WEBVTT 00:00:00.500 --> 00:00:03.868 Welcome to GCSE Edexcel Maths revision. 00:00:04.018 --> 00:00:06.979 Topic M 22: Ratio and sharing. 00:00:07.129 --> 00:00:09.924 This video covers Foundation and Higher tiers. 00:00:12.600 --> 00:00:15.924 A ratio compares quantities in a specified order. 00:00:16.074 --> 00:00:22.879 Red : blue equals 2 to 3 means two red parts for every three blue parts; reversing the order changes the ratio. 00:00:25.533 --> 00:00:31.526 Simplify by dividing all parts by their H C F to 18 to 24 equals 3 : 4. 00:00:31.676 --> 00:00:35.837 For three parts, 12 to 18 to 30 equals 2 to 3 : 5. 00:00:38.500 --> 00:00:47.297 Convert quantities to the same units before comparing: 50 centimetres represents 2 metres equals 50 to 200 equals 1 : 4. 00:00:49.967 --> 00:00:55.747 A part-to-part ratio 2 to 3 gives part-to-whole fractions 2 over 5 and 3 over 5 . 00:00:55.897 --> 00:01:00.665 The first part is 2 over 3 of the second part, but 2 over 5 of the total. 00:01:00.815 --> 00:01:03.546 Ratio bar for sharing eighty-four pounds 00:01:08.200 --> 00:01:11.101 To express one quantity as a fraction of another, 00:01:11.251 --> 00:01:19.708 use the fraction with numerator open bracket first quantity close bracket and denominator open bracket second quantity close bracket , 00:01:19.858 --> 00:01:22.034 end fraction with matching units. 00:01:22.184 --> 00:01:24.104 The fraction can exceed 1. 00:01:26.767 --> 00:01:30.717 Worked example: Share 84 pounds in ratio 2 : 5. 00:01:30.867 --> 00:01:36.596 There are 7 parts; each is 12, pounds so the shares are 24 pounds and 60 pounds. 00:01:36.746 --> 00:01:39.848 Check both their total and their simplified ratio. 00:01:42.500 --> 00:01:46.587 Worked example: A to B equals 3 to 7 and B is 28. 00:01:46.737 --> 00:01:52.655 One part is 28 divided by 7 equals 4, so A equals 12 and the total is 40. 00:01:52.805 --> 00:01:55.640 Do not divide 28 by all 10 parts. 00:01:58.300 --> 00:02:03.452 Worked example: Two shares are in ratio 3 to 5 and differ by 18 pounds. 00:02:03.602 --> 00:02:10.865 Two parts represent 18, pounds so one part is 9 pounds; the shares are 27 pounds and 45 pounds. 00:02:13.533 --> 00:02:16.835 For mixing, preserve the ratio when scaling quantities. 00:02:16.985 --> 00:02:25.719 A drink mixed concentrate : water equals 1 to 4 needs 200 ml concentrate and 800 ml water for 1 litre of drink. 00:02:28.400 --> 00:02:34.937 If a ratio describes concentrations or mixtures, be clear whether it is a mass ratio or volume ratio. 00:02:35.087 --> 00:02:38.084 Do not combine incompatible units silently. 00:02:40.767 --> 00:02:51.293 Equivalent ratios have equal quotients: a to b equals c to d means the fraction with numerator open bracket a close bracket and denominator open bracket b close bracket , 00:02:51.443 --> 00:02:59.377 end fraction equals the fraction with numerator open bracket c close bracket and denominator open bracket d close bracket , 00:02:59.527 --> 00:03:02.386 end fraction where denominators are non-zero. 00:03:02.536 --> 00:03:05.595 This links ratios to proportional relationships. 00:03:08.267 --> 00:03:12.820 If x to y equals 2 to 5, then y equals 5 over 2 x. 00:03:12.970 --> 00:03:17.067 On a y-against-x graph this is a straight line through the origin. 00:03:19.733 --> 00:03:29.673 To combine A to B equals 2 to 3 and B to C equals 4 to 5, make B match: 8 to 12 and 12 to 15, so A to B to C equals 8 to 12 : 15. 00:03:32.333 --> 00:03:36.687 Adding the same amount to both quantities generally changes their ratio. 00:03:36.837 --> 00:03:42.033 A 2 to 3 mixture does not stay in that ratio if you add 1 litre to each component. 00:03:44.700 --> 00:03:49.788 After a change, work with actual quantities or parts before simplifying the new ratio. 00:03:49.938 --> 00:03:55.249 Multiplying both quantities by the same factor preserves the ratio; adding does not. 00:03:57.900 --> 00:04:00.097 That completes Ratio and sharing. 00:04:00.247 --> 00:04:03.593 Revisit the notes and test yourself on the revision website.