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Multiplication of Decimals and Whole Numbers

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MCC6.NS.3 - Multiplication of Decimals and Whole Numbers

Have you ever been to a science museum? Have you ever had to figure out the admission cost for a group of students? Multiplication is definitely involved if you have ever tackled such a problem yourself.

Mrs. Andersen is planning a field trip to the Science Museum for her sixth grade class. She wants to spend the entire day at the museum and plans to take all twenty-two students with her. She looks up some information on the internet and finds that a regular price ticket is $12.95 and a student ticket is $10.95. However, when Mrs. Andersen checks out the group rates, she finds that the students can go for $8.95 per ticket at the group student rate. Because she is a teacher, Mrs. Andersen gets to go for free. One chaperone receives free admission also. Mrs. Andersen has a total of three chaperones attending the field trip. The other two chaperones will need to pay the regular ticket price. The class has a budget to pay for the chaperones. Mrs. Andersen assigns Kyle the job of being Field Trip Manager. She hands him her figures and asks him to make up the permission slip. Kyle is glad to do it. When collection day comes, Kyle collects all of the money for the trip. Kyle has an idea how much he should collect, what should his estimate be? Given the student price, how much money does Kyle need to collect if all 22 students attend the field trip? What is the total cost for all of the students and for the two chaperones?

While Kyle is adding up the money, you have the opportunity to figure out the answers to these two questions.

You will need to use information about multiplying decimals and whole numbers.

Pay close attention during this Concept, see if your answers match Kyle’s by the end of the Concept.

Guidance

In this Concept you will be learning about how to multiply decimals and whole numbers together. Let’s think about what it means to multiply.

Multiplication is a short-cut for repeated addition. We think about multiplication and we think about groups of numbers.

4 \times 3 = 12

Here we are saying that we have four groups of three that we are counting or we have three groups of four. It doesn’t matter which way we say it, because we still end up with twelve. When we multiply decimals and whole numbers, we need to think of it as groups too.

2(.25) = _____

Here we are multiplying two times twenty-five hundredths. Remember that when we see a number outside of the parentheses that the operation is multiplication. We can think of this as two groups of twenty-five hundredths. Let’s look at what a picture of this would look like.

Our answer is .50.

This is one way to multiply decimals and whole numbers; however we can’t always use a drawing. It just isn’t practical.

How can we multiply decimals and whole numbers without using a drawing?

We can multiply a decimal and a whole number just like we would two whole numbers. First, we ignore the decimal point and just multiply. Then, we put the decimal point in the product by counting the correct number of places.

4(1.25) = _____

Let’s start by multiplying just like we would if this were two whole numbers. We take the four and multiply it by each digit in the top number.

125 \\\underline{\times \ \quad 4}\\500

But wait! Our work isn’t finished yet. We need to add the decimal point into the product. There were two decimal places in our original problem. There should be two decimal places in our product.

& 5.00 \\& \ \nwarrow \\& \quad \text{We count in two places from right to left into our product}.

This is our final answer.

Here are a few for you to try. Multiply them just as you would whole numbers and then put in the decimal point.

Example A

3(4.52)

Solution: 13.56

Example B

5(2.34)

Solution: 11.7

Example C

7(3.56)

Solution: 24.92

Now back to Kyle and the trip to the science museum!

Now, let’s think about the estimate. About how much money should Kyle collect? The first step in working this out is to write an equation.

22 students at $8.95 per ticket = 22(8.95)

Kyle wants an estimate, so we can round 8.95 to 9

Now let’s multiply 22(9) = $198.00

Now that Kyle has an estimate, he can actually work on collecting the money and counting it. Once he has collected and counted all the money, we will be able to see if his original estimate was reasonable or not.

One week before the trip, Kyle collects $8.95 from 22 students. He multiplies his results, 22(8.95) = $196.90

Kyle can see that his original estimate was reasonable. He is excited-the estimation worked!!

Next, Kyle figures out the cost of the chaperones. There are two chaperones who each pay the regular price which is $12.95.

2(12.95) = 25.90

Finally, Kyle adds up the total.

196.90 + 25.90 = $222.80

He gives his arithmetic and money to Mrs. Andersen. She is very pleased.

The students are off to the Science Museum!!!

Vocabulary

Here are the vocabulary words in this Concept.

Multiplication
a shortcut for addition, means working with groups of numbers
Product
the answer from a multiplication problem
Estimate
an approximate answer-often found through rounding

Guided Practice

Here is one for you to try on your own.

Nine friends decided to go to a movie on Friday night. They each paid the $8.50 for admission. How much money did they spend in all?

Answer

To solve this problem, we can write a multiplication problem.

9(8.50)

Our answer is $76.50.

Video Review

Here are videos for review.

Khan Academy Multiplying Decimals 2

Multiplying Decimals by Whole Numbers

Practice

Directions: Multiply to find a product.

1. 5(1.24) = _____

2. 6(7.81) = _____

3. 7(9.3) = _____

4. 8(1.45) = _____

5. 9(12.34) = _____

6. 2(3.56) = _____

7. 6(7.12) = _____

8. 3(4.2) = _____

9. 5(2.4) = _____

10. 6(3.521) = _____

11. 2(3.222) = _____

12. 3(4.223) = _____

13. 4(12.34) = _____

14. 5(12.45) = _____

15. 3(143.12) = _____

16. 4(13.672) = _____

17. 2(19.901) = _____

18. 3(67.321) = _____

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