Maths Museum Museum
    Calculating Rods Maths Museum

Before calculators, complex multiplication was made far easier using calculating rods, also known as Napier's Bones. Using this tool, multiplication is reduced to simple addition. Each rod, or 'bone' contains a multiplication table of a number from 0 to 9 as in figure 1.

Index
1
2
3
4
5
6
7
8
9
 
5
0 / 5
1 / 0
1 / 5
2 / 0
2 / 5
3 / 0
3 / 5
4 / 0
4 / 5
3
0 / 3
0 / 6
0 / 9
1 / 2
1 / 5
1 / 8
2 / 1
2 / 4
2 / 7
7
0 / 7
1 / 4
2 / 1
2 / 8
3 / 5
4 / 2
4 / 9
5 / 6
6 / 3

To multiply two digits together such as 8 x 3, first choose the rod that shows the table of three. Using the index rod, look at the number in the eighth row, in this case, 24.

To multiply larger numbers with a single digit number (for example, 8 x 537), simply place the rods next to each other with the index rod in front. The row with the index numeral 8 indicates the result if the units, tens, hundreds, and thousands are added together as follows:

 1000s100s10s1s 
8 x 5 =40  (8 x 5 x 100)
8 x 3 = 24 (8 x 3 x 10)
8 x 7 =  56(8 x 7 x 1)
-----------------
8 x 537 =4296 

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