Do you remember Jose, who had a job at the ice cream stand in the Round Very Large Numbers to Decimal Representations Concept? Have you ever practiced recycling? Well, Jose has an idea to incorporate recycling into his job at the ice cream stand.
Jose has had many new ideas for improving life at the “Add It Up Ice Cream Stand.” His newest idea focuses on recycling. In addition to ice cream, the stand also sells sodas that are packaged in aluminum cans. Because you can turn in cans for recycling and receive some money back, Jose thinks that this could be a way for the ice cream stand to generate a little more income. He explained his idea to Mr. Harris who loved the concept. Jose put out recycling bins the first week of June. On the last day of each month, Jose took the recycled cans to the recycling center and collected money on his returns. He decided to keep track of the additional income in a small notebook. Here is what Jose collected in June, July and August.
Julie asks Jose about how much he has made in recycling. She also wants to know about how much more he made in August versus June. Jose looks at his notebook and just by looking at the numbers can’t remember how to estimate. The decimals are throwing him off.
You can help Jose, by the end of the Concept you will know how to estimate sums and differences of decimals.
Do you remember what it means to estimate ?
To estimate means to find an answer that is close to but not exact. It is a reasonable answer to a problem.
What does the word sum and the word difference mean?
If you think back, you will remember that you have already been introduced to the word sum and the word difference. A sum is the answer from an addition problem. The word difference is the answer of a subtraction problem.
How can we estimate a sum or a difference when our problem has decimals?
The easiest way to estimate a sum or a difference of decimals is to round the decimal. If we round the decimal to the nearest whole number, we can complete the problem using mental math or at least simplify the problem so that finding an answer is easier.
Estimate 15.7 + 4.9 = _____
In this problem, we only want to estimate our sum. Therefore, we can use our rules for rounding decimals to help us round each decimal to the nearest whole number.
15.7, the place being rounded is the 5, we look at the 7 and round up.
15.7 becomes 16
4.9, the place being rounded is the 4, we look at the 9 and round up.
4.9 becomes 5
Next, we rewrite the problem.
16 + 5 = 21
Our answer is 15.7 + 4.9 = 21.
We can also use rounding when estimating sums of larger numbers.
Estimate 350.12 + 120.78 = _____
We round each to the nearest whole number to find a reasonable estimate.
350.12 becomes 350.
120.78 becomes 121.
350 + 121 = 471
Our answer is 350.12 + 120.78 = 471.
What about differences in estimations with subtraction?
We can work on these problems in the same way, by rounding.
Estimate 45.78 - 22.10 = _____
45.78 rounds to 46.
22.10 rounds to 22.
46 - 22 = 24
Our answer is 45.78 - 22.10 = 24.
Now it is time for you to try a few on your own. Estimate each sum or difference using rounding.
2.67 + 3.88 + 4.10 = _____
56.7 - 22.3 = _____
$486.89 - $25.22 = _____
Now let's help Jose with his recycling dilemma. He will need to use rounding to gather the information for Julie.
The first thing that we need to do is to estimate the sum of the amounts of money that Jose collected in June, July and August.
Let’s start by rounding.
$25.77 becomes $26.00
$33.45 becomes $33.00
$47.62 becomes $48.00
Our estimated sum is $107.00.
Next, Jose works to figure out the difference between the amount of money collected in June versus August. Since both sums were similar, he decides to use rounding to estimate this difference.
June = $25.77 which rounds to $26
August = $47.62 which rounds to $48
48 - 26 = $22.00
“Congratulations Jose! Your recycling campaign is definitely working! Keep up the good work,” Julie says to Jose after seeing his results. Jose feels proud because of his accomplishment. The recycling campaign will remain at the ice cream stand.
- to find an answer that is reasonable and close to an exact answer.
- the result of an addition problem
- the result of a subtraction problem
Here is one for you to try on your own.
Estimate $588.80 - $310.11 = _____
$588.80 becomes 589 we can leave off the zeros to make it simpler to estimate
$310.11 becomes 310
589 - 310 = 279
Our answer is $588.80 - $310.11 = $279.00.
This example shows how you can use decimal estimation to approximate your answer and then compute your answer to an exact amount.
Directions: Estimate each sum or difference by rounding.
1. 56.32 + 23.12 = _____
2. 18.76 + 11.23 = _____
3. 14.56 + 76.98 = _____
4. 11.12 + 54.62 = _____
5. 33.24 + 45.32 = _____
6. 18.97 + 15.01 = _____
7. 22.43 + 11.09 = _____
8. 4.52 + 3.21 = _____
9. 19.19 + 27.75 = _____
10. 87.12 + 88.90 = _____
11. 67.19 - 33.12 = _____
12. 88.92 - 33.10 = _____
13. 76.56 - 3.45 = _____
14. 65.72 - 11.12 = _____
15. 77.34 - 43.02 = _____
16. 88.02 - 11.10 = _____
17. 89.32 - 18.03 = _____
18. 24.67 - 10.10 = _____
19. 37.82 - 14.20 = _____
20. 55.88 - 44.22 = _____
21. 334.56 - 125.86 = _____
22. 456.11 + 112.18 = _____