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Front-End Estimation

Estimate using the greatest place value

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Front-End Estimation

License: CC BY-NC 3.0

Brandon saves pennies for over a year. His sister does the same. At the end of the year, he has saved 1357 pennies, and his sister has saved 2122 pennies. Their mother tells them that they can estimate their combined number of pennies using front-end estimation. About how many pennies do Brandon and his sister have?

In this concept, you will learn how to use front-end estimation.

Sums and Differences Using Front-End Estimation

Front–end estimation is a method of estimating used when adding or subtracting numbers that are greater than 1000.

Here are the steps for front–end estimation.

  1. Keep the digits of the two highest place values in the number.
  2. Insert zeros for the other place values.

Let's look at an example.

Estimate 4597 + 3865 = _____

Follow the rules for front–end estimation since each number is over 1000.

4597 becomes 4500. The 4 and 5 are the digits of the two highest place values and you filled in zeros for the rest of the places.

3865 becomes 3800. The 3 and 8 are the digits of two highest place values and you filled in zeros for the rest of the places.

Now rewrite the problem.

4500 + 3800 = 8300

The answer is that 4597 + 3865 is approximately 8300.

Let's look at another example.

Estimate 4496 - 745 = _____

Notice that one of the numbers is over 1000 and the other is not over 1000. Use front-end estimation for the number that is over 1000 and round to the nearest hundred for the number that is under 1000.

4496 becomes 4400 using front–end estimation.

745 becomes 700 by rounding to the nearest hundred.

4400 - 700 = 3700

The answer is that 4496 - 745 is approximately 3700.

When using front–end estimation and decimals, 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.

  1. Add the front digits of the numbers being added or subtracted.
  2. Round off the decimals of the numbers being added or subtracted.
  3. Combine or subtract the results.

2.10 + 3.79 = _____

Start with the front digits of the numbers being added. That means add 2 + 3 = 5. Next, round the decimal part of each number. 0.10 stays 0.10 and 0.79 becomes 0.80.

0.10 + 0.80 = 0.90

Now add the two estimates together.

5 + 0.90 = 5.90

The answer is that 2.10 + 3.79 is approximately 5.90.

Examples

Example 1

Earlier, you were given a problem about Brandon and his sister.

Brandon has 1357 pennies and his sister has 2122. Estimate their combined number of pennies using front-end estimation.

First, check to make sure that both numbers are greater than 1000.

Yes

Next, keep the digits of the two highest place values in the number.

1357 becomes 1300

2122 becomes 2100

Then, calculate the sum.

1300 + 2100 = 3400

The answer is that 1357 + 2122 is approximately 3400.

Example 2

Estimate 16.79 + 14.12 = _____ using front-end estimation.

First, add the front digits of the numbers.

16 + 14 = 30

Next, round the decimals and add them.

0.8 + 0.1 = 0.9

Then combine the results.

30 + 0.9 = 30.9

The answer is that 16.79 + 14.12 is approximately 30.9.

Example 3

Estimate 5674 + 1256 = _____ using front-end estimation.

First, check to make sure that both numbers are greater than 1000.

Yes

Next, keep the digits of the two highest place values in the number.

5674 becomes 5600

1256 becomes 1200

Then, calculate the sum.

5600 + 1200 = 6800

The answer is that 5674 + 1256 is approximately 6800.

Example 4

Estimate 4632 - 576 = _____ using front-end estimation.

First, check to make sure that both numbers are greater than 1000.

No, one number is greater than 1000 and the other is less than 1000.

Next, keep the digits of the two highest place values in the number that is over 1000 and round the number that is less than 1000 to the nearest hundred.

4632 becomes 4600

576 becomes 600

Then, calculate the difference.

4600 - 600 = 4000

The answer is that 4632 - 576 is approximately 4000.

Example 5

Estimate 8.93 + 1.44 = _____ using front-end estimation.

First, add the front digits of the numbers.

8 + 1 = 9

Next, round the decimals and add them.

0.9 + 0.4 = 1.3

Then combine the results.

9 + 1.3 = 10.3

The answer is that 8.93 + 1.44 is approximately 10.3.

Review

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 = _____

Review (Answers)

To see the Review answers, open this PDF file and look for section 3.16. 

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Vocabulary

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

  1. [1]^ License: CC BY-NC 3.0

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