Estimating Sum and Differences

7/28/2019 Estimating Sum and Differences

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Lesson 18

ESTIMATING SUM AND DIFFERENCE OF

WHOLE NUMBERS AND DECIMALS

Lesson Objectives:

After understanding the lesson, you must be

able to:1. Define estimation.

2. Know the two methods in making estimates.

3. Learn how to estimate sum and difference and

how it is done.


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Estimation is a way of answering a problem

which does not require an exact answer. An estimate is

all that is needed when an exact value is not possible.

Estimation is easy to use and or to compute. Rounding isone way of making estimation. Each decimal number is

rounding to some place value, usually to the greatest

value and the necessary operation is performance on the

rounded decimal numbers.


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Two methods are used in making

estimation, the rounding off the desired

digit one and finding the sum of the firstdigit only. We have learned how to

round decimal numbers in this section,

first only the front digits are used. If an

improved or refined estimate is desired,the next digits are used.


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When large decimal numbers are involved, it is wise to

estimate before computing the exact and user is expectedto be about or close to the estimate.

Method 1: Sum of the First Digit only

Estimate in Addition

3.455 + 2.672 + 5.135


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Rounded off to thenearest ones

3.455 3.000

2.672 3.000

+ 5.134 + 5.00011.000

Rounded off to the nearesttenths

3.455 0.500

2.672 0.700

+ 5.134 + 0.100

1.300

to be added the first estimate

if desired or required.


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Thus the sum 3.455 + 2.672 +

5.134 can be roughly

estimated by 11.000. If a

better estimate is required or

desired, then add 1.300 to get11.300.


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Estimate 5.4721472.976543

Rounded to the nearest ones

Actual Subtraction

5.472147 5.000000 5.472147

- 2.976543 - 3.000000 - 2.976543

2.000000 2.495604


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Method 2: Rounding Method

a. Estimate the sum by rounding method in place of

whole numbers.

Example:6.567 7.000

5.482 5.000+ 4.619 +5.000

17.000


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b. Estimate the difference by rounding method.

Example: 14.525 15.000

- 11.018 - 11.000

4.000

By the rounding method, the first example is

estimated by 17.000 and the second one by 4.000. The

actual value of the sum of example no.1 is 16.668 and

the difference of example no. 2 is 3.507 respectively.

Both methods give a reasonable estimate.


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Remember:

In estimating the sums, first round each addend

to its greatest place value position. Then add. If the

estimate is close to the exact sum, it is a good estimate.

Estimating helps you expect the exact answer to beabout a little less or a little more than the estimate.

However, in estimating difference, first round the

decimal number to the nearest place value asked for.

Then subtract the rounded decimal numbers. Check theresult by actual subtraction.


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I. Estimates the sum and difference to the

greatest place value. Check how close the

estimated sum (E.S.) / estimated difference(E.D.) by getting the actual sum (A.S.) and

actual difference (A.D.).

A. Actual Sum/ Estimated Sum1. 3.417 3.000 2. 36.243 36.000

2.719 3.000 29.641 30.000

+ 1.829 + 2.00 + 110.278 + 110.000

A.S. E.S. A.S. E.S.


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3. 648.937 649.000 4. 871.055 871.000

214.562 215.000 276.386 276.000

+ 450.211 + 450.000 + 107.891 + 108.000

A.S. E.S. A.S. E.S.

5. 374.738 375.000 6. 342.165 342.000

469.345 469.000 178.627 179.000

+ 213.543 + 213.500 + 748.715 + 749.000

A.S. E.S. A.S. E.S.


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B. Actual Difference/ Estimated Difference

7. 14.255 14.000 8. 28.267 28.000

- 11.812 - 12.000 - 16.380 - 16.000

A.D. E.D A.D. E.D.

9. 345.678 346.000 10. 92.365 92.000

- 212.792 - 213.000 - 75.647 - 76.000

A.D. E.D. A.D. E.D.

11. 62.495 62.000 12. 9.2875 9.0000- 17.928 - 18.000 - 6.8340 - 7.0000

A.D. E.D. A.D. E.D.


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Match a given decimals with the correct estimated sum /

difference to the greatest placevalue.

The shortest verse in the Bibleconsists of two words.


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To find out, connect each decimals with he correct estimated

sum / difference to the greatest place value. Write the letter

that corresponds to the correct answer below it.

1. 36.5+18.91+55.41 U. 939.00

2. 639.27-422.30 S. 216.00

3. 48.21+168.2 P. 2.00004. 285.15+27.35+627.30 E. 146.000

5. 8.941-8.149 W. 28.10

6. 18.95+9.25 J. 111.00

7. 129.235+16.41 T. 537.008. 9.2875-6.834 S. 1.000

9. 989.15-451.85 E. 217.00


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_____ ______ ______ ______ ______

1 2 3 4 5

_____ ______ ______ ______6 7 8 9

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Estimating Sum and Differences