{"id":67,"date":"2022-08-16T19:46:43","date_gmt":"2022-08-16T23:46:43","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math022\/chapter\/estimating-answers-in-addition\/"},"modified":"2025-07-16T20:46:45","modified_gmt":"2025-07-17T00:46:45","slug":"estimating-answers-in-addition","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math022\/chapter\/estimating-answers-in-addition\/","title":{"raw":"Topic C: Estimating Answers in Addition","rendered":"Topic C: Estimating Answers in Addition"},"content":{"raw":"

Sometimes, an exact answer is not needed \u2014 especially when you just want a quick idea<\/strong> of what something will cost or total. This is called estimating<\/strong>. When you estimate, you round numbers and then add them. It helps you check if your final answer makes sense.<\/span><\/p>\r\n\r\n

Why Estimate?<\/span><\/h3>\r\n

Imagine you are going away for the weekend:<\/span><\/p>\r\n\r\n

    \r\n \t
  • \r\n

    Hotel: about $60<\/span><\/p>\r\n<\/li>\r\n \t

  • \r\n

    Meals: about $80<\/span><\/p>\r\n<\/li>\r\n \t

  • \r\n

    Gas: about $40<\/span><\/p>\r\n<\/li>\r\n \t

  • \r\n

    Entertainment: about $100<\/span><\/p>\r\n<\/li>\r\n<\/ul>\r\n

    Instead of calculating exactly, you might say:<\/span>
    60 + 80 + 40 + 100 = 280<\/strong><\/span>
    You estimated the total weekend cost: $280<\/strong>.<\/span><\/p>\r\n\r\n\r\n

    \r\n\r\n

    Steps to Estimate a Sum<\/span><\/h3>\r\n

    Step 1: Identify the Place to Round To<\/span><\/h3>\r\n

    Round each number to the highest place value they share<\/strong>.<\/span><\/p>\r\n\r\n

      \r\n \t
    • \r\n

      If both numbers are two-digit numbers, round to the tens.<\/span><\/p>\r\n<\/li>\r\n \t

    • \r\n

      Once again, always round to the highest place value that both numbers share<\/strong>. For example, if one number has thousands and the other has only hundreds, round both to the hundreds place. If one number has hundreds<\/strong> and the other has only tens<\/strong>, round both to the tens<\/strong> place.<\/span><\/p>\r\n<\/li>\r\n \t

    • \r\n

      If both have thousands, round to the thousands.<\/span><\/p>\r\n<\/li>\r\n<\/ul>\r\n

      This makes the numbers easier to add mentally.<\/span><\/p>\r\n\r\n

      Step 2: Round Each Number<\/span><\/h3>\r\n

      Use the digit to the right<\/strong> of the one you are rounding to.<\/span><\/p>\r\n\r\n

        \r\n \t
      • \r\n

        If it is 5 or more<\/strong>, round up<\/strong>.<\/span><\/p>\r\n<\/li>\r\n \t

      • \r\n

        If it is less than 5<\/strong>, round down<\/strong>.<\/span><\/p>\r\n<\/li>\r\n<\/ul>\r\n

        Step 3: Add the Rounded Numbers<\/span><\/h3>\r\n

        This gives your estimated sum<\/strong>.<\/span><\/p>\r\nIn these examples, estimate<\/strong> the answer. Round each number BEFORE<\/strong> you add.\r\n

        \r\n

        Example A<\/p>\r\n\r\n<\/header>\r\n

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

        Example B<\/p>\r\n\r\n<\/header>\r\n

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

        Example C<\/p>\r\n\r\n<\/header>\r\n

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

        Tip:<\/span><\/h3>\r\n

        Round both numbers to the same place<\/strong> \u2014 the highest one they both have.<\/span><\/p>\r\n\r\n

