{"id":50,"date":"2023-01-17T16:24:33","date_gmt":"2023-01-17T21:24:33","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/estimating-quotients\/"},"modified":"2025-07-03T23:58:39","modified_gmt":"2025-07-04T03:58:39","slug":"estimating-quotients","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/estimating-quotients\/","title":{"raw":"Topic E: Estimating Quotients","rendered":"Topic E: Estimating Quotients"},"content":{"raw":"

Divide Numbers That Both End With Zeros<\/h1>\r\nIn Unit 1 you learned a shortcut for multiplying numbers that end with zeros.\r\n\r\nNow you will learn a short way to divide numbers that both <\/strong>end with zeros. First do this exercise and notice the pattern in the quotients.\r\n
\r\n

Exercise 1<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nDivide. Check your work using the answer key at the end of the exercise.\r\n
    \r\n \t
  1. [latex]2 \\enclose{longdiv}{6}[\/latex]<\/li>\r\n \t
  2. [latex]20 \\enclose{longdiv}{60}[\/latex]<\/li>\r\n \t
  3. [latex]200 \\enclose{longdiv}{600}[\/latex]<\/li>\r\n \t
  4. [latex]2000 \\enclose{longdiv}{6000}[\/latex]<\/li>\r\n \t
  5. [latex]5 \\enclose{longdiv}{25}[\/latex]<\/li>\r\n \t
  6. [latex]50 \\enclose{longdiv}{250}[\/latex]<\/li>\r\n \t
  7. [latex]500 \\enclose{longdiv}{2500}[\/latex]<\/li>\r\n \t
  8. [latex]5000 \\enclose{longdiv}{25000}[\/latex]<\/li>\r\n \t
  9. [latex]14 \\enclose{longdiv}{28}[\/latex]<\/li>\r\n \t
  10. [latex]140 \\enclose{longdiv}{280}[\/latex]<\/li>\r\n \t
  11. [latex]1400 \\enclose{longdiv}{2800}[\/latex]<\/li>\r\n \t
  12. [latex]14000 \\enclose{longdiv}{28000}[\/latex]<\/li>\r\n<\/ol>\r\nAnswers to Exercise 1<\/strong>\r\n
      \r\n \t
    1. 3<\/li>\r\n \t
    2. 3<\/li>\r\n \t
    3. 3<\/li>\r\n \t
    4. 3<\/li>\r\n \t
    5. 5<\/li>\r\n \t
    6. 5<\/li>\r\n \t
    7. 5<\/li>\r\n \t
    8. 5<\/li>\r\n \t
    9. 2<\/li>\r\n \t
    10. 2<\/li>\r\n \t
    11. 2<\/li>\r\n \t
    12. 2<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nHere is the shortcut: <\/strong>\r\n\r\nWhen dividing numbers that both end with zeros, cross off the same number <\/strong>of zeros <\/strong>from the end of the divisor and the dividend. This is sometimes called cancelling zeros.<\/strong>\r\n
      \r\n

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

      \r\n

      [latex]4800 \\div 60 = 480\\cancel{0} \\div 6\\cancel{0}[\/latex]<\/p>\r\n

      [latex]\\begin{array}{r}80\\\\ 6\\enclose{longdiv}{480}\\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

      \r\n

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

      \r\n

      [latex]23000 \\div 500 = 230\\cancel{00} \\div 5\\cancel{00}[\/latex]<\/p>\r\n

      [latex]\\begin{array}{r}46\\\\ 5\\enclose{longdiv}{230} \\\\ 20 \\downarrow \\\\ \\hline 30 \\\\ 30 \\\\ \\hline 0\\end{array}[\/latex]<\/p>\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]2\\cancel{000}\\enclose{longdiv}{680\\cancel{000}}[\/latex]\r\n

      [latex]\\begin{array}{r}340 \\\\ 2\\enclose{longdiv}{680}\\\\ 6\\downarrow \\ \\\\\\hline 08 \\ \\ \\ \\\\ 8 \\downarrow \\\\ \\hline 00 \\\\ 0 \\\\ \\hline 0\\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nIf you are interested in the facts of arithmetic that make this shortcut work, ask your instructor for an explanation.<\/strong>\r\n

