{"id":43,"date":"2023-08-02T21:11:22","date_gmt":"2023-08-03T01:11:22","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math0660\/chapter\/rates\/"},"modified":"2025-02-18T14:24:05","modified_gmt":"2025-02-18T19:24:05","slug":"rates","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math0660\/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?\r\n\r\nThe ratio of this is [latex]\\dfrac{725\\text{ km}}{55\\text{ L}}[\/latex].\r\n\r\nFind 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?\r\n\r\nThe ratio is [latex]\\dfrac{$4.99}{10\\text{ lb}}=\\dfrac{499\\text{ cents}}{10 \\text{ lb}}[\/latex].\r\n\r\nFind 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

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>)?\r\n\r\nThe ratio is [latex]\\dfrac{60\\text{ oz}}{30\\text{ m}^2}[\/latex].\r\n\r\nFind 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
Exercise 1<\/h6>\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

      Exercise 2<\/h2>\r\nWrite the following ratios as rates.\r\n\r\n \r\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)<\/div>\r\n2. A ratio of distance travelled to time is called speed. What is the rate (speed) in kilometres per hour (km\/h)?\r\n\r\na. 45 km, 3 hours\r\n\r\n \r\n\r\nb. 129 km, 1.5 hours\r\n\r\n \r\n\r\nc. 65 km, 13 hours\r\n\r\n \r\n\r\n \r\n
      3. 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.<\/div>\r\n
      4. At rest, the heart beat of a mouse is 30,000 beats per 60 minutes. What is the rate of beats per minute?<\/div>\r\nAnswers to Exercise 2<\/strong>\r\n\r\n1. 7.43 L\/day\r\n\r\n2a. 15 km\/hour\r\n2b. 86 km\/hour\r\n2c. 5 km\/hour\r\n\r\n3. 23 people\/km2<\/sup>\r\n\r\n4. 500 beats\/minute\r\n
      \r\n

      Topic B: Self-Test<\/h1>\r\n<\/div>\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
            Answers to Topic B Self-Test<\/h6>\r\n1. A rate is used when a ratio compares two different kinds of measure, and when the denominator is 1.\r\n\r\n2.\r\n
              \r\n \t
            1. \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?<\/p>\n

                The ratio of this is [latex]\\dfrac{725\\text{ km}}{55\\text{ L}}[\/latex].<\/p>\n

                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?<\/p>\n

                The ratio is [latex]\\dfrac{$4.99}{10\\text{ lb}}=\\dfrac{499\\text{ cents}}{10 \\text{ lb}}[\/latex].<\/p>\n

                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

                \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>)?<\/p>\n

                The ratio is [latex]\\dfrac{60\\text{ oz}}{30\\text{ m}^2}[\/latex].<\/p>\n

                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

                Exercise 1<\/h6>\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

                    Exercise 2<\/h2>\n

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

                     <\/p>\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)<\/div>\n

                    2. A ratio of distance travelled to time is called speed. What is the rate (speed) in kilometres per hour (km\/h)?<\/p>\n

                    a. 45 km, 3 hours<\/p>\n

                     <\/p>\n

                    b. 129 km, 1.5 hours<\/p>\n

                     <\/p>\n

                    c. 65 km, 13 hours<\/p>\n

                     <\/p>\n

                     <\/p>\n

                    3. 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.<\/div>\n
                    4. At rest, the heart beat of a mouse is 30,000 beats per 60 minutes. What is the rate of beats per minute?<\/div>\n

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

                    1. 7.43 L\/day<\/p>\n

                    2a. 15 km\/hour
                    \n2b. 86 km\/hour
                    \n2c. 5 km\/hour<\/p>\n

                    3. 23 people\/km2<\/sup><\/p>\n

                    4. 500 beats\/minute<\/p>\n

                    \n

                    Topic B: Self-Test<\/h1>\n<\/div>\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
                          \n
                          Answers to Topic B Self-Test<\/h6>\n

                          1. A rate is used when a ratio compares two different kinds of measure, and when the denominator is 1.<\/p>\n

                          2.<\/p>\n

                            \n
                          1. \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":1935,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-43","chapter","type-chapter","status-publish","hentry"],"part":37,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/pressbooks\/v2\/chapters\/43","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/wp\/v2\/users\/1935"}],"version-history":[{"count":20,"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/pressbooks\/v2\/chapters\/43\/revisions"}],"predecessor-version":[{"id":472,"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/pressbooks\/v2\/chapters\/43\/revisions\/472"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/pressbooks\/v2\/parts\/37"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/pressbooks\/v2\/chapters\/43\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/wp\/v2\/media?parent=43"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/pressbooks\/v2\/chapter-type?post=43"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/wp\/v2\/contributor?post=43"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math0660\/wp-json\/wp\/v2\/license?post=43"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}