        \r\n

        Exercise One<\/p>\r\n\r\n<\/header>\r\n

        \r\n\r\nEstimate the sums. Check your work using the answer key at the end of the exercise.\r\n
          \r\n \t
        1. [latex]\\begin{array}[t]{rrrrr} &973 &\\approx &&1\\,000\\\\\r\n&496&\\approx &&500\\\\\r\n+&382&\\approx &+&400\\\\\r\n\\hline &&&& 1\\,900\\end{array}[\/latex]<\/li>\r\n \t
        2. [latex]\\begin{array}[t]{rr}& 519\\\\&439\\\\+&382\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
        3. [latex]\\begin{array}[t]{rr}& 1\\, 234 \\\\& 4\\, 567\\\\+& 7\\, 890\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
        4. [latex]\\begin{array}[t]{rr}& 3\\, 519 \\\\& 4\\, 003\\\\+& 3\\, 832\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
        5. [latex]\\begin{array}[t]{rr}& 2\\, 727 \\\\& 2\\, 329\\\\+& 9\\, 818\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
        6. [latex]\\begin{array}[t]{rr}& 4\\, 113 \\\\ &1\\, 590\\\\+& 2\\, 671\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
        7. [latex]\\begin{array}[t]{rr}& 38\\, 985 \\\\& 43\\, 691\\\\+& 8\\, 336\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
        8. [latex]\\begin{array}[t]{rr}& 42\\, 163 \\\\ &30\\, 820\\\\ &21\\, 911\\\\+& 60\\, 422\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
        9. [latex]\\begin{array}[t]{rr}& 21\\, 472 \\\\ &46\\, 371\\\\& 98\\, 393 \\\\+& 82\\, 218\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
        10. [latex]\\begin{array}[t]{rr}& 30\\, 706 \\\\ &29\\, 115\\\\& 40\\, 082\\\\+& 31\\, 621\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
        11. [latex]\\begin{array}[t]{rr}& 431\\, 391 \\\\ &554\\, 423\\\\ &913\\, 174 \\\\+& 282 \\,826\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
        12. [latex]\\begin{array}[t]{rr}& 171\\, 234 \\\\ &102\\, 085\\\\ &460\\, 892 \\\\+& 542\\, 329\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n<\/ol>\r\nAnswers to Exercise One<\/strong>\r\n
            \r\n \t
          1. 1000<\/span> + 500 + 400 = 1900<\/span><\/li>\r\n \t
          2. 500 + 400 + 400 = 1300<\/span><\/li>\r\n \t
          3. 1000<\/span>\u00a0 +\u00a0 5000<\/span>\u00a0 +\u00a0 8000<\/span>\u00a0 =\u00a0 14000<\/span><\/li>\r\n \t
          4. 4000<\/span>\u00a0 +\u00a0 4000<\/span>\u00a0 + 4000<\/span>\u00a0 =\u00a0 12000<\/span><\/li>\r\n \t
          5. 3000<\/span> + 2000<\/span> + 10000<\/span> = 15000<\/span><\/li>\r\n \t
          6. 4000<\/span> + 2000<\/span> + 3000<\/span> = 9000<\/span><\/li>\r\n \t
          7. 39000<\/span> + 44000<\/span> + 8000<\/span> = 91000<\/span><\/li>\r\n \t
          8. 40000<\/span>\u00a0 +\u00a0 30000<\/span>\u00a0 +\u00a0 20000<\/span>\u00a0 +\u00a0 60000<\/span>\u00a0 =\u00a0 150000<\/span><\/li>\r\n \t
          9. 20000<\/span>\u00a0 +\u00a0 50000<\/span>\u00a0 +\u00a0 100000<\/span>\u00a0 + 80000<\/span>\u00a0 =\u00a0 250000<\/span><\/li>\r\n \t
          10. 30000<\/span> + 30000<\/span> + 40000<\/span> + 30000<\/span> = 130000<\/span><\/li>\r\n \t
          11. 400000<\/span> + 600000<\/span> + 900000<\/span> + 300000<\/span> = 2200<\/span>000<\/span><\/li>\r\n \t
          12. 200000<\/span> + 100000<\/span> + 500000<\/span> + 500 000 = 1300<\/span>000<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

            Estimating Answers in Addition Word Problems<\/h1>\r\nWhen 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.\r\n
            \r\n

            Exercise Two<\/p>\r\n\r\n<\/header>\r\n

            \r\n\r\nEstimate the following answers. Be sure to round to the largest place value possible before adding. Remember to circle<\/span> the information and underline<\/span> what is being asked. Check your work using the answer key at the end of the exercise.\r\n\r\nExample:\r\n\r\nDuring one month, Chaska spends 11432<\/span> minutes sleeping and 5812<\/span> minutes eating. Estimate how much time he spends sleeping and eating.\r\n\r\nDuring one month, Chaska spends 11432<\/span> minutes<\/span> sleeping and 5812<\/span> minutes<\/span> eating. Estimate how much time<\/span> he spends sleeping and eating.\r\n\r\n11432<\/span> + 5812<\/span>\r\n\r\nEstimate:\r\n\r\n11000<\/span> + 6000<\/span> = 17000<\/span>\r\n\r\nChaska spent about 17000<\/span> minutes sleeping and eating.\r\n
              \r\n \t
            1. During October, Amul drove 674 kilometres, 493 kilometres, 384 kilometres and 914 kilometres. Estimate the total kilometres Amul drove.<\/li>\r\n \t
            2. The number of passengers using the ABE Taxi Company for the past three weeks were 3205<\/span> passengers, 3542<\/span> passengers and 2821<\/span> passengers. Estimate the number of passengers that used the ABE Taxi Company.<\/li>\r\n \t
            3. In 2008, the top three winning teams in the NHL were the Montreal Canadiens winning 2980<\/span> games, the Boston Bruins winning 2 669 games and the Toronto Maple Leafs winning 2535<\/span> games. Estimate the total number of games won by these three teams.<\/li>\r\n \t
            4. The three deepest lakes in the world are Baikal Lake which is 1741<\/span> metres, Tanganyika Lake which is 1471<\/span> metres and the Caspian Sea which 1025<\/span> metres. Estimate the total depth of the three lakes.<\/li>\r\n<\/ol>\r\nAnswers to Exercise Two<\/strong>\r\n
                \r\n \t
              1. 700 +\u00a0 500\u00a0 +\u00a0 400\u00a0 +\u00a0 900\u00a0 =\u00a0 2500<\/span> kilometres<\/li>\r\n \t
              2. 3000<\/span>\u00a0 +\u00a0 4000<\/span>\u00a0 + 3000<\/span>\u00a0 =\u00a0 10000<\/span> passengers<\/li>\r\n \t
              3. 3000<\/span>\u00a0 +\u00a0 3000<\/span>\u00a0 +\u00a0 3000<\/span>\u00a0 =\u00a0 9000<\/span> games<\/li>\r\n \t
              4. 2000<\/span>\u00a0 +\u00a0 1000<\/span>\u00a0 +\u00a0 1000<\/span> =\u00a0 4000<\/span> metres<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                Key Ideas to Remember<\/h2>\r\n
                  \r\n \t
                • \r\n

                  Round to the same place value<\/strong> in both numbers.<\/p>\r\n<\/li>\r\n \t

                • \r\n

                  Round up<\/strong> if the next digit is 5 or more.<\/p>\r\n<\/li>\r\n \t

                • \r\n

                  Round down<\/strong> (i.e., the digit stays the same) if it is less than 5.<\/p>\r\n<\/li>\r\n \t

                • \r\n

                  Add the rounded numbers for your estimate.<\/p>\r\n<\/li>\r\n \t

                • \r\n

                  Estimating is not exact<\/strong> \u2014 it gives you a ballpark answer<\/strong>.<\/p>\r\n<\/li>\r\n<\/ul>\r\n

                  Topic C: Self-Test<\/h1>\r\nMark\u00a0 \u00a0 \u00a0\/15\u00a0\u00a0\u00a0 Aim 11\/15<\/strong>\r\n
                    \r\n \t
                  1. Estimate the sums. Show your work. (9 marks)\r\n
                      \r\n \t
                    1. [latex]\\begin{array}[t]{rr}&7\\, 964 \\\\ &971 \\\\ &6 \\,888 \\\\+& 2\\, 021 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
                    2. [latex]\\begin{array}[t]{rr}&5 \\,365 \\\\ &5 \\,100 \\\\ &9\\, 982\\\\+& 7\\, 752 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
                    3. [latex]\\begin{array}[t]{rr}&5 \\,211 \\\\ &1 \\,982 \\\\ &3\\, 371 \\\\+& 2 \\,801 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
                    4. [latex]\\begin{array}[t]{rr}&3 \\,395 \\\\ &2 \\,709 \\\\ &18\\, 060\\\\+& 932 \\,335 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
                    5. [latex]\\begin{array}[t]{rr}&2 \\,364 \\\\ &62 \\,182 \\\\ &549\\, 272 \\\\+& 6 \\,395 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
                    6. [latex]\\begin{array}[t]{rr}&75\\, 536 \\\\&31 \\,807 \\\\&337 \\,427 \\\\+& 7 \\,912 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
                    7. [latex]\\begin{array}[t]{rr}&898\\, 402 \\\\&465 \\,766 \\\\&558\\, 485\\\\+& 324 \\,715 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
                    8. [latex]\\begin{array}[t]{rr}&6 \\,182 \\,390\\\\&2 \\,763 \\,393 \\\\&1 \\,326 \\,879 \\\\+& 2\\, 743 \\,912 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t
                    9. [latex]\\begin{array}[t]{rr}&1 \\,226 \\,590 \\\\&687 \\,029 \\\\&533 \\,905 \\\\+& 1\\, 359 \\,254 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
                    10. Estimate each of the following word problems. (6 marks) Be sure to include the unit of measure in your answer. (2 marks each)\r\nBe sure to circle<\/span> information and underline<\/span> what is being asked.\r\n
                        \r\n \t
                      1. Yuan counted 854 old books and 519 new books. Estimate how many books there were altogether.<\/li>\r\n \t
                      2. A magazine has 34783<\/span> subscribers. Last year the magazine had 26876<\/span> subscribers. Estimate how many subscribers in total.<\/li>\r\n \t
                      3. The area of Canada is 9984<\/span>670<\/span> square kilometres. The area of the United States is 9629<\/span>091<\/span> square kilometres. The area of Mexico is 1964<\/span>375<\/span> square kilometres. Estimate the total area of the three countries.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n