      \r\n

      Exercise 2<\/p>\r\n\r\n<\/header>\r\n

      \r\n\r\nQuickly\u00a0 find the quotients. Remember to cancel\u00a0 the same <\/strong>number <\/strong>of zeros in both the divisor and dividend in each question. Check your work using the answer key at the end of the exercise.\r\n
        \r\n \t
      1. [latex]30\\enclose{longdiv}{90}[\/latex]<\/li>\r\n \t
      2. [latex]40\\enclose{longdiv}{1600}[\/latex]<\/li>\r\n \t
      3. [latex]300\\enclose{longdiv}{1200}[\/latex]<\/li>\r\n \t
      4. [latex]400\\enclose{longdiv}{20000}[\/latex]<\/li>\r\n \t
      5. [latex]500\\enclose{longdiv}{35000}[\/latex]<\/li>\r\n \t
      6. [latex]700\\enclose{longdiv}{42000}[\/latex]<\/li>\r\n \t
      7. [latex]60000\\enclose{longdiv}{2400000}[\/latex]<\/li>\r\n \t
      8. [latex]800000\\enclose{longdiv}{400000000}[\/latex]<\/li>\r\n<\/ol>\r\nAnswers to Exercise 2<\/strong>\r\n
          \r\n \t
        1. 3<\/li>\r\n \t
        2. 40<\/li>\r\n \t
        3. 4<\/li>\r\n \t
        4. 50<\/li>\r\n \t
        5. 70<\/li>\r\n \t
        6. 60<\/li>\r\n \t
        7. 40<\/li>\r\n \t
        8. 500<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

          Rounding Division Questions to Estimate<\/h1>\r\nWe round numbers and estimate to get a quick answer.<\/strong>\r\n\r\nIn division, round the divisor and dividend before <\/strong>you divide.\r\n
            \r\n \t
          1. If the divisor only has one digit, do not round it,<\/li>\r\n \t
          2. Round the dividend to make the arithmetic easier for yourself.<\/li>\r\n<\/ol>\r\n
            \r\n

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

            \r\n\r\nLook at the two ways of rounding this question.\r\n

            [latex]1796 \\div 32 = [\/latex]<\/p>\r\nThe divisor (32) will round to 30. This dividend (1796) can be rounded to 1800 or to 2000. Let's try each:\r\n\r\nRound to 1800.\r\n

            [latex]\\begin{array}{r}60\\ \\ \\ \\ \\\\ 3\\cancel{0}\\enclose{longdiv}{180\\cancel{0}}\\end{array}[\/latex]<\/p>\r\nRound to 2000.\r\n

            [latex]\\begin{array}{l}\\hspace{2.5em}66\\text{ R}2\\\\3\\cancel{0}\\enclose{longdiv}{200\\cancel{0}} \\\\\\hspace{2em}18\\downarrow \\\\\\hline\\hspace{2.5em}20\\\\\\hspace{2.5em}18\\\\\\hline\\hspace{1.5cm}2\\end{array}[\/latex]<\/p>\r\nRounding 1796 to 1800 is easier arithmetic because [latex]18 \\div 3[\/latex] works out evenly, so [latex]180 \\div 3[\/latex] works out evenly. Both estimates are correct.\r\n\r\n<\/div>\r\n<\/div>\r\n

            \r\n

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

            \r\n
            \r\n\r\n2688<\/span> \u00f7 28 =\r\n
              \r\n \t
            1. Round the divisor (28) to 30.<\/li>\r\n \t
            2. Round the dividend (2688) to 2700 or to 3000.<\/li>\r\n<\/ol>\r\n<\/div>\r\n\r\n\r\n\r\n\r\n
              Round to 2700<\/td>\r\n[latex]\\begin{array}{r}90\\ \\ \\ \\ \\\\\\ 3\\cancel{0}\\enclose{longdiv}{270\\cancel{0}}\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n
              Round to 3000<\/td>\r\n[latex]\\begin{array}{r}100\\ \\ \\ \\ \\ \\\\ 3\\cancel{0}\\enclose{longdiv}{300\\cancel{0}}\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nBoth estimates are correct and both are easy to do.\r\n\r\n<\/div>\r\n<\/div>\r\n
              \r\n

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

              \r\n\r\n2893<\/span> \u00f7 47 =\r\n
                \r\n \t
              1. Round the divisor (47) to 50.<\/li>\r\n \t
              2. Round the dividend (2893<\/span>) to 2900<\/span> or 3000<\/span>.<\/li>\r\n \t
              3. Which rounded dividend will be easier to divide by 50?\r\n
                  \r\n \t
                1. Answer: The 3000 because 5 goes evenly into 30.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n

