Multiplication (often denoted by the cross symbol ×, by the mid-line dot operator ⋅, by juxtaposition, or, on computers, by an asterisk *) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.
Ancient cultures would have solved the multiplication in different ways. Knowing this will help us to understand how classic multiplication algorithm works. Now we can look how Chinese and Egyptian Multiplication methods are
Chinese Method of Multiplication
This Chinese method originally involved using bamboo sticks to help them with multiplication, arranging them horizontally and vertically, as we’ll see in the example.
Let’s find out how to multiply 31 x 42 using this method.
First, place:
3 horizontal lines separated by the same distance, and 1 more horizontal line a bit further apart.
4 vertical lines separated by the same distance, and 2 more vertical lines further apart.
Next, count the number of times each pair of lines cross. Make sure you keep track of which ones correspond to the tens and which represent units:
Where the unit lines cross, we get the units of the result (since the product of units gives units).
Where the unit lines and tens lines cross, we get the tens of the result (since the product of units and tens gives tens).
Where the tens lines cross, we get the hundreds of the result (since the product of tens gives hundreds)
Now we can arrange all the information we've obtained into the result of 31 x 42:
2 units.
10 tens, which is the same as 1 hundred.
12 hundreds, which when added to the hundred given by the 10 tens makes 13 hundred. These 13 hundreds can be written as 1 thousand and 3 hundreds.
So, we’ve got:
1 thousand, 3 hundreds, and 2 units: 1,302
Therefore we know that 31 x 42 = 1,302
Egyptian Method of Multiplication
The ancient Egyptians multiplied using a method that involved breaking down the multiplication into a series of additions, then doubling one of the factors (putting them into powers of 2).
Let’s look at how to multiply 31 x 42 using this method.
First of all, we need to place 1 and 31, and start doubling the two quantities. Like this:
We'll  get different multiplications of 31 by powers of 2, like this:
Now we need to look for the numbers that help us to solve the multiplication 31 x 42. To do this, we just need to find the powers of 2 that add up to 42:
32 + 8 + 2 = 42
At this point, we have managed to break down 31 x 42 into sums that we can calculate easily:
31 x 42 = 31 x (2 + 8 +32) = 31 x 2 + 31 x 8 + 31 x 32 = 62 + 248 + 992 = 310 + 992 = 1,302
And as you can see, the result we get once again is 31 x 42 = 1,302
I hope these multiplication methods have helped you to better understand how multiplication works. Share them with your friends, so they can become experts in multiplication too!
