Ancient Methods of Multiplication – The Egyptian Form of Multiplication

Teaching students about ancient methods of solving mathematical problems will ignite their interest in math and show them the path that different cultures took to reach to the mathematics we know today. Imagine the students ‘ reaction when you tell them that clever Ancient Egyptians only had to learn the x2 table to do multiplication!

The Ancient Egyptians used an interesting way to multiply two numbers. The algorithm draws on the binary system: multiplication by 2. They used addition to get the answer to a multiplication problem. This method is still used in many rural communities in Ethiopia, Russia, the Arab World, and the Near East.

The term that we use with Egyptian Multiplication is called Doubling. You take one number and either multiply it by 2 or you add it to itself. This is done repeatedly until you get the other number.

For example, let’s multiply 35 x 41

We write our problem horizontally and consider 35 as our first column and 41 as our second column. Underneath the first column, we write the number 1 and underneath the second column the number 41 (as in 1×41). Then we double the number 1 which becomes 2 and also double the number 41 which becomes 82. (2×41)

We continue doubling both columns the same way until we reach but not exceed the number at the top of the first column. In our case, the number at the top of our column is 35 so we may stop at the number 32. If we double once more we will reach 64 which is too high.

The next step is quite interesting. We must find a group/combination of numbers in the first column that add up to 35. The numbers that add up to 35 in the first column are 32, 2 and 1. The numbers in the second column, located directly to the right of the numbers we circled hide the answer to our problem. When added together, 1312, 82, and 41 give us the answer to 35×41 which is 1435.

Of course, students are not expected to always use this method for solving multiplication problems. However, this method helps them understand the distributive property of multiplication.

35×41=(32×41) + (8×41) + (1×41) = 1312+82+41= 1435

It also helps them see that there are many ways of solving a problem and offers good mental calculation practice. Students will also realize that they can use this method mentally for simpler multiplication problems like 4×16.

if 2×16=32 then 4×16= 64

Discuss this method with your students and see how they understand it. Have them solve more problems using this method. Ask them what are the advantages and disadvantages compared to the method they usually use.

One of my students said that he would solve this problem like this.

10×41=410 which means that 5×41=205 410+410+410+205= 10×41 =1435 He decided to multiply by 10. A different approach inspired by the Ancient Egyptians.

Try this worksheet to practice the Egyptian form of multiplication.

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