RUSSIAN PEASANT MULTIPLICATION
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Areas of interaction:
Human ingenuity, Approaches to learning
The Russian Peasant multiplication method is a method of multiplying two numbers together without the use of
multiplication tables. To use this method you need only be able to add numbers together, and be able to multiply
and divide numbers by 2.
For example, suppose we want to find 24 £ 42. We start by writing the numbers side by side:
24
42
We then work down the columns, multiplying the numbers in the left column by 2, and dividing the numbers in
the right column by 2 (rounding down when we do not get a whole number):
24
48
96
42
21
10
We continue this process until we are left with a 1 in the right column:
24
48
96
192
384
768
42
21
10
5
2
1
Next we cross out any rows where the number in the right column is even:
24
48
96
192
384
768
42
21
10
5
2
1
We then obtain the answer by adding the remaining values in the left column, which gives 48+192+768 = 1008:
Thus 24 £ 42 = 1008:
What to do:
1 Use the Russian Peasant multiplication method to perform the following calculations:
a 25 £ 19
d 33 £ 33
b 12 £ 16
e 29 £ 23
c 21 £ 65
f 26 £ 72
2 Confirm that finding 42 £ 24 produces the same answer as in the example.
3 In general, is it quicker to put the smaller number or the larger number first when using this method?
4 What are the advantages and disadvantages of this method compared with using long multiplication?
b
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a
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5 Explain why this multiplication method works.
Hint: The product of a and b is equal to the number of balls in a
rectangle with a rows and b columns.
First consider a simple example where the second number is a power
of 2, such as 12 £ 16 in 1 b. Then extend your reasoning to more
complicated examples.
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Y:\HAESE\IB_MYP3\IB_MYP3_LN\008IB_MYP3_LN.cdr Monday, 16 June 2008 9:18:42 AM PETER
Russian Peasant Multiplication
2
RESEARCH
² Research the origin of the name given to this method.
² How do computers multiply numbers? Compare this method with the Russian Peasant multiplication method.
CHALLENGE
Try to come up with a similar multiplication method which involves multiplying and dividing by 3 instead of 2.
Hint: Sometimes you will need to round down, and sometimes you will need to round up ....
Y:\HAESE\IB_MYP3\IB_MYP3_LN\003IB_MYP3_LN.cdr Thursday, 12 June 2008 4:46:08 PM PETER