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Estimate the sum or difference











































what is the difference between the sum of the two addends in problem 6 and the estimate of that sum? problem six (267+162

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Sep 10, 2010
Estimating the Sum
by: Staff


The question:

What is the difference between the sum of the two addends in problem 6 and the estimate of that sum? problem six (267+162)?

The answer:

The sum of the two addends gives an exact answer: 267 + 162 = 429

An estimate of the sum gives a fast, approximate answer.

Often it is important to estimate the sum as a double check to the magnitude of exact answer. For example, is the answer 4.29, 42.9, or four hundred and twenty-nine. Estimating the sum for your example will alert you to the fact that the final answer will be in the hundreds.

(Students should always use an estimate to check themselves. Many times a student will add numbers on a calculator, but accidentlly include an extra zero, or put the decimal point in the wrong place. The answer given by the calculator may be 2832, which is not close to the real answer. Even though the result is incorrect, the student usually says something like this: “I’m right, I did it on the calculator”. If you want to know a little more about calculators, see: http://www.solving-math-problems.com/dumb-calculator.html)

In addition, an estimate is often good enough to answer a question without spending unnecessary time computing an exact answer. For example, suppose the cost of an ice cream cone is about $2 (an estimate), and you have $3. You know right away that you can afford to buy the ice cream, without knowing that the ice cream costs exactly $1.85 + tax.

To estimate the sum in your example: (1) round both numbers, and (2) add the rounded numbers.

If both numbers are rounded to the nearest hundred:

267 = 300 (rounded to the nearest hundred)

162 = 200 (rounded to the nearest hundred)

The estimate is: 300 + 200 = 500

Of course the 500 is not completely accurate. It contains a rounding error. The question is: does the rounding error matter which respect to the problem you are trying to solve?



Thanks for writing.


Staff
www.solving-math-problems.com


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