Partial Product (Multiplication Algorithm). Review of Partial Products 1.Set up the problem...

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(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.