Partial Product Partial Product (Multiplication Algorithm)(Multiplication Algorithm)Partial Product Partial Product

(Multiplication Algorithm)(Multiplication Algorithm)

Review of Partial Products

1. Set up the problem vertically.2. Separate all parts.3. Find the products.4. Add to find the sum.

Here’s an example.

82x 3_240 6

(80+2)

(3) = 80 x 3= 2 x 3+_____

246

Try this one using your slate. Use the blank worksheet to help

guide you.

42x 3_ = 40 x 3

= 2 x 3

(40+2)

(3) 120 6+_____

126

Try another one using your slate. Use the blank worksheet to help

guide you.

71x 4_

(70+1)

(4) 280 4+_____

284

= 70 x 4= 1 x 4

Now, we are going to learn to multiply a 2 digit number by a 2 digit number using the Partial Products Algorithm.

We will use the same steps:

1. Set up the problem vertically.2. Separate all parts. 3. Find the products.4. Add to find the sum.

Here’s an example.

25 x32

(20 + 5)

(30 + 2) 600

10

40

150

You must separate and multiply all parts. Remember this phrase:

Down, down, crisscross

= 20 x 30

= 5 x 2

= 20 x 2

= 5 x 30

Find the products

.

Add.

+_____

800

Here’s another example.

54 x23

You must multiply all parts. Remember this phrase:

Down, down, crisscross

(50 + 4)

(20 + 3) = 50 x 20

= 4 x 3

= 50 x 3

= 4 x 20

Find the products

.

1000

12

150

80+_____

1242

Add.

Here is another way of looking at the problem.

Multiply 20 X 60 (tens by tens)

27X 64

Multiply 60 X 7 (tens by ones)

1,200 420 80 28

Multiply 4 X 20 (ones by tens)

Multiply 7 X 4 (ones by ones)

Add the results

+

1,728

When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer.

(20+7)

(60+4)

Multiply 40 X 50 (tens by tens)

48X 53

Multiply 50 X 8 (tens by ones)

2,000 400

120 24

Multiply 3 X 40 (ones by tens)

Multiply 8 X 3 (ones by ones)

Add the results

+

2,544

When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer.

(40+8)

(50+3)

Multiply 60 X 50 (tens by tens)

69X 58

Multiply 50 X 9 (tens by ones)

3,000 450

480 72

Multiply 8 X 60 (ones by tens)

Multiply 9 X 8 (ones by ones)

Add the results

+

4,002

When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer.

(60+9)

(50+8)

Now it’s time to try some on your own!

Use the blank paper to guide you.

59 x14

Separate the parts.

Multiply (down, down, crisscross)

Add.

(50 + 9)

(10 + 4) = 50 x 10

= 9 x 4

= 50 x 4

= 9 x 10

500

36

200

90+_____

826

Another! Use the blank paper to guide you.

84 x26

Separate the parts.

Multiply (down, down, crisscross)

Add.

(80 + 4)

(20 + 6) = 80 x 20

= 4 x 6

= 80 x 6

= 4 x 20

1600

24

480

80+_____

2184

Last One! Use the blank paper to guide you.

75 x48

Separate the parts.

Multiply (down, down, crisscross)

Add.

(70 + 5)

(40 + 8) = 70 x 40

= 5 x 8

= 70 x 8

= 5 x 40

2800

40

560

200+_____

3600

Homework* You will complete a worksheet with 4 multiplication problems which you will use Partial Products to solve.