{"id":23,"date":"2021-07-29T16:09:52","date_gmt":"2021-07-29T20:09:52","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/alfm6\/?post_type=chapter&p=23"},"modified":"2022-02-15T14:49:57","modified_gmt":"2022-02-15T19:49:57","slug":"rates","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/alfm6\/chapter\/rates\/","title":{"raw":"Topic B: Rates","rendered":"Topic B: Rates"},"content":{"raw":"When a ratio is used to compare two different kinds of measure (e.g. apples and oranges, or meters and hours), it is called a rate. The denominator must be 1.\r\n\r\n \r\n
\r\n

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

\r\n\r\nA car can drive 725 km on 55 L of gas. What is the rate in km per L? The ratio of this is [latex]\\dfrac{725\\text{ km}}{55\\text{ L}}[\/latex]. Find the rate by making the denominator 1.\r\n\r\nDivide [latex]\\dfrac{725}{55} \\div \\left(\\dfrac{55}{55}\\right) = \\dfrac{725\\div55}{55\\div55}=\\dfrac{13.18}{1}=13.18[\/latex]\r\n\r\nThe rate is 13.18 km\/L<\/strong>.\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\nSue bought 10 lb of oranges for $4.99. What is the rate in cents per pound? The ratio is [latex]\\dfrac{$4.99}{10\\text{ lb}}=\\dfrac{499\\text{ cents}}{10 \\text{ lb}}[\/latex]. Find the rate by making the denominator 1.\r\n\r\nDivide [latex] \\dfrac{499}{10} \\div \\left(\\dfrac{10}{10}\\right) =\\dfrac{499\\div10}{10\\div10}=\\dfrac{49.9}{1}=49.9[\/latex]\r\n\r\nThe rate is 49.9 \u00a2\/lb<\/strong>.\r\n\r\n<\/div>\r\n<\/div>\r\n \r\n\r\nWhen talking about rate, use the word \u2018per\u2019.\r\n\r\nIn example A, say: \u201cThe fuel economy of the car is 13.18 kilometres per litre\u201d.\r\nIn example B, say: \u201cThe oranges cost 49.9 cents per pound\u201d.\r\n\r\n \r\n
\r\n

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

\r\n\r\nIt takes 60 ounces of grass seed to plant 30 m2<\/sup> of lawn. What is the rate in ounces per square metre (m2<\/sup>)? The ratio is [latex]\\dfrac{60\\text{ oz}}{30\\text{ m}^2}[\/latex]. Find the rate by making the denominator 1.\r\n\r\nDivide [latex]\\dfrac{60}{30} \\div \\left(\\dfrac{30}{30}\\right) = \\dfrac{60\\div30}{30\\div30}=\\dfrac{2}{1}=2[\/latex]\r\n\r\nThe rate is 2 oz\/m2<\/sup><\/strong>, or 2 ounces per square metre<\/strong>.\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n

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

\r\n\r\nWrite the following ratios as rates, comparing distance to time.\r\n
    \r\n \t
  1. 120 km, 3 hours<\/li>\r\n \t
  2. 27 km, 9 hours<\/li>\r\n \t
  3. 203 km, 29 seconds<\/li>\r\n \t
  4. 444 km, 48 seconds<\/li>\r\n<\/ol>\r\nAnswers to Exercise 1<\/strong>\r\n
      \r\n \t
    1. 40 km\/hour<\/li>\r\n \t
    2. 3 km\/hour<\/li>\r\n \t
    3. 7 km\/second<\/li>\r\n \t
    4. 9.25 km\/second<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n
      \r\n

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

      \r\n\r\nWrite the following ratios as rates.\r\n
        \r\n \t
      1. A leaky faucet can lose 52 litres of water in a week. What is the rate of litres lost per day? (round to two decimal places)<\/li>\r\n \t
      2. A ratio of distance travelled to time is called speed. What is the rate (speed) in kilometres per hour (km\/h)?\r\n
          \r\n \t
        1. 45 km, 3 hours<\/li>\r\n \t
        2. 129 km, 1.5 hours<\/li>\r\n \t
        3. 65 km, 13 hours<\/li>\r\n<\/ol>\r\n <\/li>\r\n \t
        4. Vancouver Island has a population of 734,860, and a land mass of 32,134 square kilometres. What is the rate of number of people per square kilometre? (This is called population density.) Round your answer to the nearest whole number.<\/li>\r\n \t
        5. At rest, the heart beat of a mouse is 30,000 beats per 60 minutes. What is the rate of beats per minute?<\/li>\r\n<\/ol>\r\nAnswers to Exercise 2<\/strong>\r\n
            \r\n \t
          1. 7.43 L\/day<\/li>\r\n \t
          2. \r\n
              \r\n \t
            1. 15 km\/hour<\/li>\r\n \t
            2. 86 km\/hour<\/li>\r\n \t
            3. 5 km\/hour<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
            4. 23 people\/km2<\/sup><\/li>\r\n \t
            5. 500 beats\/minute<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

