Transcript Partial Products

Partial Product
(Multiplication Algorithm)
Review of Partial
Products
1.
2.
3.
4.
Set up the problem vertically.
Write the numbers in expanded form.
Find the products.
Add to find the sum.
Here’s an example.
82 (80+2)
(3)
x 3_
240 = 80 x 3
+_____
6 =2x3
246
Try this one using your slate.
Use the blank worksheet to help guide
you.
42 (40+2)
(3)
x
120
=
40
x
3
3_
6 =2x3
+_____
126
Try another one using your slate.
Use the blank worksheet to help guide
you.
71
x 4_
(70+1)
(4)
280 = 70 x 4
4 =1x4
+_____
284
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.
2.
3.
4.
Set up the problem vertically.
Write the numbers in expanded form.
Find the products.
Add to find the sum.
Here’s an example.
25 (20 + 5)
x32 (30 + 2)
600 = 20 x 30
Find the
products.
Add.
10 = 5 x 2
40 = 20 x 2
+_____
150 = 5 x 30
800
You must
separate and
multiply all
parts. Remember
this phrase:
Down, down,
crisscross
Here’s another example.
54 (50 + 4)
x23 (20 + 3)
1000 = 50 x 20
Find the
products.
Add.
12 = 4 x 3
150 = 50 x 3
+_____
80 = 4 x 20
1242
You must multiply
all parts.
Remember this
phrase:
Down, down,
crisscross
Here is another way of
looking at the problem.
When multiplying by “Partial
Products,” you must first
multiply parts of these numbers,
then you add all of the results to
find the answer.
Multiply 20 X 60 (tens by tens)
Multiply 60 X 7 (tens by ones)
Multiply 4 X 20 (ones by tens)
Multiply 7 X 4 (ones by ones)
Add the results
2 7 (20+7)
X 6 4 (60+4)
1,200
420
80
+ 28
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.
Multiply 40 X 50 (tens by tens)
Multiply 50 X 8 (tens by ones)
Multiply 3 X 40 (ones by tens)
Multiply 8 X 3 (ones by ones)
Add the results
4 8 (40+8)
X 5 3 (50+3)
2,000
400
120
+ 24
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.
Multiply 60 X 50 (tens by tens)
Multiply 50 X 9 (tens by ones)
Multiply 8 X 60 (ones by tens)
Multiply 9 X 8 (ones by ones)
Add the results
6 9 (60+9)
X 5 8 (50+8)
3,000
450
480
+ 72
4,002
Now it’s time to try some on your
own!
Use the blank paper to guide you.
Separate the parts.
Multiply (down,
down, crisscross)
Add.
59 (50 + 9)
x14 (10 + 4)
500 = 50 x 10
36 = 9 x 4
200 = 50 x 4
90 = 9 x 10
+_____
826
Another!
Use the blank paper to guide you.
Separate the parts.
Multiply (down,
down, crisscross)
Add.
84 (80 + 4)
x26 (20 + 6)
1600 = 80 x 20
24 = 4 x 6
480 = 80 x 6
80 = 4 x 20
+_____
2184
Last One!
Use the blank paper to guide you.
Separate the parts.
Multiply (down,
down, crisscross)
Add.
75 (70 + 5)
x48 (40 + 8)
2800 = 70 x 40
40 = 5 x 8
560 = 70 x 8
200 = 5 x 40
+_____
3600
Homework
* You will complete a
worksheet with 4
multiplication problems
which you will use Partial
Products to solve.