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4.2: Estimation to Check Decimal Multiplication

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Have you ever estimated a product and wondered if your answer was reasonable?

At the Science Museum, Kelly decided to buy a few books on dinosaurs to bring home. She picked three different books on different types of dinosaurs. The price of each book was $19.25.

Kelly began trying to estimate the total cost of all three books. She thinks that with her $59.00 that she will have enough money to buy them. Is she correct?

This Concept is all about estimating products when you multiply decimals. Pay close attention and you will be able to help Kelly at the end of the Concept.

Guidance

In the last Concept, you learned how to multiply a decimal with a whole number. That is the perfect thing to do if you are looking for an exact answer.

When do we estimate a product?

Remember back to when we were first working with estimation. We can use estimation whenever we don’t need to find an exact answer. As long as our answer makes sense, we can estimate.

We can use rounding to estimate.

How can we estimate a product using rounding?

When we multiply a whole number with a decimal, we can round the decimal that we are multiplying to find a reasonable estimate.

Estimate 5(1.7) = _____

In this example we were told that we could estimate, so we don’t need to worry about finding an exact answer. If we use rounding, we can round the decimal to the nearest whole number.

1.7 is closest to 2.

We round 1.7 up to 2.

Now we can rewrite the problem and multiply.

5(2) = 10

A reasonable estimate for 5(1.7) is 10.

Estimate 7(4.3) = _____

Here we can estimate by rounding the decimal.

4.3 rounds down to 4

7 \times 4 = 28

A reasonable estimate for 7(4.3) = 28

Here are a few for you to try. Estimate the following products.

Example A

4(3.2) = _____

Solution: 12

Example B

6(2.8) = _____

Solution: 18

Example C

7(5.3) = _____

Solution: 35

Do you know if Kelly will have enough money? Let's look at the original problem once again.

At the Science Museum, Kelly decided to buy a few books on dinosaurs to bring home. She picked three different books on different types of dinosaurs. The price of each book was $19.25.

Kelly began trying to estimate the total cost of all three books. She thinks that with her $59.00 that she will have enough money to buy them. Is she correct?

First, we can round to $19.00 for each book.

Next, we can multiply 19(3).

19(3) = 57

Even though this is an estimate, Kelly will have enough money to purchase all three books.

Vocabulary

Here are the vocabulary words that can be found 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.

Estimate the following product.

4(7.82)

Answer

To begin, we can round the decimal up to 8. Next, we multiply.

4 \times 8 = 32

This is our answer.

Video Review

Here are videos for review.

Khan Academy Multiplying Decimals 2

This video is a skill that you will need when estimating products.

Practice

Directions: Estimate the following products.

1. 4(3.2) = _____

2. 5(1.8) = _____

3. 6(2.3) = _____

4. 9(1.67) = _____

5. 8(4.5) = _____

6. 9(6.7) = _____

7. 4(8.1) = _____

8. 8(3.2) = _____

9. 9(9.7) = _____

10. 7(1.1) = _____

11. 8(3.5) = _____

12. 5(8.4) = _____

13. 12(9.1) = _____

14. 9(11.9) = _____

15. 6(12.3) = _____

16. 9(13.8) = _____

17. 8(14.3) = _____

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Difficulty Level:

At Grade

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Date Created:

Oct 29, 2012

Last Modified:

Dec 17, 2014
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