1.2: Estimating Answers in Addition

You have learned how to round numbers. Now, you can use that skill to quickly find an approximate sum. Often, an estimate is all you need.

If you are going away for the weekend, you have to think about how much money you will need. The hotel is about $60, meals are about $80, gas is about $40, and entertainment is about $100.

You will take $60 + $80 + $40 + $100 = $280

When solving word problems or working with a calculator, you should estimate your answer first to determine if your answer is sensible.

In these examples, estimate the answer. Round each number BEFORE you add.

Example A

[latex]\large\begin{array}[t]{rrrrr}& 53 &\text{rounds to}&&50\\ &69&\text{rounds to}&&70\\ &22&\text{rounds to}&&20\\ +&88&\text{rounds to}&+&90\\ \hline &&&& 230\end{array}[/latex]

Example B

[latex]\large\begin{array}[t]{rrrrr} &349 &\text{rounds to}&&300\\ +&682&\text{rounds to}&+&700\\ \hline &&&& 1\,000\end{array}[/latex]

Example C

[latex]\large\begin{array}[t]{rrrrr} &43\,928 &\text{rounds to}&&40\,000\\ &29\,785&\text{rounds to}&&30\,000\\ &88\,319&\text{rounds to}&&90\,000\\ +&243\, 928&\text{rounds to}&+&240\,000\\ \hline &&&& 400\,000\end{array}[/latex]

If you are estimating an answer, you usually estimate to the largest place value that you can. Your estimate will give you what is sometimes called a ballpark figure. You will have an approximate answer.

Exercise 1

Estimate the sums.

Example:     [latex]\begin{array}[t]{rrrrr} &973 &\approx &&1\,000\\ &496&\approx &&500\\ +&382&\approx &+&400\\ \hline &&&& 1\,900\end{array}[/latex]

 

  1. [latex]\begin{array}[t]{rr}& 519\\&439\\+&382\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}& 1\, 234 \\& 4\, 567\\+& 7\, 890\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}& 3\, 519 \\& 4\, 003\\+& 3\, 832\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}& 2\, 727 \\& 2\, 329\\+& 9\, 818\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}& 4\, 113 \\ &1\, 590\\+& 2\, 671\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}& 38\, 985 \\& 43\, 691\\+& 8\, 336\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}& 42\, 163 \\ &30\, 820\\ &21\, 911\\+& 60\, 422\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}& 21\, 472 \\ &46\, 371\\& 98\, 393 \\+& 82\, 218\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}& 30\, 706 \\ &29\, 115\\& 40\, 082\\+& 31\, 621\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}& 431\, 391 \\ &554\, 423\\ &913\, 174 \\+& 282 \,826\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}& 171\, 234 \\ &102\, 085\\ &460\, 892 \\+& 542\, 329\\ \hline \\ \end{array}[/latex]

Exercise 1 Answers

  1. [latex]500 + 400 + 400 = 1\,300[/latex]
  2. [latex]1\,000 + 5\,000 + 8\,000 = 14\,000[/latex]
  3. [latex]4\,000 + 4\,000 + 4\,000 =  12\,000[/latex]
  4. [latex]3\,000 + 2\,000 + 10\,000 = 15\,000[/latex]
  5. [latex]4\,000 + 2\,000 + 3\,000 = 9\,000[/latex]
  6. [latex]39\,000 + 44\,000 + 8\,000 = 91\,000[/latex]
  7. [latex]40\,000 +  30\,000 +  20\,000 +  60\,000 = 150\,000[/latex]
  8. [latex]20\,000 +  50\,000 +  100\,000  + 80\,000  =  250\,000[/latex]
  9. [latex]30\,000 + 30\,000 + 40\,000 + 30\,000 = 130\,000[/latex]
  10. [latex]400\,000 + 600\,000 + 900\,000 + 300\,000 = 2\,200\,000[/latex]
  11. [latex]200\,000 + 100\,000 + 500\,000 = 1\,300\,000[/latex]

Estimating Answers in Addition Word Problems

When solving word problems, an estimate tells you if your answer is sensible. You can use your estimate to help you check your answers. If your answer and the estimate are not close, then you know that you should add your numbers again.

Exercise 2

Estimate the following answers. Be sure to round to the largest place value possible before adding. Remember to circle the information and underline what is being asked.

Example: During one month, Chaska spends 11432 minutes sleeping and 5812 minutes eating. Estimate how much time he spends sleeping and eating.

During one month, Chaska spends 11432 minutes sleeping and 5812 minutes eating. Estimate how much time he spends sleeping and eating.

