{"id":136,"date":"2023-07-29T19:08:38","date_gmt":"2023-07-29T23:08:38","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/?post_type=chapter&p=136"},"modified":"2023-11-02T16:32:09","modified_gmt":"2023-11-02T20:32:09","slug":"understanding-ratios-2","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/chapter\/understanding-ratios-2\/","title":{"raw":"Understanding Ratios","rendered":"Understanding Ratios"},"content":{"raw":"A ratio<\/span><\/strong> is the comparison of two or more objects.\r\n\r\nA ratio of two numbers a and b can be written as\r\n

[latex]a:b[\/latex] or [latex]\\frac{a}{b}[\/latex]<\/p>\r\nA ratio of three objects a, b, and c, is usually written as\r\n

[latex]a:b:c[\/latex]<\/p>\r\nA proportion is the comparison of two or more ratios:\r\n

[latex]\\frac{a}{b}=\\frac{c}{d}=\\frac{e}{f}[\/latex]<\/p>\r\nFor example, if there is 1 boy and 3 girls you could write the ratio as:\r\n

[latex]1:3[\/latex] (for every one boy there are 3 girls)<\/p>\r\n\r\n

A Ratio Compares Values<\/h2>\r\nA ratio says how much of one thing there is compared to another thing.\r\n\r\n\"A\r\n

There are 2 green squares to 5 yellow squares.<\/strong><\/p>\r\n

The three ways to write this are [latex]2:5[\/latex], 2 to 5, or [latex]\\frac{2}{5}[\/latex]<\/strong><\/p>\r\nYou can \"scale up\" your ratio like this:\r\n

\"\"[latex]4:10[\/latex]<\/p>\r\nThe trick with ratios is to always multiply or divide the numbers by the same value.\r\n\r\n[latex]4:10[\/latex] is the same as [latex]4\\times2:10\\times2=8:20[\/latex]\r\n\r\nEverything you have read so far is part-to-part ratios. Ratios can also be a part compared to the whole number.\r\n\r\nThere are 7 fish, 5 are black and 2 are purple.\r\n\r\n\"\"\r\n

    \r\n \t
  • Part to part:<\/strong>\r\n
      \r\n \t
    • The ratio of black to purple is [latex]5:2[\/latex] or [latex]\\tfrac{5}{2}[\/latex]<\/li>\r\n \t
    • The ratio of purple to black is [latex]2:5[\/latex] or [latex]\\tfrac{2}{5}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t
    • Part to whole:<\/strong>\r\n
        \r\n \t
      • The ratio of black to all fish is [latex]5:7[\/latex] or [latex]\\tfrac{5}{7}[\/latex]<\/li>\r\n \t
      • The ratio of purple to all fish is [latex]2:7[\/latex] or [latex]\\tfrac{2}{7}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n

        Blueprints<\/h2>\r\nWhen we read blueprints in the trades, it is not often that the picture is the actual size of the object. Therefore, a ratio needs to be given to understand the scale at which the dimensions are shown in the picture compared to the real-life-sized object being built.\r\n\r\nA scale is shown as a ratio, for example [latex]1:100[\/latex]. A drawing at a scale of [latex]1:100[\/latex] means that the object is 100 times smaller than in real-life scale [latex]1:1[\/latex]. You could also say, 1 unit in the drawing is equal to 100 units in real life.\r\n\r\nA machine part, for example, may be half the size ([latex]\\tfrac{1}{2}[\/latex]\u2033 = [latex]1[\/latex]\u2033); a building may be drawn [latex]\\tfrac{1}{48}[\/latex] ([latex]\\tfrac{1}{4}[\/latex]\u2033=1\u2019-0\u201d); a map may be drawn [latex]\\tfrac{1}{200}[\/latex] size (1\u201d=100\u2019-0\u201d); and a gear in that wristwatch may be ten times size (10\u2033 = 1\u2033).\r\n\r\nBlueprint drawings are typically drawn in\r\n
          \r\n \t
        • [latex]1:20[\/latex], [latex]1:50[\/latex] or [latex]1:100[\/latex] (Metric units) or<\/li>\r\n \t
        • [latex]\\tfrac{1}{4}[\/latex]\u2033 or [latex]\\tfrac{1}{8}[\/latex]\u2033 (Imperial units) scales<\/li>\r\n<\/ul>\r\n

