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All courses Math Foundations · MF.NS.2 2 of 60
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.

Estimate a sum with rounding

Problem
Estimate the sum of \(48.6\) and \(31.2\) by rounding each number to the nearest whole number and then adding the rounded numbers.
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Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
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Hint

Look at the tenths digit of each addend. In 48.6 the tenths digit is 6, and in 31.2 it is 2.

To round to the nearest whole number, a tenths digit from 5 through 9 increases the whole number by 1. A tenths digit from 0 through 4 keeps the whole number unchanged. Round both addends before adding.

Solution walkthrough

01

Use the nearest-whole rule

\[\text{tenths}~\ge~5:~\text{increase}~\text{the}~\text{whole}~\text{number};~\text{tenths}~<~5:~\text{keep}~\text{it}\]

The prompt directs us to round each addend to the nearest whole number before adding. The tenths digit decides whether the whole-number part increases or stays the same.

02

Round both addends

\[48.6~\text{rounds}~\text{to}~49;~31.2~\text{rounds}~\text{to}~31\]

The first prompt addend, 48.6, has tenths digit 6, so 48 increases to 49. The second addend, 31.2, has tenths digit 2, so its whole-number part remains 31.

03

Add the rounded numbers

\[49~+~31~=~80\]

Substitute the rounded values from step 2 for the original addends. Adding 49 and 31 gives an estimated sum of 80.

04

Check reasonableness

\[48.6~+~31.2~=~79.8;~80~-~79.8~=~0.2\]

The exact sum is 79.8, only 0.2 below the estimate. That small difference confirms that 80 is a reasonable result of the required rounding method.

05

State the estimated sum

\[80\]

After rounding both given addends and adding, the estimated sum is 80. This matches choice A.

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Another way

  1. Group the original values as (48.6 + 0.4) + (31.2 - 0.2) = 49 + 31 - 0.2 = 79.8; this shows why the nearest-whole estimate is 80.

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Common mistake

Do not give the exact sum 79.8. The prompt requires rounding both addends first, producing 49 + 31 = 80.

Solution walkthrough video