Reveal the magic of quick calculations: the magic of math head by head and tail by tail
In the world of mathematics, there are always mysterious and interesting ways to swim in the sea of numbers. Today, I'm going to reveal a magical quick calculation method for you - the head by the head and tail by the tail method. This method is not only easy to learn, but also can get some complex math results in an instant, so that you can show off your skills in front of your friends and become a math expert!
1. What is the head-by-head and tail-by-tail method?
The head-by-head and tail-by-tail method is a method of quickly performing two-digit multiplication operations. It works by multiplying the heads of two two-digit numbers (tens of digits), then multiplying the tails of two numbers (single digits), and finally combining the two products to form the final answer. Of course, this method will require some tweaks and skills in practical application, but the basic idea is that.
Second, the specific steps of the head by head and tail by tail method
To better understand this approach, let's illustrate it with a concrete example:
Suppose we want to multiply 23 by 47, then following the method of multiplying the head by the tail by the head, we can do something like this:
Head by headFirst, we take the heads of two numbers, 2 and 4, and multiply them to get 8. This 8 is the hundredth and thousandth digit of our final answer.
Tail by tailNext, we take the tail of the two numbers, 3 and 7, and multiply them to get 21. This 21 is the ten and single digit digits of our final answer (but we need to pay attention to the carry problem).
Combine answers: Finally, we combine the results of the head by the head and the tail by the tail. However, because the tail multiplication tail gives the two-digit 21, we need to tie this 2 to the head-by-head result. Thus, 8 (the result of the head multiplied by the head) plus 2 (the carry of the tail by the tail) equals 10. So, the final answer is 1021.
Wait, something seems to be wrong here!The correct answer for 23 times 47 should be 1081, not 1021. What's going on?
3. Correction and skills of the head multiplication head and tail multiplication tail method
In fact, we also need to pay attention to some details and skills when using the head-by-head and tail-by-tail method. In the example above, we have overlooked an important step, which is that when dealing with the result of tail multiplication and tailing, if the product obtained is a single digit, then the single digit or ten digit of the answer is directly usedBut if it is a two-digit number, then the ten digits need to be added as a carry to the result of the head multiplied head. In this example, the 2 in 21 obtained by the tail multiplied tail should be rounded, but the carry should not simply be added to the 8 of the head multiplied by the head, but to the ten represented by the 8.
Therefore, the corrected calculation process should look like this:
Head multiplied by head: 2 times 4 equals 8, which represents the number above the hundred digits of the final answer.
Tail multiplied by tail: 3 times 7 equals 21, and this 2 needs to be carried forward.
Carry processing: Round 2 to 8, but the carry here is not a simple addition, but to add 8 (actually 20 + 8 = 28) and 2 to get 30, that is, 3 (hundred) and 0 (ten).
Combined answer: Combine the result 30 after the head by the head and the result 1 (single digit) after the tail by the tail to get the final answer 301, plus the ten digits 0 that was not calculated before, to get the correct answer 1081.
Of course, this correction process may seem a bit complicated, but in reality, once you get the hang of it, you can multiply two-digit numbers very quickly.
Fourth, the scope of application of the head by head and tail by tail method
It should be noted that the head-by-head and tail-by-tail multiplication method is mainly applicable to two-digit multiplication operations, and special attention needs to be paid to the carry problem when the result of tail by tail is more than 10. This method may not be as suitable for multiplication of larger digits or for more complex calculations.
V. Conclusion
Although the head-by-head and tail-by-tail method has certain limitations, it is indeed a very interesting and practical quick calculation method in specific situations. By mastering this method, you will not only be able to improve your own calculation speed, but you will also be able to showcase your mathematical talents in front of friends or colleagues. Of course, the most important thing is that learning this method will give you a deeper understanding of the charm and joy of mathematics. So, take some time to learn this amazing quick math method!
Mathematics