                  [latex]\\begin{array}{r}60\\ \\ \\ \\ \\ \\\\5\\cancel{0} \\enclose{longdiv}{300\\cancel{0}}\\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

                  \r\n

                  Exercise 3<\/p>\r\n\r\n<\/header>\r\n

                  \r\n\r\nGive an estimated quotient.\u00a0 Show your rounding. Check your work using the answer key at the end of the exercise.\r\n
                    \r\n \t
                  1. [latex]365\\enclose{longdiv}{27692}[\/latex]<\/li>\r\n \t
                  2. [latex]23\\enclose{longdiv}{34459}[\/latex]<\/li>\r\n \t
                  3. [latex]45\\enclose{longdiv}{4590}[\/latex]<\/li>\r\n \t
                  4. [latex]16\\enclose{longdiv}{6729}[\/latex]<\/li>\r\n \t
                  5. [latex]56\\enclose{longdiv}{4792}[\/latex]<\/li>\r\n \t
                  6. [latex]75\\enclose{longdiv}{7648}[\/latex]<\/li>\r\n \t
                  7. [latex]81\\enclose{longdiv}{4049}[\/latex]<\/li>\r\n \t
                  8. [latex]68\\enclose{longdiv}{5636}[\/latex]<\/li>\r\n \t
                  9. [latex]19\\enclose{longdiv}{1672}[\/latex]<\/li>\r\n \t
                  10. [latex]200\\enclose{longdiv}{20000}[\/latex]<\/li>\r\n \t
                  11. [latex]557\\enclose{longdiv}{41680}[\/latex]<\/li>\r\n<\/ol>\r\nAnswers to Exercise 3<\/strong>\r\n
                      \r\n \t
                    1. 28000<\/span> \u00f7 400 = 70<\/li>\r\n \t
                    2. 34000<\/span> \u00f7 20 =1700<\/li>\r\n \t
                    3. 5000<\/span> \u00f7 50 =100<\/li>\r\n \t
                    4. 7000<\/span> \u00f7 20 = 350<\/li>\r\n \t
                    5. 4800<\/span> \u00f7 60 = 80<\/li>\r\n \t
                    6. 8000<\/span> \u00f7 80 = 100<\/li>\r\n \t
                    7. 4000<\/span> \u00f7 80 = 50<\/li>\r\n \t
                    8. 5600<\/span> \u00f7 70 = 80<\/li>\r\n \t
                    9. 2000<\/span> \u00f7 20 = 100<\/li>\r\n \t
                    10. 20000<\/span> \u00f7 200 = 100<\/li>\r\n \t
                    11. 42000<\/span> \u00f7 600 = 70<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                      Topic E: Self-Test<\/h1>\r\nMark\u00a0 \/6\u00a0 \u00a0Aim\u00a0 5\/6<\/strong>\r\n
                        \r\n \t
                      1. Give an estimated quotient. Show your work. (6 marks)\r\n
                          \r\n \t
                        1. [latex]98\\enclose{longdiv}{8541}[\/latex]<\/li>\r\n \t
                        2. [latex]27\\enclose{longdiv}{2963}[\/latex]<\/li>\r\n \t
                        3. [latex]241\\enclose{longdiv}{26348}[\/latex]<\/li>\r\n \t
                        4. [latex]55\\enclose{longdiv}{3276}[\/latex]<\/li>\r\n \t
                        5. [latex]24\\enclose{longdiv}{1776}[\/latex]<\/li>\r\n \t
                        6. [latex]59\\enclose{longdiv}{11830}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n
                          \r\n

                          Answers to Topic E Self-Test<\/h2>\r\n
                            \r\n \t
                          1. Give an estimated quotient. Show your work.\r\n
                              \r\n \t
                            1. 8500<\/span> \u00f7 100 = 85<\/li>\r\n \t
                            2. 3000<\/span> \u00f7 30 =100<\/li>\r\n \t
                            3. 26000<\/span> \u00f7 200 =130\u00a0 or\r\n26000<\/span> \u00f7 260 =100<\/li>\r\n \t
                            4. 3000<\/span> \u00f7 60 = 50 or\r\n3000 \u00f7 50 = 60<\/li>\r\n \t
                            5. 2000<\/span> \u00f7 20 = 100 or\r\n1 800 \u00f7\u00a0 20 = 90<\/li>\r\n \t
                            6. 12000<\/span> \u00f7 60 = 200<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/section>","rendered":"

