Arithmetic Grade Five

Lesson Forty-seven: Two Column Multiplication

Inspect this multiplication problem: 

      32
    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. 

     32
   x 32 
  ------
     64  <--- A. 32 x 2 = 62 (STEP ONE: multiply top by ones of bottom)
    96   <--- B. 32 x 3 = 96 (STEP TWO: multiply top by tens of bottom)
  ------
   1022  <--- C. 960 + 62 = 1022 (STEP THREE: add up partial products)
In this example we must first find two partial products before we can add them up to get the final product. The first partial product is 64 and we get that by multiplying 32 x 2 as explained in the example. The second partial product is 96 and we get that by multiplying 32 x 3 as shown in the example. Notice that we write the 96 so that the 6 in 96 is under the tens column in the problem. That is because we are REALLY multiplying 32 x 30 since the 3 in the 32 is really worth 30 since it is in the tens column.

Once we find our partial products, we add them up. We must be sure that the partial products are properly lined up as shown in the example.

Here is another example: 


     44
   x 22 
  ------
     88  <--- A. 44 x 2 = 88 (STEP ONE: multiply top by ones of bottom)
    88   <--- B. 44 x 2 = 88 (STEP TWO: multiply top by tens of bottom)
  ------
   968  <--- C. 880 + 88 = 1768 (STEP THREE: add up partial products)
Here are some more examples for you to study: 

         31			  34			  20
       x 23			x 22			x 42
       -----			-----			-----
         93                       68		          40
        62                       68                      80
       -----                    -----                   -----
        713                      748                     840
Now you will try a few of these yourself.

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