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This method of multiplication falls somewhere between a Math trick, and a legitimate method for multiplying numbers. Some people have described this method of multiplication a "Chinese method", other people said it is a "Japanese method of multiplication" and, I have seen it described as an ancient Arabic technique. Regardless of the name,one can multiply using lines. Here are the steps involved.
Math Trick-Multiplying with lines
Multiply 12 x 21 using Lines
Step 1. For each number you will draw an equal number of lines. For the number 12 draw one line for the tens, and two lines for the ones. You don't have to use different colors, but it helps.
Step 2. Now repeat for the next number. ( 21) I have drawn two lines for the 2 (tens), and 1 line for the one (ones).
Step 3. Draw an arc around the same colored lines (tens and ones). Then intersection of the red lines represent the hundreds value, the intersection of the red and blue represent the tens value and the intersection of the blues represent the ones value.
Step 4. Count the number of intersecting lines at each group. On the far right you have 2 intersections which represents 2, in the middle you have 5 which represents 50, and on the left you have 2, which represents 200. If you have more than ten you carry the ten to the left.
1 + 4 = 5
Step 5. Write the numbers from left to right, and your answer equals 252
12 x 21 = 252
Multiply 41 x 34
Step 1. Draw your lines. Start with 41. Draw four lines representing 40, skip some space, and draw one line representing 1.
Next draw your second number, three lines representing 30, and four lines representing 4.
Step 2. Draw an arc around your same colored groups. Intersection of red/red represent 100s, the intersection of red and blues represent 10s, and the intersection of blues represent ones.
Step 3. Count each intersection of lines in the groups.
All blue = 4
Red/Blue = 19 You will need to carry a 1 to the left = 19 becomes a 9
All Red = 12 + 1 = 13
Step 4. Write the numbers from each group, and this is your answer.
16 +3 = 19
move 1 set of ten to the left = 9
12 +1 =13
How many groups should you have? A rule of thumb is to take the total number digits you are multiplying and subtract 1.
21 x 23 = 4 digits -1 = 3 groups
312 x 24 = 5 digits -1 = 4 groups
What about zero? Whenever you have a number with a zero then the you don't count the intersections of the lines touching the zero line.
I created a video with several more examples. Watch it below.
Pros This method is very visual, and can be pretty quick for multiplying smaller numbers.
It is another alternative to traditional multiplication.
I found it kinda fun.
This method will work for variables, decimals, and negative numbers.
Cons This method takes up lots of paper
It can get messy with numbers with 7,8, and 9 in them.
When you have more than four groups it can be very confusing, and difficult to count all the intersecting lines.