                              Divide Numbers That Both End With Zeros<\/h1>\n

                              In Unit 1 you learned a shortcut for multiplying numbers that end with zeros.<\/p>\n

                              Now you will learn a short way to divide numbers that both <\/strong>end with zeros. First do this exercise and notice the pattern in the quotients.<\/p>\n

                              \n
                              \n

                              Exercise 1<\/p>\n<\/header>\n

                              \n

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

                                \n
                              1. [latex]2 \\enclose{longdiv}{6}[\/latex]<\/li>\n
                              2. [latex]20 \\enclose{longdiv}{60}[\/latex]<\/li>\n
                              3. [latex]200 \\enclose{longdiv}{600}[\/latex]<\/li>\n
                              4. [latex]2000 \\enclose{longdiv}{6000}[\/latex]<\/li>\n
                              5. [latex]5 \\enclose{longdiv}{25}[\/latex]<\/li>\n
                              6. [latex]50 \\enclose{longdiv}{250}[\/latex]<\/li>\n
                              7. [latex]500 \\enclose{longdiv}{2500}[\/latex]<\/li>\n
                              8. [latex]5000 \\enclose{longdiv}{25000}[\/latex]<\/li>\n
                              9. [latex]14 \\enclose{longdiv}{28}[\/latex]<\/li>\n
                              10. [latex]140 \\enclose{longdiv}{280}[\/latex]<\/li>\n
                              11. [latex]1400 \\enclose{longdiv}{2800}[\/latex]<\/li>\n
                              12. [latex]14000 \\enclose{longdiv}{28000}[\/latex]<\/li>\n<\/ol>\n

                                Answers to Exercise 1<\/strong><\/p>\n

                                  \n
                                1. 3<\/li>\n
                                2. 3<\/li>\n
                                3. 3<\/li>\n
                                4. 3<\/li>\n
                                5. 5<\/li>\n
                                6. 5<\/li>\n
                                7. 5<\/li>\n
                                8. 5<\/li>\n
                                9. 2<\/li>\n
                                10. 2<\/li>\n
                                11. 2<\/li>\n
                                12. 2<\/li>\n<\/ol>\n<\/div>\n<\/div>\n

                                  Here is the shortcut: <\/strong><\/p>\n

                                  When dividing numbers that both end with zeros, cross off the same number <\/strong>of zeros <\/strong>from the end of the divisor and the dividend. This is sometimes called cancelling zeros.<\/strong><\/p>\n

                                  \n
                                  \n

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

                                  \n

                                  [latex]4800 \\div 60 = 480\\cancel{0} \\div 6\\cancel{0}[\/latex]<\/p>\n

                                  [latex]\\begin{array}{r}80\\\\ 6\\enclose{longdiv}{480}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n

                                  \n
                                  \n

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

                                  \n

                                  [latex]23000 \\div 500 = 230\\cancel{00} \\div 5\\cancel{00}[\/latex]<\/p>\n

                                  [latex]\\begin{array}{r}46\\\\ 5\\enclose{longdiv}{230} \\\\ 20 \\downarrow \\\\ \\hline 30 \\\\ 30 \\\\ \\hline 0\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n

                                  \n
                                  \n

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

                                  \n

                                  [latex]2\\cancel{000}\\enclose{longdiv}{680\\cancel{000}}[\/latex]<\/p>\n

                                  [latex]\\begin{array}{r}340 \\\\ 2\\enclose{longdiv}{680}\\\\ 6\\downarrow \\ \\\\\\hline 08 \\ \\ \\ \\\\ 8 \\downarrow \\\\ \\hline 00 \\\\ 0 \\\\ \\hline 0\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n

                                  If you are interested in the facts of arithmetic that make this shortcut work, ask your instructor for an explanation.<\/strong><\/p>\n

                                  \n
                                  \n

                                  Exercise 2<\/p>\n<\/header>\n

                                  \n

                                  Quickly\u00a0 find the quotients. Remember to cancel\u00a0 the same <\/strong>number <\/strong>of zeros in both the divisor and dividend in each question. Check your work using the answer key at the end of the exercise.<\/p>\n

