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The partial products algorithm - the "easy way" to multiply

This lesson explains the partial products algorithm for multiplying two- or three-digit numbers in columns that can be easier for some students than the standard algorithm of multiplication. It is a complete lesson with explanations and exercises, meant for fourth grade. In a nutshell, students break the number to multiply into parts, multiply the parts separately, and then add.



3  8
×     6

 

 

Let's multiply
6 × 38 in parts,
writing
the
numbers under
each other.

3  8
×     6

4  8

 

First multiply
6 × 8.

3  8
×     6

4  8
1  8  0


Then multiply 6
× 30 and
write the result under the 48.
Remember, the "3" is in the
tens place in the number 38
so it actually means 30.

3  8
×    6

4  8
+ 1  8  0

2  2  8

Lastly, add.

Multiply 9 × 2.
 
Then 9 × 80.
 
Add.

8  2
×     9

1  8

8  2
×     9

1  8
7  2  0

8  2
×     9

1  8
+ 7  2  0

7  3  8

Multiply 3 × 7.
 
Then 3 × 40.
 
Add. 
 

4  7
×     3

2  1

4  7
×     3

2  1
1  2  0

4  7
×     3

2  1
+ 1  2  0

1  4  1

1. Multiply.

a.



 

b.


    

c.

d.

e.

f.

 

g.

h.



Multiplying a 3-digit number
happens in exactly the same way.

You multiply in parts:
first the ones, then the tens,
then the hundreds. Lastly, add.

Just don't forget that you are
multiplying whole tens and
whole hundreds, not just
“plain” numbers.

ones:
7 × 6
 
  tens:
7 × 20
  hundreds:
7 × 500
  Add.

5  2  6
×     7

4  2

 

5  2  6
×     7

4  2
1  4  0

 

5  2  6
×     7

4  2
1  4  0
3  5  0  0

 

5  2  6
×      7

4  2
1  4  0
+  3  5  0  0

3  6  8  2

2. Multiply.

a.



 

b. c.

d.

e.

 

f.

g.

h.

i.

j.

k.

l.

3. Solve the equations.

a.   × 80 = 480

 = ________

b.  5 ×   ?   = 450

  ?   = ________

c.  900 ×  z  = 81,000

z = ________



4. Solve.

a.  58 × 5 + 291

b.  1,000 − 3 × 145

5. Solve.

a. A $236 burglar alarm is discounted
    by $40. A store buys seven. What is
    their total cost?

b. One side of a square is 248 feet.
    What is its perimeter?
 

6. Solve the equations.

a.  50 ×   ?   = 2,000

  ?   = ________

b.   × 60 = 2,400

 = ________

c.  70 ×  z  = 49,000

z = ________

d.   × 30 = 9 × 40

 = ________

e.  5 ×   ?   × 2 = 1,000

  ?   = ________

f.  40 × p = 800 × 4

p = ________

 

  Figure out the missing numbers and finish solving!
a.
      
× 7
1 4
4 9 0
+ 7 0 0
 
    
b.
        
  ×

4

       
  2 0 0
+ 1 2 0 0
  1 4 3 2
    
c.
        
  ×

9

    8 1
       
+ 6 3 0 0
  6 3 8 1


See also:

Partial products algorithm - a video lesson

Worksheet for partial products: single-digit number times a 2-digit number
Worksheet for partial products: single-digit number times a 3-digit number
Worksheet for partial products: single-digit number times a 4-digit number



This lesson is taken from my book Math Mammoth Multiplication 2. The lesson addresses the following Common Core standards for 4th grade: 4.OA.2 and 4.NBT.5.

Math Mammoth Multiplication 2

A self-teaching worktext for 4th grade that covers multiplying by whole tens and hundreds, multi-digit multiplication in columns, order of operations, word problems, scales problems, and money problems.

Download ($5.10). Also available as a printed copy.

Learn more and see the free samples!

See more topical Math Mammoth books



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