Ancient Egyptian Multiplication: A Quick and Easy Method

Have you ever wondered how ancient Egyptians performed multiplication? They didn’t have calculators or even Roman numerals! They used a clever method called Russian Peasant Multiplication, which dates back to 1650 BC and is documented in the Rind Mathematical Papyrus. This method is surprisingly efficient and involves a simple process of doubling, halving, and adding numbers.

How it Works

Let’s say we want to multiply 13 by 11. Here’s how we do it:

1. Create two columns. In the left column, write the first number (13) and keep halving it, discarding any remainders, until you reach 1. In the right column, write the second number (11) and keep doubling it.
2. Cross out any rows where the left column number is even. In our example, we would cross out the row with 6.
3. Add up the remaining numbers in the right column. This sum is the product of the original two numbers.

Here’s the breakdown:

Left Column (Halving)	Right Column (Doubling)
13	11
6	22
3	44
1	88

Adding the remaining numbers in the right column: 11 + 44 + 88 = 143. Therefore, 13 x 11 = 143.

Why Does it Work?

Russian Peasant Multiplication is based on the binary number system. In binary, every number can be expressed as a sum of powers of 2. When you halve a number, you are essentially shifting its binary representation one position to the right. When you double a number, you are shifting its binary representation one position to the left. By crossing out the even numbers in the left column, you are effectively eliminating the terms in the binary expansion of the product that correspond to powers of 2 that are not present in the original numbers.

Advantages of Russian Peasant Multiplication

• Easy to learn and apply: The method is straightforward and doesn’t require memorization of multiplication tables.
• Efficient for large numbers: It can be used for multiplying large numbers without needing to perform complex calculations.
• Historical significance: It provides a glimpse into the mathematical practices of ancient civilizations.

Try it Yourself!

Pick any two numbers and try out Russian Peasant Multiplication. You’ll be surprised how quickly and easily you can get the answer. This method is a fun and engaging way to learn about different approaches to multiplication and explore the history of mathematics.