                                    \n
                                  1. [latex]30\\enclose{longdiv}{90}[\/latex]<\/li>\n
                                  2. [latex]40\\enclose{longdiv}{1600}[\/latex]<\/li>\n
                                  3. [latex]300\\enclose{longdiv}{1200}[\/latex]<\/li>\n
                                  4. [latex]400\\enclose{longdiv}{20000}[\/latex]<\/li>\n
                                  5. [latex]500\\enclose{longdiv}{35000}[\/latex]<\/li>\n
                                  6. [latex]700\\enclose{longdiv}{42000}[\/latex]<\/li>\n
                                  7. [latex]60000\\enclose{longdiv}{2400000}[\/latex]<\/li>\n
                                  8. [latex]800000\\enclose{longdiv}{400000000}[\/latex]<\/li>\n<\/ol>\n

                                    Answers to Exercise 2<\/strong><\/p>\n

                                      \n
                                    1. 3<\/li>\n
                                    2. 40<\/li>\n
                                    3. 4<\/li>\n
                                    4. 50<\/li>\n
                                    5. 70<\/li>\n
                                    6. 60<\/li>\n
                                    7. 40<\/li>\n
                                    8. 500<\/li>\n<\/ol>\n<\/div>\n<\/div>\n

                                      Rounding Division Questions to Estimate<\/h1>\n

                                      We round numbers and estimate to get a quick answer.<\/strong><\/p>\n

                                      In division, round the divisor and dividend before <\/strong>you divide.<\/p>\n

                                        \n
                                      1. If the divisor only has one digit, do not round it,<\/li>\n
                                      2. Round the dividend to make the arithmetic easier for yourself.<\/li>\n<\/ol>\n
                                        \n
                                        \n

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

                                        \n

                                        Look at the two ways of rounding this question.<\/p>\n

                                        [latex]1796 \\div 32 =[\/latex]<\/p>\n

                                        The divisor (32) will round to 30. This dividend (1796) can be rounded to 1800 or to 2000. Let’s try each:<\/p>\n

                                        Round to 1800.<\/p>\n

                                        [latex]\\begin{array}{r}60\\ \\ \\ \\ \\\\ 3\\cancel{0}\\enclose{longdiv}{180\\cancel{0}}\\end{array}[\/latex]<\/p>\n

                                        Round to 2000.<\/p>\n

                                        [latex]\\begin{array}{l}\\hspace{2.5em}66\\text{ R}2\\\\3\\cancel{0}\\enclose{longdiv}{200\\cancel{0}} \\\\\\hspace{2em}18\\downarrow \\\\\\hline\\hspace{2.5em}20\\\\\\hspace{2.5em}18\\\\\\hline\\hspace{1.5cm}2\\end{array}[\/latex]<\/p>\n

                                        Rounding 1796 to 1800 is easier arithmetic because [latex]18 \\div 3[\/latex] works out evenly, so [latex]180 \\div 3[\/latex] works out evenly. Both estimates are correct.<\/p>\n<\/div>\n<\/div>\n

                                        \n
                                        \n

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

                                        \n
                                        \n

                                        2688<\/span> \u00f7 28 =<\/p>\n

                                          \n
                                        1. Round the divisor (28) to 30.<\/li>\n
                                        2. Round the dividend (2688) to 2700 or to 3000.<\/li>\n<\/ol>\n<\/div>\n\n\n\n\n
                                          Round to 2700<\/td>\n[latex]\\begin{array}{r}90\\ \\ \\ \\ \\\\\\ 3\\cancel{0}\\enclose{longdiv}{270\\cancel{0}}\\end{array}[\/latex]<\/td>\n<\/tr>\n
                                          Round to 3000<\/td>\n[latex]\\begin{array}{r}100\\ \\ \\ \\ \\ \\\\ 3\\cancel{0}\\enclose{longdiv}{300\\cancel{0}}\\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                          Both estimates are correct and both are easy to do.<\/p>\n<\/div>\n<\/div>\n

                                          \n
                                          \n

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

                                          \n

                                          2893<\/span> \u00f7 47 =<\/p>\n

                                            \n
                                          1. Round the divisor (47) to 50.<\/li>\n
                                          2. Round the dividend (2893<\/span>) to 2900<\/span> or 3000<\/span>.<\/li>\n
                                          3. Which rounded dividend will be easier to divide by 50?\n
                                              \n
                                            1. Answer: The 3000 because 5 goes evenly into 30.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                              [latex]\\begin{array}{r}60\\ \\ \\ \\ \\ \\\\5\\cancel{0} \\enclose{longdiv}{300\\cancel{0}}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n

