Multiplying decimals

Here you will learn about multiplying decimals, including how to multiply decimals by a whole number and multiply decimals by decimals.

Students will first learn about multiplying decimals in 5th grade math as part of their work in number and operations.

What is multiplying decimals?

Multiplying decimals is when you multiply numbers involving decimals.

Let’s look at strategies for multiplying decimal numbers.

Multiplying Decimal Number By Decimal Number
Modeling with a Hundredths Grid

Multiplying Decimals table image example 1Multiplying Decimals table image 1

Multiplying Decimals table image 2

The product is the overlapped shaded area. There are 24 shaded
squares in the overlapped area, so the product is \bf{0.24.}

Using the Algorithm

Multiplying Decimals table image example 2Multiplying Decimals table image 3

Multiplying Decimals table image 4

Multiplying Decimals table image 5

Multiplying A Whole Number By Decimal Number
Modeling with a Hundredths Grid

Multiplying Decimals table image example 3Multiplying Decimals table image 6

Multiplying Decimals table image 8

Multiplying Decimals table image 7

The product is the sum of all the shaded squares, which is 102.

The product is \bf{1.02.}

Using the Algorithm

Multiplying Decimals table image example 4Multiplying Decimals table image 9

Multiplying Decimals table image 10

Multiplying Decimals table image 11

What is multiplying decimals?

What is multiplying decimals?

Common Core State Standards

How does this relate to 5th and 6th grade math?

  • Grade 5: Number & Operations Base Ten (5.NBT.B.7)
    Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

  • Grade 6: The Number System (6.NS.B.3)
    Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

[FREE] Multiplying Decimals Worksheet (Grade 5 to 6)

[FREE] Multiplying Decimals Worksheet (Grade 5 to 6)

[FREE] Multiplying Decimals Worksheet (Grade 5 to 6)

Use this worksheet to check your grade 5 to 6 students’ understanding of multiplying decimals. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE
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[FREE] Multiplying Decimals Worksheet (Grade 5 to 6)

[FREE] Multiplying Decimals Worksheet (Grade 5 to 6)

[FREE] Multiplying Decimals Worksheet (Grade 5 to 6)

Use this worksheet to check your grade 5 to 6 students’ understanding of multiplying decimals. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE

How to multiply decimals

In order to multiply decimals using the standard algorithm.

  1. Stack the number with the most digits on top.
  2. Multiply as if the numbers were multi-digit whole numbers, regrouping when necessary.
  3. Count the number of digits after the decimal point for each factor.
  4. Put the same number of digits after the decimal point for the product.

In order to solve decimal multiplication word problems.

  1. Create an equation to model the problem.
  2. Stack the number with the most digits on top.
  3. Multiply as if the numbers were multi-digit whole numbers, regrouping when necessary.
  4. Count the number of digits after the decimal point for each factor.
  5. Put the same number of digits behind the decimal as the product.
  6. Label the product.

Multiplying decimal examples

Example 1: multiplying a decimal number by a decimal number

Find the product of 0.8 \times 0.4 .

  1. Stack the number with the most digits on top.

Both factors have the same number of digits, so it does not matter which one is on top.

Multiplying Decimals image 2 US

2Multiply as if the numbers were multi-digit whole numbers, regrouping when necessary.

Multiplying Decimals image 1 2 US

3Count the number of digits after the decimal point for each factor.

Multiplying Decimals image 34 US

Together, there are two numbers after the decimal point.

4Put the same number of digits after the decimal point for the product.

Multiplying Decimals image 2 US

Move the decimal point two decimal places. The product will have two digits after the decimal point.

The product is 0.32.

On the hundredths grid, look at the overlapped shaded region. There are 32 squares in that area which is 32 hundredths or 0.32

Multiplying Decimals image 3 US

Example 2: multiplying a decimal number by a whole number

Find the product of 1.21 \times 3 .

Stack the number with the most digits on top.

Multiply as if the numbers were multi-digit whole numbers, regrouping when necessary.

Count the number of digits after the decimal point for each factor.

Put the same number of digits behind the decimal for the product.

Example 3: multiplying a decimal number by a decimal number

Find the product of 3.4 \times 43.2 .

Stack the number with the most digits on top.

Multiply as if the numbers were multi-digit whole numbers, regrouping when necessary.

Count the number of digits after the decimal point for each factor.

Put the same number of digits behind the decimal for the product.

Example 4: multiplying a decimal by a decimal

Solve the multiplication problem, 1.642 \times 32.7 .

Stack the number with the most digits on top.

Multiply as if the numbers were multi-digit whole numbers, regrouping when necessary.

Count the number of digits after the decimal point for each factor.

Put the same number of digits behind the decimal for the product.

Example 5: word problem multiplying a whole number by a decimal number

Kit claims she has 4.5 times as many songs on her playlist as Kai. If Kai has 48 songs on his playlist, how many does Kit have on hers?

Create an equation to model the problem

Stack the number with the most digits on top.

Multiply as if the numbers were multi-digit whole numbers, regrouping when necessary.

Count the number of digits after the decimal point for each factor.

Put the same number of digits behind the decimal for the product.

Label the product.

