3.16: Front-End Estimation
In the last Concept, Jose realized that he could figure out his recycling data by using rounding. But there are other ways to estimate sums and differences. Have you ever heard of front - end estimation? In this Concept, you will learn how to use front - end estimation to help Jose.
Let's look at the dilemma again.
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.
June $25.77
July $33.45
August $47.62
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.
In this Concept, you will learn how to use front - end estimation to help Jose.
Guidance
Front–end estimation is a useful method of estimating when you are adding or subtracting numbers that are greater than 1000.
Here are the steps for front – end estimation.
- Keep the digits of the two highest place values in the number.
- Insert zeros for the other place values.
Estimate 4597 + 3865 = _____
We follow the rules for front – end estimation since each number is over 1000.
4597 becomes 4500. 4 and 5 are the digits of the two highest place values and we filled in zeros for the rest of the places.
3865 becomes 3800. 3 and 8 are the digits of two highest place values and we filled in zeros for the rest of the places.
Now we can rewrite the problem.
4500 + 3800 = 8300
Our answer for 4597 + 3865 is 8300.
What about a problem where we have one number over 1000 and one number not over 1000?
Estimate 4496 - 745 = _____
4496 becomes 4400 using front–end estimation.
745 becomes 700 by rounding to the nearest hundred.
4400 - 700 = 3700
Our answer for 4496 - 745 is 3700.'
What about front–end estimation and decimals? When using front–end estimation and decimals, we figure out how to keep the wholes separate from the parts and then combine them together. Here are the steps to front–end estimation with decimals.
- Add the front digits of the numbers being added or subtracted.
- Round off the decimals of the numbers being added or subtracted.
- Combine or subtract the results.
2.10 + 3.79 = _____
We start with the front digits of the numbers being added. That means we add 2 + 3 = 5. Next, we round the decimal part of each number. .10 stays .10 and .79 becomes .80
.80 + .10 = .90
Now we add, since that is the operation, the two estimates together.
5 + .90 = 5.90
Our answer for 2.10 + 3.79 is 5.90.
Now it is your turn to practice, notice that these examples are whole numbers and not decimals.
Example A
5674 + 1256 = _____
Solution: 5600 + 1200 = 6800
Example B
4632 - 576 = _____
Solution: 4600 - 570 = 4030
Example C
8932 + 1445 = _____
Solution: 8900 + 1400 = 10,300
Now back to Jose and his estimation dilemma.
After rounding, Jose decides to try front – end estimation to see if he can get an even more accurate estimate of the sum.
First, add the front ends, 25 + 33 + 47 = 105.
Next round the decimal parts and add them, .77 = .80, .45 = .50, .62 = .60.
\begin{align*}.80 + .50 + .60 & = 1.90 \\ 105 + 1.90 & = \$106.90\end{align*}
June = $25.77 which rounds to $26
August = $47.62 which rounds to $48
48 - 26 = $22.00
You can see that both estimation methods work!
Vocabulary
Here are the vocabulary words that are found in this Concept.
- Estimate
- to find an answer that is reasonable and close to an exact answer.
- Sum
- the result of an addition problem
- Difference
- the result of a subtraction problem
- Front end estimation
- estimating by adding the front ends of each number in the problem, then rounding and adding the decimal parts of each number.
- Works well with smaller numbers
- Rounding
- converting a number to its nearest whole number.
- Works well with larger numbers
Guided Practice
Here is one for you to try on your own.
16.79 - 14.12 = _____
Answer
We start by subtracting the front ends. 16 - 14 = 2 Next, we round the decimal parts. .79 becomes .80 and .12 becomes .10. Subtract those decimals .80 - .10 = .70. Combine for the answer = 2.70.
Our answer for 16.79 - 14.12 is 2.70.
Video Review
Here are videos for review.
This example shows how you can use decimal estimation to approximate your answer and then compute your answer to an exact amount.
Khan Academy Decimal Estimation
Practice
Directions: Estimate using front–end estimation.
1. 34.66 + 11.12 = _____
2. 43.18 + 16.75 = _____
3. 2.34 + 1.56 = _____
4. 7.89 + 5.79 = _____
5. 8.90 + 3.21 = _____
6. 7.18 - 3.13 = _____
7. 12.65 - 7.23 = _____
8. 15.70 - 11.10 = _____
9. 25.67 - 18.40 = _____
10. 78.46 - 55.21 = _____
11. 88.12 - 34.06 = _____
12. 87.43 - 80.11 = _____
13. 94.12 - 7.08 = _____
14. 98.10 - 6.01 = _____
15. 145.90 + 18.12 = _____
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Difference
The result of a subtraction operation is called a difference.Estimate
To estimate is to find an approximate answer that is reasonable or makes sense given the problem.Rounding
Rounding is reducing the number of non-zero digits in a number while keeping the overall value of the number similar.Sum
The sum is the result after two or more amounts have been added together.Image Attributions
Here you'll learn to estimate sums and differences of decimals using front - end estimation.