          To scale a Metric drawing<\/h3>\r\nMultiply the measurement on the drawing with the denominator where the denominator is the number after the colon.\r\n\r\nExample<\/strong> - Blueprint Drawing Scale [latex]1:50[\/latex]\r\n\r\nAn actual length of 1 cm is measured on a [latex]1:50[\/latex] blueprint floor plan. The physical length can be calculated as\r\n\r\n(1 cm) 50 = 50 cm\r\n

          Imperial units - US<\/h3>\r\nA [latex]\\tfrac{1}{4}[\/latex]\u2033 scale means that each [latex]\\tfrac{1}{4}[\/latex]\u2033 (inch) on the plan counts for 1\u2032 (feet) of actual physical length.\r\n\r\nTo scale a blueprint in imperial units to actual feet, multiply the measurement on the drawing (in inches decimal equivalent) with the denominator where the denominator is the bottom number.\r\n\r\nExample<\/strong> - Blueprint Drawing Scale [latex]\\tfrac{1}{4}[\/latex]\r\n\r\nAn actual length is measured to 1-3\/8\u201d on a [latex]\\tfrac{1}{4}[\/latex] blueprint floor plan. The physical length can be calculated as\r\n\r\n(1-3\/8 inch) 4 = (1.375 inch) 4\r\n\r\n= 5.5 feet\r\n\r\n= 5\u2032 6\u2033\r\n\r\nIf you know the measurement of the actual object, and have the ratio scale, you would divide <\/strong>the number of the real life measurements by the denominator of the ratio.\r\n

          Commonly Used Drawing Scales<\/h2>\r\n

          Details<\/h3>\r\n
            \r\n \t
          • [latex]1:1[\/latex]<\/li>\r\n \t
          • [latex]1:5[\/latex]<\/li>\r\n \t
          • [latex]1:10[\/latex]<\/li>\r\n \t
          • [latex]1:20[\/latex]<\/li>\r\n<\/ul>\r\n

            Component drawings, assembly<\/h3>\r\n
              \r\n \t
            • [latex]1:20[\/latex]<\/li>\r\n \t
            • [latex]1:10[\/latex]<\/li>\r\n \t
            • [latex]1:5[\/latex]<\/li>\r\n<\/ul>\r\n

              Floor plans, general arrangement (GA)<\/h3>\r\n
                \r\n \t
              • [latex]1:40[\/latex]<\/li>\r\n \t
              • [latex]1:50[\/latex]<\/li>\r\n<\/ul>\r\n

                Location plot plans<\/h3>\r\n
                  \r\n \t
                • [latex]1:80[\/latex]<\/li>\r\n \t
                • [latex]1:100[\/latex]<\/li>\r\n \t
                • [latex]1:200[\/latex]<\/li>\r\n \t
                • [latex]1:500[\/latex]<\/li>\r\n<\/ul>\r\n

                  Block plan, city maps, and larger<\/h3>\r\n
                    \r\n \t
                  • [latex]1:1000[\/latex]<\/li>\r\n \t
                  • [latex]1:1250[\/latex]<\/li>\r\n \t
                  • [latex]1:2500[\/latex]<\/li>\r\n<\/ul>\r\n

                    Ordnance survey maps<\/h3>\r\n
                      \r\n \t
                    • [latex]1:100000[\/latex]<\/li>\r\n \t
                    • [latex]1:50000[\/latex]<\/li>\r\n \t
                    • [latex]1:25000[\/latex]<\/li>\r\n \t
                    • [latex]1:10000[\/latex]<\/li>\r\n<\/ul>","rendered":"