              Topic B: Self-Test<\/h1>\r\nMark\u00a0 \u00a0 \u00a0 \u00a0\/7\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Aim\u00a0 \u00a0 \u00a0 \u00a0 6\/7<\/strong>\r\n
                \r\n \t
              1. Write the definition.\r\n(1 mark)<\/strong>\r\n
                  \r\n \t
                1. Rate<\/li>\r\n<\/ol>\r\n <\/li>\r\n \t
                2. Write the following ratios as rates. Round people to the nearest person.\r\n(6 marks)<\/strong>\r\n
                    \r\n \t
                  1. 12 cups water, 3 cups sugar<\/li>\r\n \t
                  2. 72 metres, 24 seconds<\/li>\r\n \t
                  3. 1,365,000 people, 4,000 km2<\/sup><\/li>\r\n \t
                  4. 5,000 cars on the road, 250 bikes on the road<\/li>\r\n \t
                  5. 12 cups of flour, 12 tsp. of baking powder<\/li>\r\n \t
                  6. 8 litres of gas, 2 litres of oil<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n \r\n
                    \r\n

                    Answers to Topic B Self-Test<\/h2>\r\n
                      \r\n \t
                    1. A rate is used when a ratio compares two different kinds of measure, and when the denominator is 1.<\/li>\r\n \t
                    2. \r\n
                        \r\n \t
                      1. 4 cups of water\/cups of sugar<\/li>\r\n \t
                      2. 3 m\/second<\/li>\r\n \t
                      3. 341 people km2<\/sup><\/li>\r\n \t
                      4. 20 cars\/bike<\/li>\r\n \t
                      5. 1 cup flour\/tsp baking powder<\/li>\r\n \t
                      6. 4 litres gas\/litre oil<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/div>","rendered":"

                        When a ratio is used to compare two different kinds of measure (e.g. apples and oranges, or meters and hours), it is called a rate. The denominator must be 1.<\/p>\n

                         <\/p>\n

                        \n
                        \n

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

                        \n

                        A car can drive 725 km on 55 L of gas. What is the rate in km per L? The ratio of this is [latex]\\dfrac{725\\text{ km}}{55\\text{ L}}[\/latex]. Find the rate by making the denominator 1.<\/p>\n

                        Divide [latex]\\dfrac{725}{55} \\div \\left(\\dfrac{55}{55}\\right) = \\dfrac{725\\div55}{55\\div55}=\\dfrac{13.18}{1}=13.18[\/latex]<\/p>\n

                        The rate is 13.18 km\/L<\/strong>.<\/p>\n<\/div>\n<\/div>\n

                        \n
                        \n

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

                        \n

                        Sue bought 10 lb of oranges for $4.99. What is the rate in cents per pound? The ratio is [latex]\\dfrac{$4.99}{10\\text{ lb}}=\\dfrac{499\\text{ cents}}{10 \\text{ lb}}[\/latex]. Find the rate by making the denominator 1.<\/p>\n

                        Divide [latex]\\dfrac{499}{10} \\div \\left(\\dfrac{10}{10}\\right) =\\dfrac{499\\div10}{10\\div10}=\\dfrac{49.9}{1}=49.9[\/latex]<\/p>\n

                        The rate is 49.9 \u00a2\/lb<\/strong>.<\/p>\n<\/div>\n<\/div>\n

                         <\/p>\n

                        When talking about rate, use the word \u2018per\u2019.<\/p>\n

                        In example A, say: \u201cThe fuel economy of the car is 13.18 kilometres per litre\u201d.
                        \nIn example B, say: \u201cThe oranges cost 49.9 cents per pound\u201d.<\/p>\n

                         <\/p>\n

                        \n
                        \n

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

                        \n

                        It takes 60 ounces of grass seed to plant 30 m2<\/sup> of lawn. What is the rate in ounces per square metre (m2<\/sup>)? The ratio is [latex]\\dfrac{60\\text{ oz}}{30\\text{ m}^2}[\/latex]. Find the rate by making the denominator 1.<\/p>\n

