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# Multiplication by Drawing Lines

Two numbers can be visually multiplied by drawing lines and counting intersections. Though this method is very simple, it may take longer time if used with large numbers or numbers with large digits. (Note: speed math calculator can be used to practise problems using this method.)

## Example: Calculate 13 × 32

First number is 13
first digit: 1 => draw 1 horizontal line
next digit: 3 => draw 3 horizontal lines

Second number is 32
first digit: 3 => draw 3 vertical lines
next digit: 2 => draw 2 vertical lines

Count intersections, starting from rightmost group.

6 intersections in rightmost group. So, write 6 as rightmost digit of answer.

11 intersections in next group. So, write 1 as next digit of answer and take 1 as carry.

3 intersections in next group. 3 plus carried 1 is 4. So, write 4 as next digit of answer.

## Example: Calculate 123 × 321

First number is 123
first digit: 1 => draw 1 horizontal line
next digit: 2 => draw 2 horizontal lines
next digit: 3 => draw 3 horizontal lines

Second number is 321
first digit: 3 => draw 3 vertical lines
next digit: 2 => draw 2 vertical lines
next digit: 1 => draw 1 vertical line

Count intersections, starting from rightmost group.

3 intersections in rightmost group. So, write 3 as rightmost digit of answer.

8 intersections in next group. So, write 8 as next digit of answer.

14 intersections in next group. So, write 4 as next digit of answer and take 1 as carry.

8 intersections in next group. 8 plus carried 1 is 9. So, write 9 as next digit of answer.

3 intersections in next group. So, write 3 as next digit of answer.

## Example: Calculate 231 × 302

First number is 231
first digit: 2 => draw 2 horizontal lines
next digit: 3 => draw 3 horizontal lines
next digit: 1 => draw 1 horizontal line

Second number is 302
first digit: 3 => draw 3 vertical lines
next digit: 0 => draw 1 vertical line in different color to represent zero
next digit: 2 => draw 2 vertical lines

Count intersections, starting from rightmost group. Note that intersections made by zero lines will not be counted.

2 intersections in rightmost group. So, write 2 as rightmost digit of answer.

6 intersections in next group. So, write 6 as next digit of answer.

7 intersections in next group. So, write 7 as next digit of answer.

9 intersections in next group. So, write 9 as next digit of answer.

6 intersections in next group. So, write 6 as next digit of answer.

## Example: Calculate 412 × 12

First number is 412
first digit: 4 => draw 4 horizontal lines
next digit: 1 => draw 1 horizontal line
next digit: 2 => draw 2 horizontal lines

Second number is 12
first digit: 1 => draw 1 vertical line
next digit: 2 => draw 2 vertical lines

Count intersections, starting from rightmost group.

4 intersections in rightmost group. So, write 4 as rightmost digit of answer.

4 intersections in next group. So, write 4 as next digit of answer.

9 intersections in next group. So, write 9 as next digit of answer.

4 intersections in next group. So, write 4 as next digit of answer.