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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.