                        Divide [latex]\\dfrac{60}{30} \\div \\left(\\dfrac{30}{30}\\right) = \\dfrac{60\\div30}{30\\div30}=\\dfrac{2}{1}=2[\/latex]<\/p>\n

                        The rate is 2 oz\/m2<\/sup><\/strong>, or 2 ounces per square metre<\/strong>.<\/p>\n<\/div>\n<\/div>\n

                        \n
                        \n

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

                        \n

                        Write the following ratios as rates, comparing distance to time.<\/p>\n

                          \n
                        1. 120 km, 3 hours<\/li>\n
                        2. 27 km, 9 hours<\/li>\n
                        3. 203 km, 29 seconds<\/li>\n
                        4. 444 km, 48 seconds<\/li>\n<\/ol>\n

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

                            \n
                          1. 40 km\/hour<\/li>\n
                          2. 3 km\/hour<\/li>\n
                          3. 7 km\/second<\/li>\n
                          4. 9.25 km\/second<\/li>\n<\/ol>\n<\/div>\n<\/div>\n
                            \n
                            \n

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

                            \n

                            Write the following ratios as rates.<\/p>\n

                              \n
                            1. A leaky faucet can lose 52 litres of water in a week. What is the rate of litres lost per day? (round to two decimal places)<\/li>\n
                            2. A ratio of distance travelled to time is called speed. What is the rate (speed) in kilometres per hour (km\/h)?\n
                                \n
                              1. 45 km, 3 hours<\/li>\n
                              2. 129 km, 1.5 hours<\/li>\n
                              3. 65 km, 13 hours<\/li>\n<\/ol>\n

                                 <\/li>\n

                              4. Vancouver Island has a population of 734,860, and a land mass of 32,134 square kilometres. What is the rate of number of people per square kilometre? (This is called population density.) Round your answer to the nearest whole number.<\/li>\n
                              5. At rest, the heart beat of a mouse is 30,000 beats per 60 minutes. What is the rate of beats per minute?<\/li>\n<\/ol>\n

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

                                  \n
                                1. 7.43 L\/day<\/li>\n
                                2. \n
                                    \n
                                  1. 15 km\/hour<\/li>\n
                                  2. 86 km\/hour<\/li>\n
                                  3. 5 km\/hour<\/li>\n<\/ol>\n<\/li>\n
                                  4. 23 people\/km2<\/sup><\/li>\n
                                  5. 500 beats\/minute<\/li>\n<\/ol>\n<\/div>\n<\/div>\n

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

                                    Mark\u00a0 \u00a0 \u00a0 \u00a0\/7\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Aim\u00a0 \u00a0 \u00a0 \u00a0 6\/7<\/strong><\/p>\n

                                      \n
                                    1. Write the definition.
                                      \n(1 mark)<\/strong><\/p>\n
                                        \n
                                      1. Rate<\/li>\n<\/ol>\n

                                         <\/li>\n

                                      2. Write the following ratios as rates. Round people to the nearest person.
                                        \n(6 marks)<\/strong><\/p>\n
                                          \n
                                        1. 12 cups water, 3 cups sugar<\/li>\n
                                        2. 72 metres, 24 seconds<\/li>\n
                                        3. 1,365,000 people, 4,000 km2<\/sup><\/li>\n
                                        4. 5,000 cars on the road, 250 bikes on the road<\/li>\n
                                        5. 12 cups of flour, 12 tsp. of baking powder<\/li>\n
                                        6. 8 litres of gas, 2 litres of oil<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                           <\/p>\n

                                          \n

                                          Answers to Topic B Self-Test<\/h2>\n
                                            \n
                                          1. A rate is used when a ratio compares two different kinds of measure, and when the denominator is 1.<\/li>\n
                                          2. \n
                                              \n
                                            1. 4 cups of water\/cups of sugar<\/li>\n
                                            2. 3 m\/second<\/li>\n
                                            3. 341 people km2<\/sup><\/li>\n
                                            4. 20 cars\/bike<\/li>\n
                                            5. 1 cup flour\/tsp baking powder<\/li>\n
                                            6. 4 litres gas\/litre oil<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n","protected":false},"author":103,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-23","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapters\/23","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/wp\/v2\/users\/103"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapters\/23\/revisions"}],"predecessor-version":[{"id":1254,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapters\/23\/revisions\/1254"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapters\/23\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/wp\/v2\/media?parent=23"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapter-type?post=23"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/wp\/v2\/contributor?post=23"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/wp\/v2\/license?post=23"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}