                      A ratio<\/span><\/strong> is the comparison of two or more objects.<\/p>\n

                      A ratio of two numbers a and b can be written as<\/p>\n

                      [latex]a:b[\/latex] or [latex]\\frac{a}{b}[\/latex]<\/p>\n

                      A ratio of three objects a, b, and c, is usually written as<\/p>\n

                      [latex]a:b:c[\/latex]<\/p>\n

                      A proportion is the comparison of two or more ratios:<\/p>\n

                      [latex]\\frac{a}{b}=\\frac{c}{d}=\\frac{e}{f}[\/latex]<\/p>\n

                      For example, if there is 1 boy and 3 girls you could write the ratio as:<\/p>\n

                      [latex]1:3[\/latex] (for every one boy there are 3 girls)<\/p>\n

                      A Ratio Compares Values<\/h2>\n

                      A ratio says how much of one thing there is compared to another thing.<\/p>\n

                      \"A<\/p>\n

                      There are 2 green squares to 5 yellow squares.<\/strong><\/p>\n

                      The three ways to write this are [latex]2:5[\/latex], 2 to 5, or [latex]\\frac{2}{5}[\/latex]<\/strong><\/p>\n

                      You can “scale up” your ratio like this:<\/p>\n

                      \"\"[latex]4:10[\/latex]<\/p>\n

                      The trick with ratios is to always multiply or divide the numbers by the same value.<\/p>\n

                      [latex]4:10[\/latex] is the same as [latex]4\\times2:10\\times2=8:20[\/latex]<\/p>\n

                      Everything you have read so far is part-to-part ratios. Ratios can also be a part compared to the whole number.<\/p>\n

                      There are 7 fish, 5 are black and 2 are purple.<\/p>\n

                      \"\"<\/p>\n

                        \n
                      • Part to part:<\/strong>\n
                          \n
                        • The ratio of black to purple is [latex]5:2[\/latex] or [latex]\\tfrac{5}{2}[\/latex]<\/li>\n
                        • The ratio of purple to black is [latex]2:5[\/latex] or [latex]\\tfrac{2}{5}[\/latex]<\/li>\n<\/ul>\n<\/li>\n
                        • Part to whole:<\/strong>\n
                            \n
                          • The ratio of black to all fish is [latex]5:7[\/latex] or [latex]\\tfrac{5}{7}[\/latex]<\/li>\n
                          • The ratio of purple to all fish is [latex]2:7[\/latex] or [latex]\\tfrac{2}{7}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

                            Blueprints<\/h2>\n

                            When we read blueprints in the trades, it is not often that the picture is the actual size of the object. Therefore, a ratio needs to be given to understand the scale at which the dimensions are shown in the picture compared to the real-life-sized object being built.<\/p>\n

                            A scale is shown as a ratio, for example [latex]1:100[\/latex]. A drawing at a scale of [latex]1:100[\/latex] means that the object is 100 times smaller than in real-life scale [latex]1:1[\/latex]. You could also say, 1 unit in the drawing is equal to 100 units in real life.<\/p>\n

                            A machine part, for example, may be half the size ([latex]\\tfrac{1}{2}[\/latex]\u2033 = [latex]1[\/latex]\u2033); a building may be drawn [latex]\\tfrac{1}{48}[\/latex] ([latex]\\tfrac{1}{4}[\/latex]\u2033=1\u2019-0\u201d); a map may be drawn [latex]\\tfrac{1}{200}[\/latex] size (1\u201d=100\u2019-0\u201d); and a gear in that wristwatch may be ten times size (10\u2033 = 1\u2033).<\/p>\n

                            Blueprint drawings are typically drawn in<\/p>\n

                              \n
                            • [latex]1:20[\/latex], [latex]1:50[\/latex] or [latex]1:100[\/latex] (Metric units) or<\/li>\n
                            • [latex]\\tfrac{1}{4}[\/latex]\u2033 or [latex]\\tfrac{1}{8}[\/latex]\u2033 (Imperial units) scales<\/li>\n<\/ul>\n

