Arithmetic Grade Five

Lesson Forty-nine: Two Column Multiplication

Inspect this multiplication problem: 

    1132
    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 four-digit number on the top. 

   1132
   x 32 
  ------
   2262  <--- A. 1132 x 2 = 2262 (STEP ONE: multiply top by ones of bottom)
  3396   <--- B. 1132 x 3 = 3396 (STEP TWO: multiply top by tens of bottom)
  ------
  36222  <--- C. 33960 + 2262 = 36222 (STEP THREE: add up partial products)
So, we find our partial products and then 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: 


   1414
   x 22 
  ------
   2828  <--- A. 1414 x 2 = 2828 (STEP ONE: multiply top by ones of bottom)
  2828   <--- B. 1414 x 2 = 2828 (STEP TWO: multiply top by tens of bottom)
  ------
  31108  <--- C. 28280 + 2828 = 31108 (STEP THREE: add up partial products)
Here are some more examples for you to study: 

       3231			2134			1420
       x 23			x 22			x 12
       -----			-----			-----
       9693                     4268		        2840
      6462                     4268                    1420
      ------                   ------                  ------
      74313                    46948                   17040
Now you will try a few of these yourself.

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