Arithmetic Grade Four

Lesson Fifty: Two Column Multiplication

Inspect this multiplication problem: 

     132
    x 23 
   ------
Since we don't have to do any carrying, finding the answer to this problem is really easy, but now we have a two-digit number on the bottom. 

    132
   x 32 
  ------
    262  <--- A. 132 x 2 = 262 (STEP ONE: multiply top by ones of bottom)
   396   <--- B. 132 x 3 = 396 (STEP TWO: multiply top by tens of bottom)
  ------
   4222  <--- C. 3960 + 262 = 4222 (STEP THREE: add up partial products)
So, we find our partial products and the we add them up. Remember that the second partial product must be lined up so that its ones column is under the first partial products's tens column (as shown in the above example).

Here is another example: 


    414
   x 22 
  ------
    828  <--- A. 44 x 2 = 828 (STEP ONE: multiply top by ones of bottom)
   828   <--- B. 44 x 2 = 828 (STEP TWO: multiply top by tens of bottom)
  ------
   9108  <--- C. 8280 + 828 = 9108 (STEP THREE: add up partial products)
Here are some more examples for you to study: 

        231			 134			 420
       x 23			x 22			x 12
       -----			-----			-----
        693                      268		         840
       462                      268                     420
       -----                    -----                   -----
       5313                     2948                    5040
Now you will try a few of these yourself.

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