How to Multiply

Summary

This tutorial introduces a unique Japanese method of multiplying numbers visually by substituting digits with lines and dividing the pattern into zones. The process involves drawing lines for each digit, marking zones where lines intersect, and counting the intersections to get the product. Examples include multiplying 13 by 21 to get 273, and more complex calculations like 321 times 13 resulting in 4,000,173. The video demonstrates an alternative to traditional multiplication, though it humorously acknowledges that a calculator might be more practical.

Takeaways

• 📚 The video introduces a unique Japanese multiplication technique using lines to represent digits.
• 📝 The method involves drawing lines for each digit of the numbers involved in the multiplication.
• 🔢 The first digit dictates the number of lines drawn diagonally, with spaces for each subsequent digit.
• 📐 After drawing the lines, they are separated into zones where the lines cross each other.
• 🔍 Each zone is then counted for the number of line crossings, which contributes to the final multiplication result.
• 📉 For numbers larger than 9, the first digit is carried over to the next zone and added to its count.
• 🔄 The process is demonstrated with examples such as 13 x 21, 32 x 12, and 14 x 23.
• 📈 The technique can be applied to larger numbers, including three-digit multiplication, as shown with 321 x 13.
• 🤔 The video acknowledges that while the method is interesting, a calculator might be more practical for complex calculations.
• 👍 The presenter encourages viewers to explore more 'useless' tricks on their YouTube channel.
• 🎶 The video concludes with a light-hearted reminder to have fun and thanks the viewers for watching.

Q & A

What is the origin of the multiplication technique described in the video?

The multiplication technique described in the video originates from Japan.

What is the basic concept of the multiplication method shown in the video?

The basic concept involves substituting numbers for lines and drawing them in a specific pattern to visually represent the multiplication process.

How is the first part of the multiplication process demonstrated with the example of 13 times 21?

The first part involves drawing lines for each digit of the numbers 13 and 21, with spaces in between, and then marking three separate zones where the lines cross.

What is the process of counting the lines in each zone after drawing them out?

Starting from the right-hand zone, count the number of times any of the lines cross and write that number down, then move to the next zone and repeat the process.

What is the result of the multiplication example 13 times 21 using the described technique?

The result of the multiplication example 13 times 21 is 273.

How does the technique handle the multiplication of numbers that result in a two-digit number in a zone?

If the number of crosses in a zone is a two-digit number, the last digit is left in place, and the first digit is carried over to the next zone, where it is added to the number of crosses in that zone.

What is the result of the multiplication example 14 times 23 using the technique?

The result of the multiplication example 14 times 23 is 322.

How does the technique adapt to multiplying larger numbers, such as a three-digit number by a two-digit number?

The technique involves drawing lines for each digit of the larger numbers, marking out the zones, and counting the crosses in each zone, carrying over digits as necessary.

What is the result of the multiplication example 321 times 13 using the technique?

The result of the multiplication example 321 times 13 is 4,000,173.

What advice does the video give if someone finds the multiplication technique difficult to follow?

The video suggests using a calculator if the technique is difficult to follow.

How can viewers find more content like the multiplication technique shown in the video?

Viewers can find more content by clicking on the links on the right-hand side or by visiting the presenter's YouTube channel page.

Outlines

00:00

📚 Japanese Lime Multiplication Technique

This paragraph introduces a unique method of multiplication that originates from Japan, where numbers are represented by lines drawn on paper. The process begins with drawing lines corresponding to the digits of the numbers involved in the multiplication. For instance, the number 13 is represented by one straight line followed by a space and then three parallel lines. The same is done for the second number, 21. The lines are then separated into zones where they cross, and the number of crossings in each zone is counted to form the product. The example given is 13 times 21, which results in 273. The technique is demonstrated with additional examples, such as 32 times 12 and 14 times 23, showing how to handle carrying over when the count exceeds a single digit. The paragraph concludes with a more complex example involving larger numbers, illustrating how to manage multiple zones and carry over digits across zones.

Keywords

💡Multiplication

Multiplication is a mathematical operation that involves combining groups of equal size. In the context of the video, it is the primary operation being demonstrated through a unique method. The video showcases how to multiply two numbers together using a visual technique involving lines to represent digits, which is a creative and unconventional approach to understanding multiplication.

💡Technique

A technique refers to a method or way of carrying out an activity. In this video, the term is used to describe the specific method of multiplication that originates from Japan. The technique involves drawing lines to represent numbers and counting intersections to find the product, offering a visual and hands-on approach to learning multiplication.

💡Substituting

Substituting in this context means replacing one thing with another. The video explains substituting numbers with lines or 'limes' as a way to visualize the multiplication process. This substitution is a key part of the technique, allowing viewers to see the multiplication as a pattern of lines crossing rather than abstract numbers.

💡Lines

In the script, lines are used to represent the digits of the numbers being multiplied. Each digit is represented by a certain number of parallel lines drawn in a specific pattern. The concept is central to the technique being taught, as the lines and their intersections form the visual basis for calculating the product.

💡Zones

Zones in this context refer to the separate areas created by the intersection of lines. After drawing the lines for the numbers, the technique involves dividing the drawing into zones where the lines cross. Each zone is then used to count the number of intersections, which contributes to the final product of the multiplication.

💡Carrying over

Carrying over is a concept used in arithmetic when a number exceeds the base of the numeral system, typically 10 in the decimal system. In the video, when the count of intersections in a zone exceeds 9, the excess is carried over to the next zone, adding to the count there. This is demonstrated when multiplying larger numbers, where the technique must account for two-digit results from the intersections.

