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.

Step 1: The grid.

Picture of The grid.
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.

shazni3 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)  shazni3 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 +


shazni Kiteman3 years ago
Thank you! that is soooo lovely....is there some more methods ...like 8 times and 7 times and 6 times??? :-)
Kiteman (author)  shazni3 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 Kiteman3 years ago
Thanks! my daughter is showing off the finger method to all :-)
cammers3 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.
rimar20003 years ago
Nice, I liked the method of fingers.
Chikara5 years ago
I use this method, but I've always called it Lattice.
Foaly7 Chikara4 years ago
Goodhart5 years ago
Cool ! another perspective. I love finding different ways to do the same thing.
macmaniac5 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)  macmaniac5 years ago
Thank you!
 I believe this is also called "Lattice Multiplication"?
Jayefuu5 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)  Jayefuu5 years ago
Jayefuu Kiteman5 years ago
long? no calculator? by hand? Other than that you're covered :D
Kiteman (author)  Jayefuu5 years ago
Sorted, thanks.