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# 3.24: Problem Solving Plan, Estimation with Decimals

Difficulty Level: At Grade Created by: CK-12
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Practice Problem Solving Plan, Estimation with Decimals

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Jose has enjoyed working all summer. He loved helping Mr. Harris and his recycling idea ended up being very profitable. Jose began the summer with an estimate of how much money he thought he would make. He earned $7.00 per hour and he worked ten 30-hour weeks. Jose ended up earning$2100.00 for the summer, and he is very pleased with his accomplishment. Now that the summer is over, Jose wishes to spend part of his money on new clothes for school. He has selected the following items.

$19.95$32.95

$46.75 Jose brought$100.00 with him to purchase the items.

If he estimates the total cost, what would it be?

#### Example B

Jesse ran 16.5 miles one day and 22.8 miles the next. What is his estimated total mileage?

Solution: 40 miles

#### Example C

Kara biked 25.75 miles one day and 16.2 miles the next. What is her estimated total mileage?

Solution: 42 miles

Remember Jose? Jose brought $100.00 with him to purchase the items. If he estimates the total cost, what would it be? How much change will Jose receive from the$100.00?

We could use a couple of different strategies to estimate the total of Jose’s purchases.

We could use rounding or front–end estimation.

Let’s use rounding first.

$19.95 rounds to$20.00

$32.95 rounds to$33.00

$46.75 rounds to$47.00

Our estimate is 100.00. Hmmm. Ordinarily, rounding would give us an excellent estimate, but in this case our estimate is the amount of money Jose wishes to pay with. Because of this, let’s try another strategy. Let’s use front–end estimation and see if we can get a more accurate estimate. 19+32+461+1+80=97=2.80\begin{align*}19 + 32 + 46 & = 97 \\ 1 + 1 + 80 & = 2.80\end{align*} Our estimate is99.80.

With front–end estimation, we can estimate the Jose will receive .20 change from his $100.00. While he isn’t going to get a lot of change back, he is going to receive some change so he does have enough money to make his purchases. ### Vocabulary Here are the vocabulary words in this Concept. Round to value a number given place value and to move it up or down given place value Estimate an approximate solution to a problem ### Guided Practice Here is one for you to try on your own. Tina is working to buy presents for her family for the holidays. She has picked out a cd for her brother for$14.69, a vase for her Mother at $32.25 and a picture frame for her father at$23.12. Use rounding to estimate the sum of Tina’s purchases.

To use rounding, we first round each item that Tina bought to the nearest whole dollar.

$32.25 rounds to$32.

$23.12 rounds to$23.

32+23=55\begin{align*}32 + 23 = 55\end{align*}

The estimated cost of Tina's purchases is $55.00. ### Video Review Here is a video for review. ### Practice Directions: Look at each problem and use what you have learned about estimation to solve each problem. 1. Susan is shopping. She has purchased two hats at$5.95 each and two sets of gloves at $2.25 each. If she rounds each purchase price, how much can she estimate spending? 2. If she uses front–end estimation, how does this change her answer? 3. Which method of estimation gives us a more precise estimate of Susan’s spending? 4. If she brings$20.00 with her to the store, about how much change can she expect to receive?

5. If she decided to purchase one more pair of gloves, would she have enough money to make this purchase?

6. Would she receive any change back? If yes, about how much?

7. Mario is working at a fruit stand for the summer. If a customer buys 3 oranges at $.99 a piece and two apples for$.75 a piece, about how much money will the customer spend at the fruit stand? Use rounding to find your answer.

8. What is the estimate if you use front–end estimation?

9. Why do you think you get the same answer with both methods?

10. If the customer gives Mario a \$10.00 bill, about how much change should the customer receive back?

11. Christina is keeping track of the number of students that have graduated from her middle school over the past five years. Here are her results.

2004 – 334

2005 – 367

2006 – 429

2007 – 430

2008 – 450

Estimate the number of students who graduated in the past five years.

12. Did you use rounding or front–end estimation?

13. Why couldn’t you use front–end estimation for this problem?

14. Carlos has been collecting change for the past few weeks. He has 5 nickels, 10 dimes, 6 quarters and four dollar bills. Write out each money amount.

15. Use rounding to estimate the sum of Carlos’ money.

16. Use front–end estimation to estimate the sum of Carlos’ money.

17. Which method gives you a more accurate estimate? Why?

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

Estimate

To estimate is to find an approximate answer that is reasonable or makes sense given the problem.

Round

To round is to reduce the number of non-zero digits in a number while keeping the overall value of the number similar.

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