Long Multiplication
Contents of this Page
What is a Multiplication of Numbers with 3 Digits?
Standard Method 
Abyssinian Farmers' Multiplication
Grid Method
Cross Method 
Strip Method
Multiplication on the Internet
To the Main Page  "Mathematische Basteleien"

What is a Multiplication of Numbers with 3 Digits? top
...... If you must multiply numbers with several digits, you must use the "written" multiplication as we say in Germany. 

There are various methods of multiplication on this website with 896x271 as an example.

Standard Method in Germany top
1) Problem

2) Multiply 3x

3) Add 6x

4) Result

Background: 896*271 = (800+90+6)*271 =  800*271+90*271+6*271 

Variations of this method 
Detailed, for beginners

In the past


English Method

Abyssinian Farmers' Multiplication    top
1) Halve 9x without remainder and double.9x.
2) Delete the lines with even numbers in the left-hand column
3) Add 6x
4) Result
Lines with even numbers are deleted, because the Abyssinian Farmers think: "Even numbers give bad luck."
This method is also called Russian farmers' method. 

Background:  896*271 = (512+256+128)*271 = (2^9+2^8+2^7)*271 = 2^9*271+2^8*271+2^7*271  = 34688+69376+138752 = 242816. 
The first factor becomes a binary number. - The multiplication is reduced to halving and doubling. 

Neper's Grid method top
1) Problem

2) Multiply 9x

3) Add 6x

4) Result

Another shape

896*271 = (800+90+6)*(200+70+1)=8*2*10.000+8*7*1000+8*1*100 + 9*2*1000+9*7*100+9*1*10 + 6*2*100+6*7*10+6*1.

Cross Method   top
Draw the following picture and give a figure to each part.

Write corresponding digits on the ends of the lines. 
The product is 

Form terms of the numbers and calculate. 

Keep the results in your head. 

Write down the results and take into account the amount carried over.

Write down this picture only in this method.

896*271 = (800+90+6)*(200+70+1)=8*2*10.000+8*7*1000+8*1*100 + 9*2*1000+9*7*100+9*1*10 + 6*2*100+6*7*10+6*1.

Peter Müller from Saarbrücken sent me this method. Thanks. 

Strip method    top
Write the second factor on a strip of paper, move the strip to the left, multiply and add. 

Overall view

Background: 896*271 = (800+90+6)*(200+70+1)
= 8*2*10,000+8*7*1000+8*1*100 + 9*2*1000+9*7*100+9*1*10 + 6*2*100+6*7*10+6*1.

Multiplication on the Internet      top


Schriftliche Multiplikation, Multiplikation, Russische Bauernmultiplikation


Alexander Bogomolny (Cut The Knot)
Peasant MultiplicationLong Multiplication

Multiplication, Multiplication algorithmAncient Egyptian multiplication

References  top
Ewald Fettweis: Wie man einstens rechnete, Leipzig 1923
Walter Sperling: Auf du und du mit Zahlen, Rüschlikon-Zürich 1955 

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