1. Partial Product (Multiplication Algorithm)

2. Review of Partial Products
Set up the problem vertically.
Separate all parts.
Find the products.
Add to find the sum.

3. 82 x 3_ (80+2) (3) 240 6 246 = 80 x 3 = 2 x 3 Here’s an example.
+_____
246

4. Try this one using your slate
Try this one using your slate. Use the blank worksheet to help guide you. 42
x 3_
(40+2)
(3)
120 6
= 40 x 3
= 2 x 3
+_____
126

5. Try another one using your slate
Try another one using your slate. Use the blank worksheet to help guide you. 71
x 4_
(70+1)
(4)
280 4
= 70 x 4
= 1 x 4
+_____
284

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

7. We will use the same steps:
Set up the problem vertically.
Separate all parts.
Find the products.
Add to find the sum.

8. 25 x32 (20 + 5) (30 + 2) 800 Here’s an example. +_____ = 20 x 30 600
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
600 10 40
150
Find the products.
+_____
800
Add.

9. Here’s another example.54
x23
(50 + 4)
(20 + 3)
You must multiply all parts. Remember this phrase:
Down, down, crisscross
= 50 x 20
= 4 x 3
= 50 x 3
= 4 x 20
1000 12
150 80
Find the products.
+_____
1242
Add.

10. Here is another way of looking at the problem.

11. 2 7 X 6 4 1,200 420 80 28 + 1,728 Partial Product (20+7) (60+4)
When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer. X 6 4
(60+4)
1,200
Multiply 20 X 60 (tens by tens)
420
Multiply 60 X 7 (tens by ones) 80
Multiply 4 X 20 (ones by tens) 28 +
Multiply 7 X 4 (ones by ones)
Add the results
1,728

12. 4 8 X 5 3 2,000 400 120 24 + 2,544 Partial Product (40+8) (50+3)
When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer. X 5 3
(50+3)
2,000
Multiply 40 X 50 (tens by tens)
400
Multiply 50 X 8 (tens by ones)
120
Multiply 3 X 40 (ones by tens) 24 +
Multiply 8 X 3 (ones by ones)
Add the results
2,544

13. 6 9 X 5 8 3,000 450 480 72 + 4,002 Partial Product (60+9) (50+8)
When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer. X 5 8
(50+8)
3,000
Multiply 60 X 50 (tens by tens)
450
Multiply 50 X 9 (tens by ones)
480
Multiply 8 X 60 (ones by tens) 72 +
Multiply 9 X 8 (ones by ones)
Add the results
4,002

14. Now it’s time to try some on your own! Use the blank paper to guide you.59
x14
(50 + 9)
(10 + 4)
Separate the parts.
Multiply (down, down, crisscross)
Add.
500 36
200 90
= 50 x 10
= 9 x 4
= 50 x 4
= 9 x 10
+_____
826

15. Another! Use the blank paper to guide you.84
x26
(80 + 4)
(20 + 6)
Separate the parts.
Multiply (down, down, crisscross)
Add.
1600 24
480 80
= 80 x 20
= 4 x 6
= 80 x 6
= 4 x 20
+_____
2184

16. Last One! Use the blank paper to guide you.75
x48
(70 + 5)
(40 + 8)
Separate the parts.
Multiply (down, down, crisscross)
Add.
2800 40
560
200
= 70 x 40
= 5 x 8
= 70 x 8
= 5 x 40
+_____
3600

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