# 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 multiply6 × 38 in parts,writing thenumbers undereach other.
 3  8 ×     6 4  8

 First multiply6 × 8.
 3  8×     6 4  8 1  8  0
 Then multiply 6 × 30 andwrite the result under the 48.Remember, the "3" is in thetens place in the number 38so it actually means 30.
 3  8×    6 4  8+ 1  8  0 2  2  8

Multiply 9 × 2.

Then 9 × 80.

 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.

 4  7 ×     3 2  1
 4  7×     3 2  11  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,

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
 5  2  6 ×     7 4  2

 5  2  6×     7 4  21  4  0

 5  2  6×     7 4  21  4  0 3  5  0  0

 5  2  6×      7 4  21  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

Partial products algorithm - a video lesson

This lesson is taken from Maria Miller's book Math Mammoth Multiplication 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

#### 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.