[latex]1\,432 + 5\,812[/latex]

Estimate:

[latex]11\,000 + 6\,000 = 17\,000[/latex]

Chaska spent about 17000 minutes sleeping and eating.

  1. During October, Amul drove 674 kilometres, 493 kilometres, 384 kilometres and 914 kilometres. Estimate the total kilometres Amul drove.
  2. The number of passengers using the ABE Taxi Company for the past three weeks was 3205 passengers, 3542 passengers and 2821 passengers. Estimate the number of passengers that used the ABE Taxi Company.
  3. In 2008, the top three winning teams in the NHL were the Montreal Canadiens, winning 2980 games, the Boston Bruins, winning 2669 games, and the Toronto Maple Leafs, winning 2535 games. Estimate the total number of games won by these three teams.
  4. The three deepest lakes in the world are Baikal Lake at 1741 metres, Tanganyika Lake at 1471 metres and the Caspian Sea at 1025 metres. Estimate the total depth of the three lakes.

Exercise 2 Answers

  1. [latex]700 +  500  +  400  +  900  =  2\,500[/latex] kilometres
  2. [latex]3\,000  +  4\,000  + 3\,000 =  10\,000[/latex] passengers
  3. [latex]3\,000  +  3\,000 +  3\,000  =  9\,000[/latex] games
  4. [latex]2\,000 +  1\,000  +  1\,000 =  4\,000[/latex] metres

1.2: Practice Questions

  1. Estimate the sums. Show your work.
    1. [latex]\begin{array}[t]{rr}&7\, 964 \\ &971 \\ &6 \,888 \\+& 2\, 021 \\ \hline \\ \end{array}[/latex]
    2. [latex]\begin{array}[t]{rr}&5 \,365 \\ &5 \,100 \\ &9\, 982\\+& 7\, 752 \\ \hline \\ \end{array}[/latex]
    3. [latex]\begin{array}[t]{rr}&5 \,211 \\ &1 \,982 \\ &3\, 371 \\+& 2 \,801 \\ \hline \\ \end{array}[/latex]
    4. [latex]\begin{array}[t]{rr}&3 \,395 \\ &2 \,709 \\ &18\, 060\\+& 932 \,335 \\ \hline \\ \end{array}[/latex]
    5. [latex]\begin{array}[t]{rr}&2 \,364 \\ &62 \,182 \\ &549\, 272 \\+& 6 \,395 \\ \hline \\ \end{array}[/latex]
    6. [latex]\begin{array}[t]{rr}&75\, 536 \\&31 \,807 \\&337 \,427 \\+& 7 \,912 \\ \hline \\ \end{array}[/latex]
    7. [latex]\begin{array}[t]{rr}&898\, 402 \\&465 \,766 \\&558\, 485\\+& 324 \,715 \\ \hline \\ \end{array}[/latex]
    8. [latex]\begin{array}[t]{rr}&6 \,182 \,390\\&2 \,763 \,393 \\&1 \,326 \,879 \\+& 2\, 743 \,912 \\ \hline \\ \end{array}[/latex]
    9. [latex]\begin{array}[t]{rr}&1 \,226 \,590 \\&687 \,029 \\&533 \,905 \\+& 1\, 359 \,254 \\ \hline \\ \end{array}[/latex]

     

  2. Estimate for each of the following word problems. Be sure to include the unit of measure in your answer.
    Be sure to circle information and underline what is being asked.

    1. Yuan counted 854 old books and 519 new books. Estimate how many books there were altogether.
    2. A magazine has 34783 subscribers. Last year, the magazine had 26876 subscribers. Estimate how many subscribers the magazine had in total.
    3. The area of Canada is 9984670 square kilometres. The area of the United States is 9629091 square kilometres. The area of Mexico is 1964375 square kilometres. Estimate the total area of the three countries.

1.2: Practice Answers

  1. Estimate the sums.
    1. 18000
    2. 28000
    3. 13000
    4. 955000
    5. 619000
    6. 553000
    7. 2300000
    8. 13000000
    9. 3800000

     

  2. Estimate for each of the following word problems.
    1. 1400 books
    2. 60000 subscribers
    3. 22000000 square kilometres

Attribution

This chapter has been adapted from Topic C: Estimating Answers in Addition in Adult Literacy Fundamental Mathematics: Book 2 – 2nd Edition (BCcampus) by Wendy Tagami and Liz Girard (2022), which is under a CC BY 4.0 license.

License

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Intermediate PreAlgebra: Building Success Copyright © 2024 by Kim Tamblyn, TRU Open Press is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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