Instructables

Napier's bones, without the bones.

Picture of Napier's bones, without the bones.
Napier's bones are an easy way of multiplying large numbers without losing track of all the columns, rows, carrying...

The original version (repeated in this instructable) consisted of sticks (bones) with numbers marked on them, but that's not so portable.

The process can, though, be repeated with pencil and paper.

In school, this method is suitable for classes of most ages who are getting to grips with multiplying larger numbers.

In the UK, KS2 and upwards.
 
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Step 1: The grid.

Picture of The grid.
Napiers1.jpg
You start with a grid, sized to match the digits of your numbers.

For instance, if you are multiplying 748x43, you need a grid of 3x2 squares.

Draw diagonal lines across the grid (top-right to bottom-left), extending them to below the grid (see the examples in the images).

Write your numbers outside the grid (in the templates, I have drawn dotted-squares to show you where).

If you are not used to using the grids, or are just too lazy to draw them yourself, you can use the templates I have added to this Instructable.

The large sheet, with every size of grid on it, is a resource I created for my maths class, some of whom have poor motor skills, so can't draw straight lines without help.



Step 2: The easy bit.

You don't get your final answer by magic, but it's not too hard as long as you know your basic tables up to 9.

Multiply each digit on the top row by each digit on the side column.  This can mean doing quite a few calculations, but they are all simple.

If the result of a calculation has two digits, the "tens" digit gets written above the diagonal line, and the "units" digit gets written below it.  For instance, 6x7=42, so write the 4 above and the 2 below (4/2).

If the result of a calculation is only one digit, write a zero above the diagonal line (2x3=6, so you write 0/6)

(You would not normally do this in coloured ink, but I have used it for clarity.)

shazni2 years ago
my 9 yr old daughter finds maths very difficult...they cant use calculators in school...only paper, pen, and their brains!...needless to say...she loved the finger method of the 9 time tables...wish i could find other methods for the rest!
Kiteman (author)  shazni2 years ago
You can do your 11 times table by adding the number to itself, but with one number moved one place to the left.

eg 11 x 42 (forgive the layout - you can easily do this in your head)

42_
_42 +

462

shazni Kiteman2 years ago
Thank you! that is soooo lovely....is there some more methods ...like 8 times and 7 times and 6 times??? :-)
Kiteman (author)  shazni2 years ago
Well, 8s are just your 4s, but doubled, but I'm afraid that 7s and 6s are best learned the old-fashioned way.
shazni Kiteman2 years ago
Thanks! my daughter is showing off the finger method to all :-)
cammers2 years ago
Thank you Kiteman. That's brilliant.
Too late to soften the hell that was my maths class at school, but I will certainly be using these techniques from now on, and teaching them to my children.
rimar20002 years ago
Nice, I liked the method of fingers.
Chikara4 years ago
I use this method, but I've always called it Lattice.
Foaly7 Chikara3 years ago
Yep.
Same.
Goodhart4 years ago
Cool ! another perspective. I love finding different ways to do the same thing.
macmaniac4 years ago
I've been using this method for long multiplication for a long time - it's the best by far. Good 'ible on it, as always.
Kiteman (author)  macmaniac4 years ago
Thank you!
 I believe this is also called "Lattice Multiplication"?
Jayefuu4 years ago
Awesome ible. While the title made me laugh I don't think it'll help many people find it :( Hope your keywords are good!
Kiteman (author)  Jayefuu4 years ago
Jayefuu Kiteman4 years ago
long? no calculator? by hand? Other than that you're covered :D
Kiteman (author)  Jayefuu4 years ago
Sorted, thanks.