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Magical Algorithms in Jiangsu Maths

School News March 23, 2021
Magical Algorithms in Jiangsu Maths

In Grade 3 Maths, WASCZ Pupils have learnt to use the column method and  have been very successful at using this. However, if we want to calculate the multiplication between several-digit numbers, e.g. 12345×54321, what should we do? If we still insist on using the column method, it would be very complicated and also very easy to make mistakes. You might think: why not use the calculator?

Smart choice!

However, I want to introduce you a magic way of calculating multiplication, which is quite simple.



This magical algorithm originated with the Italian mathematician Pacioli in his book “Summary of arithmetic, geometry, ratio and proportion” which introduced the calculation method of the multiplication between two numbers - “Lattice Multiplication”. After this method was introduced to China, the mathematician Cheng Dawei in Ming Dynasty renamed it “Pu Di Jing” in his book “ Algorithm Collection”.

Let’s make an example: when we multiply 345 with 78, the first step is that we put the numbers “3, 4, 5 “ above the lattice and numbers”7 and 8” on the right of the lattice. The second step is to multiply 7 with each number of 345 and write the arithmetic product in the lattice from right to left. Repeat the process with 8. The third step is to add the arithmetic product according to the diagonal line, and we can get the answer “26910”.





When our kids are calculating “46×78”,they all tried the magical method and got the answer “3588”, but they are curious if the answer is correct, so they use their familiar way-vertical form to prove it, which turns out to be the same. They were all fascinated by the magical algorithm, and they want to be challenged.