                        Answers to Topic C Self-Test<\/h2>\r\n
                          \r\n \t
                        1. \r\n
                            \r\n \t
                          1. 18000<\/span><\/li>\r\n \t
                          2. 28000<\/span><\/li>\r\n \t
                          3. 13000<\/span><\/li>\r\n \t
                          4. 956000<\/span><\/li>\r\n \t
                          5. 619000<\/span><\/li>\r\n \t
                          6. 453000<\/span><\/li>\r\n \t
                          7. 2300<\/span>000<\/span><\/li>\r\n \t
                          8. 13000<\/span>000<\/span><\/li>\r\n \t
                          9. 3800<\/span>000<\/span><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
                          10. \r\n
                              \r\n \t
                            1. 1400<\/span> books<\/li>\r\n \t
                            2. 60000<\/span> subscribers<\/li>\r\n \t
                            3. 22000<\/span>000<\/span> square kilometres<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"

                              Sometimes, an exact answer is not needed \u2014 especially when you just want a quick idea<\/strong> of what something will cost or total. This is called estimating<\/strong>. When you estimate, you round numbers and then add them. It helps you check if your final answer makes sense.<\/span><\/p>\n

                              Why Estimate?<\/span><\/h3>\n

                              Imagine you are going away for the weekend:<\/span><\/p>\n

                                \n
                              • \n

                                Hotel: about $60<\/span><\/p>\n<\/li>\n

                              • \n

                                Meals: about $80<\/span><\/p>\n<\/li>\n

                              • \n

                                Gas: about $40<\/span><\/p>\n<\/li>\n

                              • \n

                                Entertainment: about $100<\/span><\/p>\n<\/li>\n<\/ul>\n

                                Instead of calculating exactly, you might say:<\/span>
                                60 + 80 + 40 + 100 = 280<\/strong><\/span>
                                You estimated the total weekend cost: $280<\/strong>.<\/span><\/p>\n

                                \n

                                Steps to Estimate a Sum<\/span><\/h3>\n

                                Step 1: Identify the Place to Round To<\/span><\/h3>\n

                                Round each number to the highest place value they share<\/strong>.<\/span><\/p>\n

                                  \n
                                • \n

                                  If both numbers are two-digit numbers, round to the tens.<\/span><\/p>\n<\/li>\n

                                • \n

                                  Once again, always round to the highest place value that both numbers share<\/strong>. For example, if one number has thousands and the other has only hundreds, round both to the hundreds place. If one number has hundreds<\/strong> and the other has only tens<\/strong>, round both to the tens<\/strong> place.<\/span><\/p>\n<\/li>\n

                                • \n

                                  If both have thousands, round to the thousands.<\/span><\/p>\n<\/li>\n<\/ul>\n

                                  This makes the numbers easier to add mentally.<\/span><\/p>\n

                                  Step 2: Round Each Number<\/span><\/h3>\n

                                  Use the digit to the right<\/strong> of the one you are rounding to.<\/span><\/p>\n

                                    \n
                                  • \n

                                    If it is 5 or more<\/strong>, round up<\/strong>.<\/span><\/p>\n<\/li>\n

                                  • \n

                                    If it is less than 5<\/strong>, round down<\/strong>.<\/span><\/p>\n<\/li>\n<\/ul>\n

