Multiply using partial products

The 5 steps below will quickly show you how to multiply using partial products. Here, we will do the multiplication for a two-digit number by another two-digit number. For example, the figure below shows how to quickly multiply 26 by 45.

If you did not quite understand the example in the figure below, keep reading since we broke the multiplication down into 5 steps.

If you multiply a two-digit number by another two-digit number, you will have 4 partial products.

Here is how to multiply using partial products step by step

Step 1

       Tens   Ones
         4   5 
   x    2   6
 __________   
   8  0   0 <---------- partial product

Multiply the tens by the tens: 2 tens x 4 tens = 20 x 40 = 800.

Step 2

       Tens   Ones
         4   5 
   x    2   6
 __________   
   1  0   0 <---------- partial product

Multiply the ones by the tens: 5 ones x 2 tens = 5 x 20 = 100.

Step 3

      Tens   Ones
         4   5 
   x    2   6
 __________   
   2  4   0 <---------- partial product

Multiply the tens by the ones: 4 tens x 6 ones  = 40 x 6 = 240

Step 4

       Tens   Ones
         4   5 
   x    2   6
 __________   
       3    0 <---------- partial product

Multiply the ones by the ones: 5 ones x 6 ones  = 30 ones = 30

Step 5

          Tens   Ones
             4   5 
       x    2   6
    __________   
       8  0   0
      1  0   0
      2  4   0
          3   0
 _________
 1   1  7   0 

Just add the four partial products to get the answer: 800 + 100 + 240 + 30 = 1170

So, 26 x 45 = 1170

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