Math 6
Unit 1
Lesson 9
Multiplying Decimals
Earning Money
There are many ways that people work to earn an income.
Sometimes people do not have a regular job but they
find a way to make money to buy the things they need
or want. There are people that make crafts or perform
services to earn a living.
Reflection
Can you name ways that you have earned money?
Lian is making wooden toys with her dad to sell so
she can earn money for a scooter she wants to buy.
Lian earns $24.25 for each wooden toy she makes.
If she sells 8 wooden toys in one week how much
will she earn?
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Math 6
Unit 1
Lesson 9: Multiplying Decimals
This story problem can be modelled:
This story problem can be expressed as a number sentence:
24.25 x 8 = money earned in one week
To solve the number sentence you must be able to multiply a decimal by
a whole number:
24.25 x 8 = 194.00
Lian will earn $194.00 by selling her 8 wooden toys.
Reflection
Can you think of a time when you needed to multiply
a dollar amount by a number?
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Unit 1
Lesson 9: Multiplying Decimals
Objectives for this Lesson
In this lesson you will explore the following concepts:
• Predict products of decimals, using estimation strategies
• Place the decimal point in a product
• Solve a given problem that involves multiplication of decimals
Multiplication Review
There are several methods you can use to multiply a two to four digit number
by a one digit number. Here are some examples that you may have experienced
in prior years.
Distributive Property
You can use the distributive property in two ways:
1. Using expanded notation:
Multiply 453 x 8.
Write 453 in expanded form:
Multiply each part by 8:
Add each product:
400 + 50 + 3
(400 x 8) + (50 x 8) + (3 x 8)
3 200 + 400 + 24
3 624
2. Using traditional columns:
Multiply 218 x 7.
218
x 7
56
70
+ 1 400
1 526
Math 6
Multiply by the ones place.
Multiply by the tens place.
Multiply by the hundreds place.
Add.
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Unit 1
Lesson 9: Multiplying Decimals
• G
o online to complete the Concept Capsule: Understanding the Distributive
Property Using Base 10 Blocks.
Multiplication by Regrouping
The regrouping method is the most common:
Multiply 315 x 4.
2
315
x 4
0
1. Multiply 4 x 5.
2. P
ut the ones
digit of the
answer below.
3. P
ut the tens
digit of the
answer above
the tens digit
of the problem.
2
315
x 4
60
1. M
ultiply 4 x 1
and add 2.
2. P
lace below the
tens digit.
2
315
x 4
1 260
1. M
ultiply 4 x 3
place below
the hundreds.
Now It’s Your Turn!
Multiply.
a. 234 x 8
b. 195 x 3
c. 3 427 x 5
b. 585
c. 17 135
Solutions
a. 1 872
Modelling Decimal Multiplication
You can multiply a decimal by a whole number using the same methods that you
used to multiply two whole numbers. The hardest part of multiplying decimals is
placing the decimal point in the product. To understand where the decimal is
placed it helps to first have an image of the operation.
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Math 6
Unit 1
Lesson 9: Multiplying Decimals
You can use grid paper to model decimal multiplication. You will use a 10 x 10
grid to model the value of 1. Here are the values of each:
Value of 1
Value of 0.1
one row or column
Value of 0.01
one square
Let’s try this together! Use a sheet of Grid Paper to help you with the next
problem. You will find Grid Paper at the back of this Unit in your Workbook.
Example 1
Find the product: 2.4 x 3.
Model 2.4 using grid paper. Place the 10 x 10 squares side by side
with no spaces:
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Unit 1
Lesson 9: Multiplying Decimals
Now model 3 going down from the first square of 2.4:
2.4
3
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Unit 1
Lesson 9: Multiplying Decimals
Now fill in the rest of the rectangle:
2.4
3
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Unit 1
Lesson 9: Multiplying Decimals
Now you need to regroup the tenths to make a one:
2.4
10 columns
make 1 whole.
3
10 remaining
columns = 0.2.
6 wholes
Finally you are ready to write the answer:
2.4 x 3 = ?
Based on grid paper model:
+
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6
1
0.2
7.2 =
Math 6
Unit 1
Lesson 9: Multiplying Decimals
Let’s Explore
Exploration 1: Modelling Decimal Multiplication
Materials: Unit 1, Lesson 9, Exploration 1 page in your Workbook, Grid Paper from the
back of this Unit in your Workbook (2 pages), Pencil
For 1 – 3: Draw your models on Grid Paper.