Example 6: word problem multiplying decimal number by a decimal number

On Jupiter, objects weigh about 2.4 times as much as they do on Earth. How much would a 9.45 -pound puppy weigh on Jupiter?

Create an equation to model the problem

Stack the number with the most digits on top.

Multiply as if the numbers were multi-digit whole numbers, regrouping when necessary.

Count the number of digits after the decimal point for each factor.

Put the same number of digits behind the decimal for the product.

Label the product.

Teaching tips for multiplying decimals

  • In 5th grade math, students are first taught about decimal multiplication using visual models such as hundredths grids. As they develop understanding they are able to connect the algorithm of multi-digit multiplication to the multiplication of decimals.

  • Explore other strategies for decimal multiplication such as partial products, which emphasize the distributive property and may be easier for students to understand.

  • Although practicing the skill of decimal multiplication is important, do not rely on practice worksheets to develop deep understanding. Using visual models, hands-on activities, and digital games are very effective alternatives to multiplication problem worksheets.

Our favorite mistakes

  • Placing the decimal point in the wrong position in the answer (product)
    It is important to remember to count the number of places that are in both factors. The total number of digits to the right of the decimal point is how many the answer should have to the right of the decimal point.

  • Leaving the decimal point out completely

  • Thinking that the decimal points of the products need to line up before multiplying like they do in addition of decimals

Practice multiplying decimals questions

1. Find the product of the numbers.

 

14 \times 4.37 = \; ?

6118
GCSE Quiz False

6.118
GCSE Quiz False

611.8
GCSE Quiz False

61.18
GCSE Quiz True

4.37 has more digits than 14, so it will go on top.

 

Multiplying Decimals image 26 US

 
In total, there are two decimal places after the decimal point. Move the decimal point two decimal places. The answer will have two digits after the decimal point.
 
Product = \; 61.18

2. Find the product of the two numbers.

 

5.21 \times 1.6 = \; ?

8.336
GCSE Quiz True

83.36
GCSE Quiz False

0.8336
GCSE Quiz False

833.6
GCSE Quiz False

5.21 has more digits than 1.6, so it will go on top.

 

Multiplying Decimals image 27 US

 

There are a total of three digits after the decimal point. Move the decimal point three decimal places
 

Product = \; 8.336

3. Find the product of the numbers.

 

0.264 \times 1.1 = \; ?

1.2904
GCSE Quiz False

0.2904
GCSE Quiz True

2.9040
GCSE Quiz False

29.0400
GCSE Quiz False

0.264 has more digits than 1.1, so it will go on top.

 

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There are a total of four digits after the decimal point. Move the decimal point four decimal places.

 

Product = \; 0.2904

4. Kaylee went to the bookstore to buy 6 books she needed for her class. If the books cost \$17.25 each, how much did she spend on her books?

\$103.50
GCSE Quiz True

\$103
GCSE Quiz False

\$13.50
GCSE Quiz False

\$103.05
GCSE Quiz False
17.25 \times 6 = \; ?

 

If one book costs \$17.25, then six books will cost 6 \times \$17.25.
 
17.25 has more digits, so it will go on top.
 
Multiplying Decimals image 29 US
 

There are a total of two digits after the decimal point. Move the decimal point two decimal places.

 

Kaylee will spend \$103.25 on the 6 books.

5. The local farmer sold 13.2 pounds of tomatoes. She sold 2.5 times more apples than tomatoes. How many pounds of apples did she sell?

33.3 pounds

GCSE Quiz False

33 pounds

GCSE Quiz True

3.3 pounds

GCSE Quiz False

33.33 pounds

GCSE Quiz False

2.5 times more pounds of apples were sold than tomatoes. Multiply 2.5 times 13.2.
 

13.2 \times 2.5 = \; ?

 
13.2 has more digits than 2.5, so it will go on top.
 
Multiplying Decimals image 30 US
 

There are a total of two digits after the decimal point. Move the decimal point two decimal places.

 

33.00 = 33 pounds of apples were sold.

Multiplying decimals FAQs:

Do you have to use the standard algorithm for multi-digit whole number multiplication to multiply decimals?

No, you can use the strategy that works best for you. For example, you can use partial products to multiply decimals the way you would multi-digit whole numbers.
\bf{1.2} \; \textbf{×} \; \bf{3.4}


Can I change the decimal to a fraction to multiply instead of using decimals?

Yes, in 6th grade, you will become very familiar with changing decimals to fractions and fractions to decimals. However, there are certain situations where keeping the number as a decimal might be easier.

What types of decimals are multiplied in 5th and 6th grade?

Work typically involves multiplying numbers that have values in either the tenths place, hundredths place and/or the thousandths place.

What are the mathematical terms for the parts of a multiplication equation?

\begin{aligned} & \quad \quad \bf{1.3} \quad \quad \textbf{×} \quad \quad \bf{3.4} \quad \quad \textbf{=} \quad \quad \bf{4.08} \\ & \quad \quad \;\; \text{⇧} \quad \quad \quad \quad \quad \; \text{⇧} \quad \quad \quad \quad \quad \;\; \text{⇧}\\ & \text{multiplicand} \quad \; \text{multiplier} \quad \quad \text{product} \end{aligned}

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