What is a Multiplication of Numbers with 3 Digits?  top

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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 

Detailed, for beginners

In the past

rare

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

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.

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  896 *271.

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.

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

German

Wikipedia
Multiplikation,  Russische Bauernmultiplikation,  

Alexander Bogomolny (Cut The Knot)
Peasant Multiplication,  Long Multiplication,  

Wikipedia
Multiplication,  Multiplication algorithm,  Ancient Egyptian multiplication,  

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