## Japanese Method of Multiplication:

Japanese method is one of the easiest method of multiplication, where we draw lines instead of numbers for multiplication & we get result without doing calculation.

This method is applicable for 2-digits, 3-digits & more digits also. It is interesting and very easy way of multiplication, where we get our answer by drawing lines only. Here we explained first example step by step so any one can understand this technique easily.

**Ex. i) 12 X 21**

**Step 1: First convert the number 12 in line form**

For number 12 first we draw 1 line in some specific angle & then draw 2 lines parallel to this one line after some space as shown below.

**Step 2: Now convert Number 21 in line form**

Now we will draw lines for second number i.e. 21 in opposite angle of previous lines. We draw lines such as the new lines intersect the old one as shown in figure.

As shown in figure we draw first 2- blue line for number 2 & then parallel to this we draw one line after some space.

**Step 3: Now next step is counting the intercept points & write down then in proper order**.

**Ans = 252 **

**Explanation**:

As shown in figure we divide the intersect points by drawing the curve lines. Then count the intersect point & write down the number.

1. As shown in fig. in right hand side there are 2-intersect points, so our rightmost digit is 2.

2. In left side again we have 2- intersect points so our leftmost digit is 2.

3. In middle there are 5 intersect point so our middle digit is 5.

**Ans, 13 X 21 = 252**

**Ex. ii) 31 X 23 (Carryover Example)**

**Explanation**:

As shown in fig we draw parallel lines for number 31(black) & in opposite angle we draw lines(blue) for number 23 that intersect to each other at some points. We denote this points by dot & count of dot is mentioned in the fig. which is nothing but our answer,

Ans = 6: (9+2) :3 = 6:**1**1:3

As in middle we get 11 so we take 1 & carryover other 1 in left hand side digit,

Ans = (6+1) :1:3 = 713

**Ans 31 X 23 = 713**

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**Ex. iii) 211 X 121**

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**Ans =25531**

**Explanation:**

For 3-digit number also the method is same as 2-digit. Only the number of curved lines is increases as shown in fig.

**Try this:**

i) 12 X 23 ii) 32 X 11 iii) 301 X 121 iv) 112 X 123

**Find the following links to study more:**

i) Multiplication tricks by Vedic Mathematics

ii) Vinculum number in Vedic Mathematics

iii) Easy way to learn tables from 11 to 99

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