                              To scale a Metric drawing<\/h3>\n

                              Multiply the measurement on the drawing with the denominator where the denominator is the number after the colon.<\/p>\n

                              Example<\/strong> – Blueprint Drawing Scale [latex]1:50[\/latex]<\/p>\n

                              An actual length of 1 cm is measured on a [latex]1:50[\/latex] blueprint floor plan. The physical length can be calculated as<\/p>\n

                              (1 cm) 50 = 50 cm<\/p>\n

                              Imperial units – US<\/h3>\n

                              A [latex]\\tfrac{1}{4}[\/latex]\u2033 scale means that each [latex]\\tfrac{1}{4}[\/latex]\u2033 (inch) on the plan counts for 1\u2032 (feet) of actual physical length.<\/p>\n

                              To scale a blueprint in imperial units to actual feet, multiply the measurement on the drawing (in inches decimal equivalent) with the denominator where the denominator is the bottom number.<\/p>\n

                              Example<\/strong> – Blueprint Drawing Scale [latex]\\tfrac{1}{4}[\/latex]<\/p>\n

                              An actual length is measured to 1-3\/8\u201d on a [latex]\\tfrac{1}{4}[\/latex] blueprint floor plan. The physical length can be calculated as<\/p>\n

                              (1-3\/8 inch) 4 = (1.375 inch) 4<\/p>\n

                              = 5.5 feet<\/p>\n

                              = 5\u2032 6\u2033<\/p>\n

                              If you know the measurement of the actual object, and have the ratio scale, you would divide <\/strong>the number of the real life measurements by the denominator of the ratio.<\/p>\n

                              Commonly Used Drawing Scales<\/h2>\n

                              Details<\/h3>\n
                                \n
                              • [latex]1:1[\/latex]<\/li>\n
                              • [latex]1:5[\/latex]<\/li>\n
                              • [latex]1:10[\/latex]<\/li>\n
                              • [latex]1:20[\/latex]<\/li>\n<\/ul>\n

                                Component drawings, assembly<\/h3>\n
                                  \n
                                • [latex]1:20[\/latex]<\/li>\n
                                • [latex]1:10[\/latex]<\/li>\n
                                • [latex]1:5[\/latex]<\/li>\n<\/ul>\n

                                  Floor plans, general arrangement (GA)<\/h3>\n
                                    \n
                                  • [latex]1:40[\/latex]<\/li>\n
                                  • [latex]1:50[\/latex]<\/li>\n<\/ul>\n

                                    Location plot plans<\/h3>\n
                                      \n
                                    • [latex]1:80[\/latex]<\/li>\n
                                    • [latex]1:100[\/latex]<\/li>\n
                                    • [latex]1:200[\/latex]<\/li>\n
                                    • [latex]1:500[\/latex]<\/li>\n<\/ul>\n

                                      Block plan, city maps, and larger<\/h3>\n
                                        \n
                                      • [latex]1:1000[\/latex]<\/li>\n
                                      • [latex]1:1250[\/latex]<\/li>\n
                                      • [latex]1:2500[\/latex]<\/li>\n<\/ul>\n

                                        Ordnance survey maps<\/h3>\n
                                          \n
                                        • [latex]1:100000[\/latex]<\/li>\n
                                        • [latex]1:50000[\/latex]<\/li>\n
                                        • [latex]1:25000[\/latex]<\/li>\n
                                        • [latex]1:10000[\/latex]<\/li>\n<\/ul>\n","protected":false},"author":2001,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-136","chapter","type-chapter","status-publish","hentry"],"part":116,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapters\/136","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/wp\/v2\/users\/2001"}],"version-history":[{"count":6,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapters\/136\/revisions"}],"predecessor-version":[{"id":894,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapters\/136\/revisions\/894"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/parts\/116"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapters\/136\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/wp\/v2\/media?parent=136"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapter-type?post=136"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/wp\/v2\/contributor?post=136"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/wp\/v2\/license?post=136"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}