                                    Step 3: Add the Rounded Numbers<\/span><\/h3>\n

                                    This gives your estimated sum<\/strong>.<\/span><\/p>\n

                                    In these examples, estimate<\/strong> the answer. Round each number BEFORE<\/strong> you add.<\/p>\n

                                    \n
                                    \n

                                    Example A<\/p>\n<\/header>\n

                                    \n

                                    [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]<\/p>\n<\/div>\n<\/div>\n

                                    \n
                                    \n

                                    Example B<\/p>\n<\/header>\n

                                    \n

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

                                    \n
                                    \n

                                    Example C<\/p>\n<\/header>\n

                                    \n

                                    [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]<\/p>\n<\/div>\n<\/div>\n

                                    Tip:<\/span><\/h3>\n

                                    Round both numbers to the same place<\/strong> \u2014 the highest one they both have.<\/span><\/p>\n

                                    \n
                                    \n

                                    Exercise One<\/p>\n<\/header>\n

                                    \n

                                    Estimate the sums. Check your work using the answer key at the end of the exercise.<\/p>\n

                                      \n
                                    1. [latex]\\begin{array}[t]{rrrrr} &973 &\\approx &&1\\,000\\\\ &496&\\approx &&500\\\\ +&382&\\approx &+&400\\\\ \\hline &&&& 1\\,900\\end{array}[\/latex]<\/li>\n
                                    2. [latex]\\begin{array}[t]{rr}& 519\\\\&439\\\\+&382\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                    3. [latex]\\begin{array}[t]{rr}& 1\\, 234 \\\\& 4\\, 567\\\\+& 7\\, 890\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                    4. [latex]\\begin{array}[t]{rr}& 3\\, 519 \\\\& 4\\, 003\\\\+& 3\\, 832\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                    5. [latex]\\begin{array}[t]{rr}& 2\\, 727 \\\\& 2\\, 329\\\\+& 9\\, 818\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                    6. [latex]\\begin{array}[t]{rr}& 4\\, 113 \\\\ &1\\, 590\\\\+& 2\\, 671\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                    7. [latex]\\begin{array}[t]{rr}& 38\\, 985 \\\\& 43\\, 691\\\\+& 8\\, 336\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                    8. [latex]\\begin{array}[t]{rr}& 42\\, 163 \\\\ &30\\, 820\\\\ &21\\, 911\\\\+& 60\\, 422\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                    9. [latex]\\begin{array}[t]{rr}& 21\\, 472 \\\\ &46\\, 371\\\\& 98\\, 393 \\\\+& 82\\, 218\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                    10. [latex]\\begin{array}[t]{rr}& 30\\, 706 \\\\ &29\\, 115\\\\& 40\\, 082\\\\+& 31\\, 621\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                    11. [latex]\\begin{array}[t]{rr}& 431\\, 391 \\\\ &554\\, 423\\\\ &913\\, 174 \\\\+& 282 \\,826\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                    12. [latex]\\begin{array}[t]{rr}& 171\\, 234 \\\\ &102\\, 085\\\\ &460\\, 892 \\\\+& 542\\, 329\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<\/ol>\n

                                      Answers to Exercise One<\/strong><\/p>\n

                                        \n
                                      1. 1000<\/span> + 500 + 400 = 1900<\/span><\/li>\n
                                      2. 500 + 400 + 400 = 1300<\/span><\/li>\n
                                      3. 1000<\/span>\u00a0 +\u00a0 5000<\/span>\u00a0 +\u00a0 8000<\/span>\u00a0 =\u00a0 14000<\/span><\/li>\n
                                      4. 4000<\/span>\u00a0 +\u00a0 4000<\/span>\u00a0 + 4000<\/span>\u00a0 =\u00a0 12000<\/span><\/li>\n
                                      5. 3000<\/span> + 2000<\/span> + 10000<\/span> = 15000<\/span><\/li>\n
                                      6. 4000<\/span> + 2000<\/span> + 3000<\/span> = 9000<\/span><\/li>\n
                                      7. 39000<\/span> + 44000<\/span> + 8000<\/span> = 91000<\/span><\/li>\n
                                      8. 40000<\/span>\u00a0 +\u00a0 30000<\/span>\u00a0 +\u00a0 20000<\/span>\u00a0 +\u00a0 60000<\/span>\u00a0 =\u00a0 150000<\/span><\/li>\n
                                      9. 20000<\/span>\u00a0 +\u00a0 50000<\/span>\u00a0 +\u00a0 100000<\/span>\u00a0 + 80000<\/span>\u00a0 =\u00a0 250000<\/span><\/li>\n
                                      10. 30000<\/span> + 30000<\/span> + 40000<\/span> + 30000<\/span> = 130000<\/span><\/li>\n
                                      11. 400000<\/span> + 600000<\/span> + 900000<\/span> + 300000<\/span> = 2200<\/span>000<\/span><\/li>\n
                                      12. 200000<\/span> + 100000<\/span> + 500000<\/span> + 500 000 = 1300<\/span>000<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n

                                        Estimating Answers in Addition Word Problems<\/h1>\n

                                        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.<\/p>\n

                                        \n
                                        \n

                                        Exercise Two<\/p>\n<\/header>\n

                                        \n

                                        Estimate the following answers. Be sure to round to the largest place value possible before adding. Remember to circle<\/span> the information and underline<\/span> what is being asked. Check your work using the answer key at the end of the exercise.<\/p>\n

                                        Example:<\/p>\n

                                        During one month, Chaska spends 11432<\/span> minutes sleeping and 5812<\/span> minutes eating. Estimate how much time he spends sleeping and eating.<\/p>\n

                                        During one month, Chaska spends 11432<\/span> minutes<\/span> sleeping and 5812<\/span> minutes<\/span> eating. Estimate how much time<\/span> he spends sleeping and eating.<\/p>\n

                                        11432<\/span> + 5812<\/span><\/p>\n

                                        Estimate:<\/p>\n

                                        11000<\/span> + 6000<\/span> = 17000<\/span><\/p>\n

                                        Chaska spent about 17000<\/span> minutes sleeping and eating.<\/p>\n

                                          \n
                                        1. During October, Amul drove 674 kilometres, 493 kilometres, 384 kilometres and 914 kilometres. Estimate the total kilometres Amul drove.<\/li>\n
                                        2. The number of passengers using the ABE Taxi Company for the past three weeks were 3205<\/span> passengers, 3542<\/span> passengers and 2821<\/span> passengers. Estimate the number of passengers that used the ABE Taxi Company.<\/li>\n
                                        3. In 2008, the top three winning teams in the NHL were the Montreal Canadiens winning 2980<\/span> games, the Boston Bruins winning 2 669 games and the Toronto Maple Leafs winning 2535<\/span> games. Estimate the total number of games won by these three teams.<\/li>\n
                                        4. The three deepest lakes in the world are Baikal Lake which is 1741<\/span> metres, Tanganyika Lake which is 1471<\/span> metres and the Caspian Sea which 1025<\/span> metres. Estimate the total depth of the three lakes.<\/li>\n<\/ol>\n

                                          Answers to Exercise Two<\/strong><\/p>\n

                                            \n
                                          1. 700 +\u00a0 500\u00a0 +\u00a0 400\u00a0 +\u00a0 900\u00a0 =\u00a0 2500<\/span> kilometres<\/li>\n
                                          2. 3000<\/span>\u00a0 +\u00a0 4000<\/span>\u00a0 + 3000<\/span>\u00a0 =\u00a0 10000<\/span> passengers<\/li>\n
                                          3. 3000<\/span>\u00a0 +\u00a0 3000<\/span>\u00a0 +\u00a0 3000<\/span>\u00a0 =\u00a0 9000<\/span> games<\/li>\n
                                          4. 2000<\/span>\u00a0 +\u00a0 1000<\/span>\u00a0 +\u00a0 1000<\/span> =\u00a0 4000<\/span> metres<\/li>\n<\/ol>\n<\/div>\n<\/div>\n

                                            Key Ideas to Remember<\/h2>\n
                                              \n
                                            • \n

                                              Round to the same place value<\/strong> in both numbers.<\/p>\n<\/li>\n

                                            • \n

                                              Round up<\/strong> if the next digit is 5 or more.<\/p>\n<\/li>\n

                                            • \n

                                              Round down<\/strong> (i.e., the digit stays the same) if it is less than 5.<\/p>\n<\/li>\n

                                            • \n

                                              Add the rounded numbers for your estimate.<\/p>\n<\/li>\n

                                            • \n

                                              Estimating is not exact<\/strong> \u2014 it gives you a ballpark answer<\/strong>.<\/p>\n<\/li>\n<\/ul>\n