1. Make a model of 1.8 x 2 and find the solution.
2. Make a model of 3.5 x 3 and find the solution.
3.Create your own multiplication sentence. Make a model of your
sentence and solve.
• G
o online to watch the Notepad Tutor Lesson: Multiplication with Decimals
(1-Digit Whole Number Multiplier).
Placing the Decimal Point
You can solve a multiplication sentence that has a decimal without using a
model. Use a traditional multiplication method such as distributive property
or regrouping, and place the decimal point in the proper place. The process
should be:
1. Estimate your solution.
2. Multiply as though you have whole numbers.
3. Place the decimal in the product.
To place the decimal you simply count the number of decimal places in each
factor. If the two factors have a total of 2 decimal places then your product
also will.
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Math 6
Unit 1
Lesson 9: Multiplying Decimals
Example 2
Multiply 4 x $6.18.
1. E
stimate by
rounding the
decimal to
the nearest
whole number.
2. M
ultiply as if you
have two whole
numbers. You will
ignore the decimal
for now.
3
3. C
ount the number of places
after the decimal in each
factor. Next, find the total
number of decimal places in
the product.
3
4 x $6 = $24
$6.18
$6.18
Your answer
should be
about $24.
x
x
4
24 72
4
24.72
2 places after
the decimal
0 places after
+ the decimal
2 places after
the decimal
Now compare your estimate to your solution. $24.72 is close to $24 so your
solution should be $24.72.
Example 3
Multiply 5 x 0.819 cm.
1. E
stimate by
rounding the
decimal to
the nearest
whole number.
2. M
ultiply as if you
have two whole
numbers. You will
ignore the decimal
for now.
4
4
3. C
ount the number of places
after the decimal in each
factor. Next, find the total
number of decimal places in
the product.
4
4
5 x 1 cm = 5 cm
0.819
0.819
Your answer
should be about
5 cm.
x
x
5
4 095
5
4.095
3 places after
the decimal
0 places after
+ the decimal
3 places after
the decimal
Since the estimate 5 cm is close to the product 4.095 cm you are right!
Your solution is 4.095 cm.
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Unit 1
Lesson 9: Multiplying Decimals
Let’s Practice
• In your Workbook turn to Unit 1, Lesson 9 and complete 1 to 16.
Problem Solving
Sometimes the problem you need to work out is in a story or word problem.
That means you will need to figure out the number sentence first. Here is a word
problem that shows one method for solving the problem.
Example 4
Last week Daksha worked 3.5 hours on Wednesday and 4.5 hours on Friday.
Daksha makes $7.65 per hour. How much money did Daksha earn last week?
Make a plan:
Daksha’s earnings = # hours worked x $ per hour
You know: Daksha worked 3.5 hours and 4.5 hours in one week.
Daksha earns $7.65 per hour.
There are two parts:
1. Find the number of hours Daksha worked.
2. Multiply by $7.65.
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Math 6
Unit 1
Lesson 9: Multiplying Decimals
The number of hours Daksha worked:
Wednesday hours + Friday hours = Number of hours worked
3.5 hrs + 4.5 hrs = Number of hours worked
1
3.5
Add: + 4.5
8.0
Estimate the product:
$8 per hour x 8 hours = $ 64
Multiply and place the decimal:
5 4
7.65
x
8
61.20
2 places after
the decimal
0 places after
+ the decimal
2 places after
the decimal
The estimate of $64 is close to the product $61.20.
State the solution:
Daksha earned $61.20 last week.
Remember, you can always use other methods
to solve a problem. You can use picture models,
repeated addition, or distributive property.
There are a number of alternatives!
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Unit 1
Lesson 9: Multiplying Decimals
Let’s Explore
Exploration 2: Choosing Jobs
Materials: Unit 1, Lesson 9, Exploration 2 page in your Workbook, Pencil
You need to choose a job. Job A pays $8.58 per hour and Job B pays
$11.32 per hour.
1. Reflect: Is it always better to take a higher paying job?
Why or why not?
2. Would you choose Job A or Job B?
3. Why did you choose Job ___ ?
4.Would you choose Job A for 8 hours or Job B for 8 hours?
Explain your reasoning.
5.Would you choose Job A for 4 hours or Job B for 7 hours?
Explain your reasoning.
6.Would you choose Job A for 6 hours or Job B for 3 hours?
Explain your reasoning.
Let’s Practice
• In your Workbook turn to Unit 1, Lesson 9 and complete 17 to 19.
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Math 6
Unit 1
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Lesson 9: Multiplying Decimals