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Math: Adventure Math: Tricks of the Champions

Only geniuses can do that! Mistake. In the second part of our math series, we show you some nifty calculation methods. Difficult tasks will no longer scare you

Calculate 97 x 93 in your head? With some of the tasks that you see on these pages, you will first think: At most geniuses can do that! Mistake. They have come up with ways that anyone can crack such head nuts. In the second part of our series we show you some of the most sophisticated calculation methods.

Calculate with your fingers

To get started, a simple trick with which you can multiply single-digit numbers by 9. We'll show you using the 7 x 9 example

How are you?

Just hold both hands in front of you with your fingers spread. Now count from left to right to the seventh finger and bend it. Six fingers have now stopped to his left. That's the tens. To the right of the bent finger you have the one. So the result is: 60 + 3 = 63!

Multiply by 5 in a flash

Sometimes it's better to replace one heavy bill with two light ones. This shows this method, with which you can multiply numbers by 5. Example: 84 x 5

How are you?

5 is nothing other than ½ × 10. Instead of 84 × 5, you can therefore also calculate: 84 × ½ × 10. Spelled another way: 84: 2 × 10 Let's do it in sequence:

First step: 84 : 2 = 42

Second step: Multiply the result by 10 - so just add a 0: 42 × 10 = 420

Of course, the trick also works with odd numbers. Let's look at 65 × 5! In the first step there is a comma in the result (... yuck): 65: 2 = 32.5 But that disappears immediately in the second. Because multiplying by 10 just means moving the decimal point one place to the right: 32.5 × 10 = 325

Big numbers? Make it small!

The following trick is a continuation of the previous one and works for large numbers that can be broken down into several packets of even numbers. Let's look at the number 4,418,296. Example: 4 418 296 × 5

How are you?

First step: Divides 4 418 296 into small blocks: 44/18/296

Second step: Now continue as in the previous trick. So first divide by 2. Make sure that the number of digits in each block remains the same: 22/09/148

Third step: Put them back together and multiply by 10 (so add a 0). The result is already there: 22 091 480

Calculate like Gauss

Carl Friedrich Gauß (1777–1855) was a brilliant mathematician. He allegedly discovered the following trick when he was only seven years old! Back then, his math teacher asked him (to annoy him) what would happen if you added up all the numbers from 1 to 100. Gauss thought for a moment and gave the correct answer: 5050.

How are you?

Imagine that you write down all the numbers next to each other. So left the 1, then the 2, the 3 ... to the far right 100. What do you get when you add the first (1) and the last (100) number? Sure: 101. Now add up the second and second from last number, and third and third from last and so on:

2 + 99

3 + 98

...

Every time the result is 101! In total you get 50 pairs, or in other words:

50 × 101 =

50 × 100 + 50 × 1 = 5000 + 50 =

5050

Vedic multiply

This method is named after ancient Indian scriptures, the Vedas. One thing is certain: You can use it to multiply numbers that are both just under 100 or 1000. Example: 98 × 93

How are you

First step: Write the numbers next to each other.

98 93

Second step: Calculate the respective difference to 100 and write the numbers in the line below.

98 93

2 7

Third step: Subtract one of the lower numbers from the one diagonally above it (whether the left from the right or vice versa does not matter):

93– 2 = 91

Fourth step: Write the same number of zeros after it:

9100

Fifth step: Now multiply the bottom two.

2 × 7 = 14

Sixth step: Add up the numbers (i.e. 9100 and 14) and you get the result: 9114

The trick of the mathematician

The mathematician Jakow Trachtenberg (1888–1953) worked out a whole series of great arithmetic tricks. The special thing about it: Trachtenberg multiplied by adding up numbers. Many of the fastest mental computers in the world today use Trachtenberg's system. Let's look at how it multiplies by 11. Example: 72 × 11

How are you

Pull the first and second numbers apart ...

7 2

... and write the sum of the two in the middle. You already have the result:

7 / 7 + 2 / 2 = 792

Wow! The trick also works with larger numbers. You just have to add each digit with its neighbor and put the result in the middle:

536 × 11 = 5 / 5 + 3 / 3 + 6 / 6 = 5896

Attention: If a sum is greater than 9, the 1 adds to the number to the left of it, so:

83 × 11 = 8/8 + 3/3 or 8/11/3 = 913

For specialists

Some computing tricks only work in special cases. With this one you can quickly multiply two-digit numbers if their first digits (the tens) are the same and the last digits (the ones) add up to 10. Example: 97 × 93

Small check: 7 + 3 = 10. Okay!

How are you?

Multiply the tens and make the first one larger:

10 × 9 = 90

Now multiply the ones:

3 × 7 = 21

and put both numbers together. You already have the result: 9021

Attention: If you get a single-digit result for the ones, put a 0 in front of it:

91 × 99 = 9009

The trick also works with three-digit numbers: Example: 135 x 135

14 x 13 = 182 and 5 x 5 = 25

That results in: 18225

Chinese multiply

This trick supposedly originated in China. It can be used to easily multiply two or three-digit numbers. Without doing a single multiplication! Example: 32 × 21

How are you?

First step: