in the 1, 2 ,4 and 8 rows

For small numbers this method works fine. For large numbers for instance, 82 * 99 , the table will be prohibitive. Despite this flaw, you might still teach it to your child. After he masters it, assure him he is now ready to master  another multiplication algorithm that is easy to learn. Click the link to an algorithm that is easy to learn and is not restrictive in any way.

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