Partial-Products Multiplication
for Decimals
Partial-products multiplication can be applied to decimal multiplication.
The only difference is that the decimal place value will be ignored until
the end solution is recorded. Students find this algorithm particularly
helpful for estimating the location of the decimal point. The challenge is
to understand where to correctly position the decimal point in the product,
a process that requires greater number sense and estimation skills than
required in whole number multiplication.
Methods that improve students’ understanding of decimal multiplication
include using models (base-10 blocks) to show repeated addition or groupings,
using calculators to look for patterns in the decimals, and rounding factors
to find a reasonable estimate, or magnitude estimate, for the product.
Build Understanding
If students need to review the whole-number version of this algorithm, refer
them to pages 43–45.
Review the process of making a magnitude estimate of the product in a decimal
multiplication problem. Write the problem 3.8 º 4.3 on the board. Explain
that each of these numbers can be rounded to 4. Since 4 º 4 = 16, the product
will be in the tens. Have students practice finding magnitude estimates for
problems like this on their own. Provide opportunities to share strategies.
Using page 51, explain that students should first make a magnitude estimate
for the answer. Then they should multiply just as they would with the wholenumber version of the partial-products algorithm. Finally, they should use
their magnitude estimate to help them place the decimal point in the answer.
Use questions like the following to guide students through each example:
• How can you tell how many partial products you will end up with?
(Observing how many times each digit in one factor must be multiplied by
each digit in the other factor tells how many partial products there will be.)
Page 51
Answer Key
• What is a reasonable estimate for the answer of this problem?
• Based on the estimate, where will you place the decimal point?
1. 29.88
Error Alert Be sure students remember to ignore the decimal points as
they work the problem using the partial-products algorithm for whole numbers.
Once the total for the partial product is recorded, check to see that students
use their magnitude estimate to help them place the decimal point correctly in
the answer. If needed, require students to record their magnitude estimate so
you can check their understanding.
2. 33.32
3. 24.284
4. 62.175
Check Understanding
5. 33.12
Write 4.5 ∗ 32 on the board and solve it using the partial-products algorithm,
ignoring the decimal point. Then have a volunteer or two come to the board
and point to each pair of digits that were multiplied to produce each partial
product. Have students also explain how they would use a magnitude estimate
for the product to help them decide where to place the decimal point. Repeat
the process until you are reasonably certain that most of your students
understand the algorithm. Then assign the “Check Your Understanding”
exercises at the bottom of page 51. (See answers in margin.)
6. 19.72
7. 53.82
8. 48.0501
50
Copyright © Wright Group/McGraw-Hill
Multiplication
• Which two digits are multiplied to get the first partial product?
Teacher Notes
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Partial-Products Multiplication for Decimals
First, make a magnitude estimate. Next, multiply each digit in the
bottom factor by each digit in the top factor. Then add all of the
partial products. Use your magnitude estimate to correctly place
the decimal point in the product.
Example
Step 2: Multiply as you would for
whole numbers.
Multiply 60 ∗ 70.
Copyright © Wright Group/McGraw-Hill
Multiply 60 ∗ 4.
Multiply 9 ∗ 70.
Multiply 9 ∗ 4.
Add the partial products.
→
→
→
→
→
Step 3: Place the decimal point
correctly in the answer.
Since the magnitude
estimate is in the tens,
the product must be in
the tens.
7.4 ∗ 6.9
74
∗ 69
4200
240
630
+ 36
5106
(factor)
(factor)
Multiplication
Step 1: Make a magnitude estimate.
Round 7.4 to 7 and 6.9 to 7.
Since 7 º 7 = 49, the product will
be in the tens.
7.4 * 6.9 = 51.06
(product)
Check Your Understanding
Solve the following problems.
1. 8.3 ∗ 3.6
2. 6.8 ∗ 4.9
3. 5.2 ∗ 4.67
4. 8.29 ∗ 7.5
5. 7.2 ∗ 4.6
6. 5.8 ∗ 3.4
7. 6.9 ∗ 7.8
8. 6.09 ∗ 7.89
Write your answers on a separate sheet of paper.
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