Line Multiplication

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A Line Multiplication Example

Line Multiplication is one of the visual ways to multiply two numbers.  Though multiplication is a standard subject in elementary math, the line method of multiplying is uncommon.  To get an idea of what this type of multiplication is like, let’s look at an example multiplication problem: 34 x 12.

To do this multiplication using lines, you draw a figure like the one above with the original problem written widely.  Your figure should contain three lines under the 3, four lines under the 4, one line under the 1, and two lines under the 2.  The lines representing 34 slant down to the right; the lines representing 12 slant down and to the left.  Dots mark the places where the lines cross.

8 dots represent the ones. 10 dots represent the tens.  3 dots representing the hundreds.  Since 10 tens equals 1 hundred, the dots represent 4 hundreds (3 original plus 1 carried over) and 8 ones.  This answer is written as 408.

Standard Multiplication

In the standard method for multiplying, most children would set up their multiplication like the one below: with 34 on top and 12 on the bottom.  They start by multiplying 2 x 4 to get 8. Then, they multiply 2 x 3 to get 6.  This produces 68. You can continue following the standard algorithm to get the answer by adding 68 and 340 to get 408.

A disadvantage of this standard multiplication method is that it does not extend to algebraic expressions involving variables like x. For students who only know this method of multiplication, they will need to learn a new way of multiplying when they get to algebra.  On the other hand, Line multiplication works for multiplying two single-variable expressions such as 3x+4 and x+ 2.

Advantages of Knowing Different Methods of Multiplication

Even before learning algebra, it’s helpful for students to know more than one method of multiplication.  Students can check a problem by using a second method of multiplication.  Sometimes one method is much easier than another for a particular problem.

The ability to multiply in different ways allows students to “see” multiplication from different points of view.  Multiplication is not just one memorized algorithm.  Deeper understanding helps students in their future math classes when multiplication is applied to variables, matrices, and other math objects.  Future blog posts will explore other methods of multiplication.

For More Examples

For further exploration,  Wikihow gives a detailed step-by-step explanation of the Line Multiplication method for this problem.   TheMediaVault’s two minute video presents a quick example of solving a different line multiplication problem.