Peasant multiplication: Difference between revisions
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The method works because 27 * 82 = 27 * (64 + 16 + 2). |
The method works because multiplication is [[distributive property|distributive]], so 27 * 82 = 27 * (64 + 16 + 2). |
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This method was known to ancient Egtyptians as |
This method was known to ancient Egtyptians as |
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Revision as of 01:23, 13 October 2003
Peasant multiplication is an old algorithm for multiplication. It requires no use of a multiplication table; however, it requires that the user be able to divide by 2. The user must also know how to add.
- Write the two numbers (A and B) you wish to multiply, each at the head of a column.
- Starting with A, divide by 2 (if the result is not an integer, subtract 0.5 from it) until there is nothing left to divide. Write the series of results under A.
- Starting with B, keep doubling until you have doubled it as many times as you divided the first number. Write the series of results under B.
- Add up all the numbers in the B-column that are next to an odd number in the A-column. This gives you the result.
Example: 27 times 82
| A-column | B-column | Add this |
| 27 | 82 | 82 |
| 13 | 164 | 164 |
| 6 | 328 | |
| 3 | 656 | 656 |
| 1 | 1312 | 1312 |
| Result: 2214 | ||
The method works because multiplication is distributive, so 27 * 82 = 27 * (64 + 16 + 2).
This method was known to ancient Egtyptians as mediation and duplation, where mediation means halving one number and duplation means doubling the other number. It is still used by peasants in some areas, such as Russia.