In the Japanese language a calculator is pronounced as Dentaku which is written as 電卓, and is a widely used tool by Japanese in almost every field of life, but the crux is they don’t use the same way as we do, their multiplication, division, and subtraction operation differ a little bit from other people.
In this article, we will look specifically into the unique way the Japanese use to multuiply number which may be a new thing for you to learn some amazing stuff.. BTW before going into detail of this, if you want to see a japanese calculator or Dentaku you can visit (https://webdentaku.org/) which work the same way as other calculators but our topic is to focus on something else.
When a normal person plans to multiply some numbers, he likely envisions the traditional multiplication operation that involves carrying numbers, making calculations, and carefully adding them together. But in Japan, there’s an intriguing alternative method of multiplication, known as the “Japanese multiplication method” or simply “Japanese multiplication system,” which stands out for its simplicity, visual appeal, and creative approach. Although it’s not widely known outside of Japan, this method offers an interesting and accessible way to teach multiplication, especially for young learners. But how exactly does it work?
A Visual and Geometric Approach
The Japanese way of multiplication in normal words is often referred to as “line multiplication” or “stick multiplication” because it uses intersecting lines drawn on paper to represent numbers.
The method we’re talking about is simple along with both visual and tactile, making it particularly effective for visual learners.
At its core, the process is truly based on breaking down the numbers into their place values and using geometric shapes as values to actually represent those values. Here’s a details breakdown of how this actually and mathematically works:
Step-by-Step Process
Let’s take a real example of multiplying two numbers like 23 by 45 the Japanese way we are highlighting.
1) Draw lines to represent the numbers:
Start by drawing lines for each digit present in the numbers you are multiplying.
For the number 23, draw 2 straight vertical lines on the left side of your paper (representing 20) and 3 vertical lines next to them (representing 3).
For the number 45, draw 4 straight vertical lines on the top (representing 40) and 5 vertical lines beneath them (representing 5).
2) Create a grid of intersections:
The lines from the first number will intersect with the second number lines.
You’ll end up with a grid intersection point representing a product of digits from the two numbers.
3) Count the intersections:
The next step is to count the number of intersections in each section of the grid we have, which corresponds to the multiplication of each digit pair.
The intersections in the first section, where the 20 lines meet the 40 lines, represent 20 × 40 = 800.
The intersections in the second section, where the 20 lines meet the 5 lines, represent 20 × 5 = 100.
The intersections in the third section, where the 3 lines meet the 40 lines, represent 3 × 40 = 120.
The intersections in the fourth section, where the 3 lines meet the 5 lines, represent 3 × 5 = 15.
4) Add the totals:
Now, sum up all the results of these intersections:
800 + 100 + 120 + 15 = 1035.
And there you have it! The product of 23 and 45 is 1035, achieved through this simple yet visually rich and amazing process.
There are many Japanese calculators working on the base of this procedure, if you wish to have one installed on your computer or phone, you can visit here.
Why It’s So Effective
The Japanese multiplication method offers several advantages, the most prominent benefit of it is saving time, particularly when it comes to teaching young students or those struggling with traditional multiplication algorithms:
- Visual and Intuitive: The method appeals to students who are more at ease of visual learning because it turns abstract numbers into something tangible and physical. Also this fulfills the criteria that a picture speaks thousands of words.
- Engagement: This unique method is highly engaging, as it involves drawing and counting, turning the math process into a more interactive experience. This hands-on approach helps to demystify multiplication for children who might feel overwhelmed by traditional methods or those students who may not be comfortable learning complex numbers.
- Flexibility: Although the grid method works best with multi-digit numbers, it can also be used to multiply numbers with single-digit or even more complex equations. The concept remains consistent regardless of the size of the numbers involved in it, making it a versatile technique.
- Building Mathematical Intuition: With the mechanical process of multiplication, this method assists students greatly in visualizing how multiplication works in the real sense in a more holistic way. Rather than simply memorizing steps, students can begin to see how multiplication breaks down into smaller, super easy, and manageable parts.
The Cultural Roots
While the method itself is visually striking, it’s important to remember that the Japanese method of multiplication is not just a simple trick to solve some problems, but you may not this that this is rooted in a cultural tradition of embracing different learning styles.
Japan’s educational system has long-emphasized methods that foster creativity and critical thinking. The Japanese approach to mathematics often includes techniques that combine logic and creativity, making learning both fun and effective at the same time.
FYI, this method has similarities with the ancient Chinese method of multiplication, known as the “lattice method” or “Chinese multiplication,” which also uses a grid to break down the multiplication process into smaller steps. While both methods share geometric principles, the Japanese version tends to be simpler and more visual, making it easier for beginners.
Conclusion:
The Japanese multiplication method offers a fascinating alternative to traditional multiplication techniques and an edge over complex techniques. Its visual, practical approach makes it a valuable tool for students, especially those who may find conventional methods confusing or difficult to proceed. By embracing creativity and geometric thinking, this method fosters a deeper understanding of multiplication that is both fun and engaging at the same time.