                                              \n
                                              \n

                                              Exercise 3<\/p>\n<\/header>\n

                                              \n

                                              Give an estimated quotient.\u00a0 Show your rounding. Check your work using the answer key at the end of the exercise.<\/p>\n

                                                \n
                                              1. [latex]365\\enclose{longdiv}{27692}[\/latex]<\/li>\n
                                              2. [latex]23\\enclose{longdiv}{34459}[\/latex]<\/li>\n
                                              3. [latex]45\\enclose{longdiv}{4590}[\/latex]<\/li>\n
                                              4. [latex]16\\enclose{longdiv}{6729}[\/latex]<\/li>\n
                                              5. [latex]56\\enclose{longdiv}{4792}[\/latex]<\/li>\n
                                              6. [latex]75\\enclose{longdiv}{7648}[\/latex]<\/li>\n
                                              7. [latex]81\\enclose{longdiv}{4049}[\/latex]<\/li>\n
                                              8. [latex]68\\enclose{longdiv}{5636}[\/latex]<\/li>\n
                                              9. [latex]19\\enclose{longdiv}{1672}[\/latex]<\/li>\n
                                              10. [latex]200\\enclose{longdiv}{20000}[\/latex]<\/li>\n
                                              11. [latex]557\\enclose{longdiv}{41680}[\/latex]<\/li>\n<\/ol>\n

                                                Answers to Exercise 3<\/strong><\/p>\n

                                                  \n
                                                1. 28000<\/span> \u00f7 400 = 70<\/li>\n
                                                2. 34000<\/span> \u00f7 20 =1700<\/li>\n
                                                3. 5000<\/span> \u00f7 50 =100<\/li>\n
                                                4. 7000<\/span> \u00f7 20 = 350<\/li>\n
                                                5. 4800<\/span> \u00f7 60 = 80<\/li>\n
                                                6. 8000<\/span> \u00f7 80 = 100<\/li>\n
                                                7. 4000<\/span> \u00f7 80 = 50<\/li>\n
                                                8. 5600<\/span> \u00f7 70 = 80<\/li>\n
                                                9. 2000<\/span> \u00f7 20 = 100<\/li>\n
                                                10. 20000<\/span> \u00f7 200 = 100<\/li>\n
                                                11. 42000<\/span> \u00f7 600 = 70<\/li>\n<\/ol>\n<\/div>\n<\/div>\n

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

                                                  Mark\u00a0 \/6\u00a0 \u00a0Aim\u00a0 5\/6<\/strong><\/p>\n

                                                    \n
                                                  1. Give an estimated quotient. Show your work. (6 marks)\n
                                                      \n
                                                    1. [latex]98\\enclose{longdiv}{8541}[\/latex]<\/li>\n
                                                    2. [latex]27\\enclose{longdiv}{2963}[\/latex]<\/li>\n
                                                    3. [latex]241\\enclose{longdiv}{26348}[\/latex]<\/li>\n
                                                    4. [latex]55\\enclose{longdiv}{3276}[\/latex]<\/li>\n
                                                    5. [latex]24\\enclose{longdiv}{1776}[\/latex]<\/li>\n
                                                    6. [latex]59\\enclose{longdiv}{11830}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n
                                                      \n

                                                      Answers to Topic E Self-Test<\/h2>\n
                                                        \n
                                                      1. Give an estimated quotient. Show your work.\n
                                                          \n
                                                        1. 8500<\/span> \u00f7 100 = 85<\/li>\n
                                                        2. 3000<\/span> \u00f7 30 =100<\/li>\n
                                                        3. 26000<\/span> \u00f7 200 =130\u00a0 or
                                                          \n26000<\/span> \u00f7 260 =100<\/li>\n
                                                        4. 3000<\/span> \u00f7 60 = 50 or
                                                          \n3000 \u00f7 50 = 60<\/li>\n
                                                        5. 2000<\/span> \u00f7 20 = 100 or
                                                          \n1 800 \u00f7\u00a0 20 = 90<\/li>\n
                                                        6. 12000<\/span> \u00f7 60 = 200<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/section>\n","protected":false},"author":999,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-50","chapter","type-chapter","status-publish","hentry"],"part":35,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/50","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":4,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/50\/revisions"}],"predecessor-version":[{"id":217,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/50\/revisions\/217"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/parts\/35"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/50\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/media?parent=50"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapter-type?post=50"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/contributor?post=50"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/license?post=50"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}