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Maria Zeltser - How to Calculate Like a Magician?

30.05.2017

Most schoolchildren think that Mathematics is boring and complicated. When they need to calculate in their notebooks, or – god forbid – in front of the blackboard, it will take a lot of time and oftentimes leads to erroneous results. It turns out there is no need to go through all that trouble, says Associate Professor of Mathematics at the Tallinn University School of Digital Technologies, Maria Zeltser.

Simple and elegant methods of calculating quickly have been discovered ages ago. Some of the easiest ways of calculating were discovered in India over 2500 years ago.

Let’s see how easy it can be. Say we need to multiply 112 and 107. They are both close to 100. Let’s take the number 100 as a basis and show the multipliers as: 112=100+12; 107=100+7. Let’s write down the calculation as:

112 + 12
x
107 + 7

To find the answer, we only need two parts. The right side of the answer is equal to the multiplication of the two numbers on the right: 12x7=84. The left side is to be calculated diagonally: 112+7=119. If we join the two sides, we get 11,984, which is the correct answer.

Note that the right side of the answer must have as many numbers as there are zeroes in the base number. For example, if we multiply 997 by 988, the basis is 1000 with three zeroes. The calculation looks like this:

997 – 3
x
988 – 12

The right side of the answer is -3x(-12)=36. As the base number had three zeroes, write it down as 036. The left side will be 997-12=985. Write down 985,036. Check it with your calculator – bingo!

The same method also works when one of the numbers is larger, and the other one is smaller than the base number. Let’s multiply 995 by 1012. The base number is still 1000.

995 – 5
x
1012 + 12

The right side is (-5)x12= -60, but as the base has three zeroes, let’s write it down as -060. The left side is 995+12=1007. How do we continue, when there’s a negative answer? We lend a ‘one’ from the left side (1007-1=1006), and calculate the right side as 1000-060=940. This adds up to 1,006,940.

Got it? Next time surprise your friends with your speed calculation abilities. After some practice, you’ll calculate faster in your head than it takes you to enter the numbers in your calculator.

Is mathematics boring and complicated? Certainly not!