Unit 2: Addition
Topic C: 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 about $80, gas about $40, and entertainment about $100. You will take $60 + $80 + $40 + $100 = $280
When you are solving word problems or working with a calculator, you should estimate your answer first so you can tell 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, usually you 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 One
Estimate the sums. Check your work using the answer key at the end of the exercise.
- [latex]\begin{array}[t]{rrrrr} &973 &\approx &&1\,000\\ &496&\approx &&500\\ +&382&\approx &+&400\\ \hline &&&& 1\,900\end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 519\\&439\\+&382\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 1\, 234 \\& 4\, 567\\+& 7\, 890\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 3\, 519 \\& 4\, 003\\+& 3\, 832\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 2\, 727 \\& 2\, 329\\+& 9\, 818\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 4\, 113 \\ &1\, 590\\+& 2\, 671\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 38\, 985 \\& 43\, 691\\+& 8\, 336\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 42\, 163 \\ &30\, 820\\ &21\, 911\\+& 60\, 422\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 21\, 472 \\ &46\, 371\\& 98\, 393 \\+& 82\, 218\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 30\, 706 \\ &29\, 115\\& 40\, 082\\+& 31\, 621\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 431\, 391 \\ &554\, 423\\ &913\, 174 \\+& 282 \,826\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 171\, 234 \\ &102\, 085\\ &460\, 892 \\+& 542\, 329\\ \hline \\ \end{array}[/latex]
Answers to Exercise One
- 1000 + 500 + 400 = 1900
- 500 + 400 + 400 = 1300
- 1000 + 5000 + 8000 = 14000
- 4000 + 4000 + 4000 = 12000
- 3000 + 2000 + 10000 = 15000
- 4000 + 2000 + 3000 = 9000
- 40000 + 40000 + 8000 = 88000
- 40000 + 30000 + 20000 + 60000 = 150000
- 20000 + 50000 + 100000 + 80000 = 250000
- 30000 + 30000 + 40000 + 30000 = 130000
- 400000 + 600000 + 900000 + 300000 = 2200000
- 200000 + 100000 + 500000 + 500000 = 1300000
Estimating Answers in Addition Word Problems
When you are 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 Two
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. Check your work using the answer key at the end of the exercise.
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.
11432 + 5812
Estimate:
11000 + 6000 = 17000
Chaska spent about 17000 minutes sleeping and eating.
- During October, Amul drove 674 kilometres, 493 kilometres, 384 kilometres and 914 kilometres. Estimate the total kilometres Amul drove.
- The number of passengers using the ABE Taxi Company for the past three weeks were 3205 passengers, 3542 passengers and 2821 passengers. Estimate the number of passengers that used the ABE Taxi Company.
- In 2008, the top three winning teams in the NHL were the Montreal Canadiens winning 2980 games, the Boston Bruins winning 2 669 games and the Toronto Maple Leafs winning 2535 games. Estimate the total number of games won by these three teams.
- The three deepest lakes in the world are Baikal Lake which is 1741 metres, Tanganyika Lake which is 1471 metres and the Caspian Sea which 1025 metres. Estimate the total depth of the three lakes.
Answers to Exercise Two
- 700 + 500 + 400 + 900 = 2500 kilometres
- 3000 + 4000 + 3000 = 10000 passengers
- 3000 + 3000 + 3000 = 9000 games
- 2000 + 1000 + 1000 = 4000 metres
Topic C: Self-Test
Mark /15 Aim 11/15
- Estimate the sums. Show your work. (9 marks)
- [latex]\begin{array}[t]{rr}&7\, 964 \\ &971 \\ &6 \,888 \\+& 2\, 021 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&5 \,365 \\ &5 \,100 \\ &9\, 982\\+& 7\, 752 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&5 \,211 \\ &1 \,982 \\ &3\, 371 \\+& 2 \,801 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&3 \,395 \\ &2 \,709 \\ &18\, 060\\+& 932 \,335 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&2 \,364 \\ &62 \,182 \\ &549\, 272 \\+& 6 \,395 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&75\, 536 \\&31 \,807 \\&337 \,427 \\+& 7 \,912 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&898\, 402 \\&465 \,766 \\&558\, 485\\+& 324 \,715 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&6 \,182 \,390\\&2 \,763 \,393 \\&1 \,326 \,879 \\+& 2\, 743 \,912 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&1 \,226 \,590 \\&687 \,029 \\&533 \,905 \\+& 1\, 359 \,254 \\ \hline \\ \end{array}[/latex]
- Estimate each of the following word problems. (6 marks) Be sure to include the unit of measure in your answer. (2 marks each)
Be sure to circle information and underline what is being asked.- Yuan counted 854 old books and 519 new books. Estimate how many books there were altogether.
- A magazine has 34783 subscribers. Last year the magazine had 26876 subscribers. Estimate how many subscribers in total.
- 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.
Answers to Topic C Self-Test
-
- 18000
- 28000
- 13000
- 955000
- 619000
- 553000
- 2300000
- 13000000
- 3800000
-
- 1400 books
- 60000 subscribers
- 22000000 square kilometres