# 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.

## Common Core 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.

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.

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

1.21 has more digits than 3, so 1.21 will be on top.

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

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

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

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

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

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

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

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?

4.5 \times 48 = \; ?

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

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

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

The product is 216.0 or 216

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?

9.45 \times 2.4 = \; ?

9.45 has more digits, so it will go on top.

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

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

The puppy will weigh 22.68 pounds on Jupiter.

### 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

6.118

611.8

61.18

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

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

83.36

0.8336

833.6

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

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

0.2904

2.9040

29.0400

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

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

\$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. 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

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.

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?