Partial product

Question

Compute 34 * 26 using the method of partial products. Use the base-ten grid below to illustrate the partial products in a rectangular array. 

Answer 1

When using partial products method, you are multiplying the numbers based on place value.  In other words, it utilizes the distributive property.

 

  34

x 26

_____

 

 

If we look at the units place, we take 4x6.  Then we see the 34 as a 30 and multiply it by 6.

 

So far you have,

 

4 x 6 = 24

30 x 6 = 180

 

 

Now we look at the tens place.  Use 26 as the reference value.

 

20 x 4 = 80

20 x 30 = 600

 

 

Finally, just add the 4 products.

 

     24

   180

     80

+ 600

_____

   884 = actual product

 

 

If we write this using distributive property, we have

 

6 x (4 + 30) + 20 x (4 + 30) =

 

(6 x 34) + (20 x 34) =

 

34 x (6 + 20) =

 

34 x 36   --->  this is the original form of the product

 

_________________________________________________________________________________

 

Now to use the base-ten grid.

 

bit = 1 block

long = 10 blocks

flat = 100 blocks

 

On the vertical side of the grid, insert 3 longs and 4 bits.

On the horizontal side of the grid, insert 2 longs and 6 bits.

 

You should have an L-shape pattern in that construction.

 

Now take the area covered using only the long blocks.

 

30 blocks x 20 blocks = 600 blocks  - 1st area

 

 

Now take the area covered by 2 longs and 4 bits.

 

20 blocks x 4 blocks = 80 blocks - 2nd area

 

 

Take the area covered by 3 longs and 6 bits,

 

30 blocks x 6 blocks = 180 blocks - 3rd area

 

 

Finally, take the area covered only using bits.

 

4 blocks x 6 blocks = 24 blocks - 4th area

 

 

Add up these subareas to get your product.