Editing Napier's bones (section)

===Multiplication by a small single-digit number===

The first example computes {{nowrap|1=425 × 6}}.

Napier's bones for 4, 2, and 5 are placed into the board, in [[sequence]]. These bones show the larger figure which will be multiplied. The numbers lower in each column, or bone, are the digits found by ordinary multiplication tables for the corresponding integer, positioned above and below a diagonal line. (For example, the digits shown in the seventh row of the 4 bone are {{frac|2|8}}, representing {{nowrap|1=7 × 4 = 28}}.) In the example below for {{nowrap|1=425 × 6}}, the bones are here depicted as red (4), yellow (2), and blue (5).
[[File:Napier's Bones ex 1 pic 1.png|center|125px|First step of solving 6 x 425]]
The left-most column, preceding the bones shown coloured, may represent the 1 bone. (A blank space or zero to the upper left of each digit, separated by a diagonal line, should be understood, since {{nowrap|1=1 × 1 = 01}}, {{nowrap|1=1 × 2 = 02}}, {{nowrap|1=1 x 3 = 03}}, etc.) A small number is chosen, usually 2 through 9, by which to multiply the large number. In this example the small number by which to multiply the larger is 6. The horizontal row in which this number stands is the only row needed to perform the remaining calculations and may now be viewed in isolation.
[[File:Napier's Bones ex 1 pic 2.png|center|300px|Second step of solving 6 x 425]]
For the calculation, the digits separated by vertical lines (i.e. paired between diagonal lines, crossing over from one bone to the next) are added together to form the digits of the product. The final (right-most) number on that row will never require addition, as it is always isolated by the last diagonal line, and will always be the final digit of the product. In this example, there are four digits, since there are four groups of bone values lying between diagonal lines. The product's digits will stand in the order as calculated left to right. Apart from the first and the final digit, the product's digits will each be the sum of two values taken from two different bones.
[[File:Napier's Bones ex 1 pic 3.png|center|175px|Third step of solving 6 x 425]]
Bone values are added together, as described above, to find the digits of the product. In this diagram, the third product digit from the yellow and blue bones have their relevant values coloured green. Each sum is written in the space below. The sequence of the summations from left to right produces the figure of 2550. Therefore, the solution to multiplying 425 by 6 is 2550.