*If children can draw lines, count dots and add, they can multiply numbers. Multiplication is easy if we use the right methods. Here is one of the amazing tricks to multiply single or two-digit numbers.*

**This Japanese technique reduces the time needed to multiply numbers.** Children can use it to multiply single digit and double digit numbers. It is an **easy to grasp** trick and it makes multiplication fun. Following are three examples to learn this trick:

### Example 1: Multiplication of single digit numbers

Let us multiply four with three [4 x 3 =?]

**Step 1**: Draw four vertical lines for four (See the dark blue lines in fig.1)

**Step 2**: Draw three horizontal lines, for three, over the vertical lines (See the sky blue lines in fig.1)

**Step 3**: Count the total number of joints (fig.2)

The total number of joints is the answer. **The answer to 4 X 3 =12**

### Example 2: Multiplication of two digit numbers, case I

This procedure is little different. Let us multiply thirteen with twelve [13 X 12 =?]

**Step 1**: Draw one vertical line towards left hand side for one and three vertical lines for three towards right hand side. (See the dark blue lines in fig.3)

**Step 2**: Draw one horizontal line toward top for one and two horizontal lines towards bottom for two. (See the sky blue lines in fig.3)

**Step 3**: Count the number of joints in each corner of the figure.

The number of joints towards top left corner of the square is the first digit of the answer.

Sum of the number of joints in the bottom left and the top right corner of the square is the middle digit of the answer.

The number of joints in the bottom right corner of the square is the last digit of the answer.

**Answer to 13 X 12 =156**

**Note:** This will work to multiply any two two-digit numbers, but if any of the three sums have 10 or more points in them, be sure to carry the tens digit to the left, just as we would if we were adding. We will explore the procedure in next example.

### Example 3: Multiplication of two digit numbers, case II

Let us multiply thirty two with forty-one [32 X 41 =?]

**Step 1**: Draw three vertical lines towards left for three and two vertical lines for two towards right. (See the dark blue lines in the figure.4)

**Step 2**: Draw four horizontal lines towards top for one and one horizontal lines towards bottom for one. (See the sky blue lines in figure.4)

**Step 3**: Count the number of joints in each corner of the figure.

The number of joints towards top left corner is twelve. Sum the number of joints in bottom left and top right corners of the square, is eleven and the number of joints in the bottom right corner of the square are two.

Take a note of how the summation is done to get 1312:

Here first and second sums have more then 10 points in them, third sum has less then 10 points. The third sum has become last figure; the ten digit of second sum has been carried over to the left.

**Answer to 32 X 41 =1312**

#### Presentation suggestions:

First do the multiplication suggested in figure 1 and 2. Then try harder problems like 13 X 12 & 32 X 41.

#### The Math Behind the trick:

The number of lines are like placeholders (at powers of 10: 1, 10, 100, etc.), and the number joint is a product of the number of lines. We are summing up all the products that are coefficients of the same power of 10. In the second example:

13 X 12 = (1*10 + 3) * (1*10 + 2) =1*1*100 + 1*2*10 + 3*1*10 + 3*2 = 156

The diagram displays this multiplication visually. In the top left region there are 1*1=1 dots. In the middle region (left bottom and right top) there are 1*3 + 2*1= 5 dots. In the bottom region (right bottom) there are 2*3=6 dots. This method does exactly what you would do if you wrote out the multiplication the long way and added the columns.

Note: This method can also be generalized to products of three-digit numbers (or more).

#### Advantage:

You should have noticed by now, this method does not require children to recall tables. This reduces mental stress when solving word problems. While solving complex word problems this can become a distinctive advantage and reduce their dependency on calculators.