Kit has [katex] 216 [/katex] songs on her playlist.

The puppy will weigh [katex] 22.68 [/katex] pounds on Jupiter.

Multiplying Decimals - Math Steps, Examples & Questions

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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
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 A Whole Number By Decimal Number
Modeling with a Hundredths Grid
The product is the sum of all the shaded squares, which is $102.$ The product is $\bf{1.02.}$
Using the Algorithm

What is multiplying decimals?

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

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

DOWNLOAD FREE

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

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

DOWNLOAD FREE

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.

How to multiply decimals

In order to multiply decimals using the standard algorithm.

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 after the decimal point for the product.

In order to solve decimal multiplication word problems.

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 as the product.
Label the product.

Multiplying decimal examples

Example 1: multiplying a decimal number by a decimal number

Find the product of $0.8 \times 0.4$ .

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.

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

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

Together, there are two numbers after the decimal point.

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

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 $0.32$

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.

$1.21$ has more digits than $3,$ so $1.21$ will be 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.

In total, there are two decimal places after the decimal point.

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

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

The product is $3.63$

Looking at the hundredths grids, you can see there are $3$ groups of $1.21$ that represent $363$ shade squares, $363$ squares $= \; 3.63$

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.

$43.2$ has more digits than $3.4,$ so it will go 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.

In total, there are two decimal places after the decimal point.

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

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

The product is $146.88$

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.

$1.642$ has more digits than $32.7,$ so it will go 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.

In total, there are four decimal places after the decimal point.

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

Move the decimal point four decimal places. The answer has four digits after the decimal point.

The product is $53.6934$

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

$4.5 \times 48 = \; ?$

Stack the number with the most digits on top.

$48$ and $4.5$ have the same number of digits. It does not matter which one goes 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.

In total, there is one decimal place after the decimal point.

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

Move the decimal point one decimal place. The product will have one digit after the decimal point.

The product is $216.0$ or $216$

Label the product.

Kit has $216$ songs on her playlist.

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

$9.45 \times 2.4 = \; ?$

Stack the number with the most digits on top.

$9.45$ has more digits, so it will go 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.

In total, there are three decimal places after the decimal point.

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

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

The product is $22.680$ or $22.68$

Label the product.

The puppy will weigh $22.68$ pounds on Jupiter.

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

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

DOWNLOAD FREE

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

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

DOWNLOAD FREE

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

6118

6.118

611.8

61.18

$4.37$ 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 $= \; 61.18$

8.336

83.36

0.8336

833.6

$5.21$ 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 $= \; 8.336$

1.2904

0.2904

2.9040

29.0400

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

Multiplying Decimals image 28 US

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

Product $= \; 0.2904$

\$103.50

\$103

\$13.50

\$103.05

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.

$33.3$ pounds

$33$ pounds

$3.3$ pounds

$33.33$ pounds

$2.5$ 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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