💡Digits

Digits are the individual numerical values in a number, such as the '1' in '13' or the '2' in '21'. The video script uses the term to describe the numbers that are drawn as lines, with each digit represented by a corresponding number of lines. The digits are fundamental to the multiplication technique as they dictate the number of lines drawn and, consequently, the number of intersections.

💡Intersections

Intersections are the points where the drawn lines cross each other. The video technique relies on counting these intersections within each zone to determine the digits of the product. The number of intersections is directly related to the result of the multiplication, making it a key concept in understanding the technique.

💡Product

In mathematics, the product is the result of a multiplication operation. The video demonstrates how to find the product of two numbers using the unique line-drawing technique. The final step of counting intersections in the zones gives the digits of the product, such as '273' for the multiplication of '13' and '21'.

💡Tutorial

A tutorial is an instructional set of materials or a lesson plan designed to teach a specific skill or concept. The video is described as a tutorial, aiming to teach viewers the unconventional multiplication technique. The script provides step-by-step instructions and examples to guide the viewers through the process.

Highlights

Introduction of a simple Japanese multiplication technique using lime-like lines.

Demonstration of multiplying 13 by 21 using the line drawing method.

Explanation of drawing one straight line for the first digit and three parallel lines for the second digit in the multiplication of 13 by 21.

Illustration of drawing two lines for the first digit and one line for the last digit in the multiplication of 13 by 21.

Process of dividing the drawn pattern into three zones to count the intersections.

Counting the intersections in each zone to get the product of 13 times 21, which is 273.

Example of multiplying 32 by 12 using the same technique.

Drawing the pattern for 32 times 12 and marking zones for counting intersections.

Counting the intersections in the zones to find the product of 32 times 12, which is 384.

Multiplication of 14 by 23 with the line drawing technique, including carrying over numbers.

Explanation of carrying over when the count of intersections exceeds a single digit.

Final product of 322 for the multiplication of 14 by 23 using the line drawing method.

Introduction to multiplying larger numbers with the line drawing technique.

Process of drawing lines for a three-digit number and a two-digit number for multiplication.

Marking out four zones for counting intersections in the multiplication of a three-digit by a two-digit number.

Counting intersections and carrying over numbers to find the product of 321 times 13, which is 4,000,173.

Conclusion of the tutorial with a humorous suggestion to use a calculator if the technique is too complex.

Invitation to explore more 'useless tricks' and to subscribe to the YouTube channel for similar content.

Transcripts

today I'm going to show you a really

simple way to multiply two numbers

together this technique originates from

Japan and involves substituting numbers

for limes

we'll start with 13 times 21 as we can

see the first digit in this equation is

1 which means we draw one straight line

diagonally like this the next digit is 3

so we leave a little space then draw

three lines parallel to the first one

like this after the multiplication sign

the first number we have is 2 so we draw

two lines next to each other from here

to here and the final digit is 1 so we

draw one line from here to here that's

the first part complete and it should

look something like this once we've

drawn it out we need to separate it into

three separate zones where the lines

cross like this then starting from the

right-hand zone we need to count how

many times any of the lines cross in

this case 3 we write that here and move

on to the next zone so again we count

how many times the lines cross one two

three four five six seven and write it

at the top then move on to the last zone

and do exactly the same again 1 2 to 7 3

and that gives us our answer

13 times 21 is 273 pretty cool huh so

here's another quick example 32 times 12

the first digit of the first number is 3

so we draw three lines here the next

number is 2 so draw two lines here then

we have the multiplication sign and the

next number is 1 so it will one line

from here to here

and the final number is 2 so draw two

lines here then we mark out our three

zones again and starting from the right

start counting the dots 1 2 3 4 1 2 3 4

5 6 7 8

write that here and finally 1 2 3 3 8 4

384 there we have our answer

simples but it does get a little more

complicated if we add more lines I'll

show you

let's multiply 14 by 23 so draw out the

pattern 1 1 2 3 4 2 and 1 2 3 mark out

our zones

now let's count the dots starting from

the right we have 1 2 3 4 5 6 7 8 9 10

11 12 so we'll write 12 up here but if

this number is ever more than 9 in other

words if it's a two-digit number we

leave the last digit where it is but we

take the first number carry it over to

the next zone and add it to the number

of dots in this zone

I'll show you so we have 1 2 3 4 5 6 7 8

9 10 11 dots or line crosses in this

zone we add that to the one we carried

over from the last zone and that gives

us 12 so now we have to do exactly the

same again

leave the last digit where it is carry

the first digit over to the next zone

and add it to the number of dots in this

zone in this case two dots giving us a

total of three and that gives us our

answer 3 2 - 14 x 23 is 322 we'll now go

one step further and look at multiplying

even larger numbers so the first number

we have now is a three-digit number

start by drawing out the lines for the

first digit leave a space then do the

lines for the second digit then leave

another space and do the lines for the

last digit next we have a multiplication

symbol then we draw out the lines for

the next number once we've drawn out the

pattern will mark out the zones this

time as you can see they'll actually be

four zones then starting from the right

again we'll count out the dots 3 1 at

the bottom 2 3 4 5 6 7 then 1 2 3 4 5 6

7 8 9 10 11 so again we leave the last

digit there carry the first digit over

to the next zone and add it to the dots

1 2 3 plus 1 gives us 4 4 1 7 3

so our answer 321 times 13 is 4,000 173

I hope you've been able to follow this

tutorial if you haven't my advice would

be just use a calculator but if you like

this video I want to see more useless

tricks click on the links on the right

hand side or take a look at my youtube

channel page

have fun and as always thanks for

watching

[Music]