                                              Topic C: Self-Test<\/h1>\n

                                              Mark\u00a0 \u00a0 \u00a0\/15\u00a0\u00a0\u00a0 Aim 11\/15<\/strong><\/p>\n

                                                \n
                                              1. Estimate the sums. Show your work. (9 marks)\n
                                                  \n
                                                1. [latex]\\begin{array}[t]{rr}&7\\, 964 \\\\ &971 \\\\ &6 \\,888 \\\\+& 2\\, 021 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                                2. [latex]\\begin{array}[t]{rr}&5 \\,365 \\\\ &5 \\,100 \\\\ &9\\, 982\\\\+& 7\\, 752 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                                3. [latex]\\begin{array}[t]{rr}&5 \\,211 \\\\ &1 \\,982 \\\\ &3\\, 371 \\\\+& 2 \\,801 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                                4. [latex]\\begin{array}[t]{rr}&3 \\,395 \\\\ &2 \\,709 \\\\ &18\\, 060\\\\+& 932 \\,335 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                                5. [latex]\\begin{array}[t]{rr}&2 \\,364 \\\\ &62 \\,182 \\\\ &549\\, 272 \\\\+& 6 \\,395 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                                6. [latex]\\begin{array}[t]{rr}&75\\, 536 \\\\&31 \\,807 \\\\&337 \\,427 \\\\+& 7 \\,912 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                                7. [latex]\\begin{array}[t]{rr}&898\\, 402 \\\\&465 \\,766 \\\\&558\\, 485\\\\+& 324 \\,715 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                                8. [latex]\\begin{array}[t]{rr}&6 \\,182 \\,390\\\\&2 \\,763 \\,393 \\\\&1 \\,326 \\,879 \\\\+& 2\\, 743 \\,912 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n
                                                9. [latex]\\begin{array}[t]{rr}&1 \\,226 \\,590 \\\\&687 \\,029 \\\\&533 \\,905 \\\\+& 1\\, 359 \\,254 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<\/ol>\n<\/li>\n
                                                10. Estimate each of the following word problems. (6 marks) Be sure to include the unit of measure in your answer. (2 marks each)
                                                  \nBe sure to circle<\/span> information and underline<\/span> what is being asked.<\/p>\n
                                                    \n
                                                  1. Yuan counted 854 old books and 519 new books. Estimate how many books there were altogether.<\/li>\n
                                                  2. A magazine has 34783<\/span> subscribers. Last year the magazine had 26876<\/span> subscribers. Estimate how many subscribers in total.<\/li>\n
                                                  3. The area of Canada is 9984<\/span>670<\/span> square kilometres. The area of the United States is 9629<\/span>091<\/span> square kilometres. The area of Mexico is 1964<\/span>375<\/span> square kilometres. Estimate the total area of the three countries.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                    Answers to Topic C Self-Test<\/h2>\n
                                                      \n
                                                    1. \n
                                                        \n
                                                      1. 18000<\/span><\/li>\n
                                                      2. 28000<\/span><\/li>\n
                                                      3. 13000<\/span><\/li>\n
                                                      4. 956000<\/span><\/li>\n
                                                      5. 619000<\/span><\/li>\n
                                                      6. 453000<\/span><\/li>\n
                                                      7. 2300<\/span>000<\/span><\/li>\n
                                                      8. 13000<\/span>000<\/span><\/li>\n
                                                      9. 3800<\/span>000<\/span><\/li>\n<\/ol>\n<\/li>\n
                                                      10. \n
                                                          \n
                                                        1. 1400<\/span> books<\/li>\n
                                                        2. 60000<\/span> subscribers<\/li>\n
                                                        3. 22000<\/span>000<\/span> square kilometres<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"author":999,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-67","chapter","type-chapter","status-publish","hentry"],"part":55,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/pressbooks\/v2\/chapters\/67","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":9,"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/pressbooks\/v2\/chapters\/67\/revisions"}],"predecessor-version":[{"id":340,"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/pressbooks\/v2\/chapters\/67\/revisions\/340"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/pressbooks\/v2\/parts\/55"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/pressbooks\/v2\/chapters\/67\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/wp\/v2\/media?parent=67"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/pressbooks\/v2\/chapter-type?post=67"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/wp\/v2\/contributor?post=67"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math022\/wp-json\/wp\/v2\/license?post=67"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}