Explaining one of the Trickiest Ratio Questions

hey guys and welcome to another video in these next series of videos I'm going to do I'm going to pick out extremely hard exam questions that have come out over the past few years and I'm going to show you the exact problem solving methods that you can do so in terms of the video I had previously where I told you how you can get a grade insert whatever like 5 6 7 8 9 I mentioned that in order to get the grade seven 8 and N you really need to get at get good at problem solving it's not just about being able to do the maths it's about applying the maths in order to get to an answer answer and so that's the idea behind this set of videos if you want there is a video where I go through all of ratios from grade 3 to Grade 9 which I'll link in the description that's going to be more of teaching you how to actually do ratios this is going to be teaching you the problem solving elements so anyways this question is super super famous I wouldn't be surprised if it comes up in your mocks or your end of year exams but we have four types of cards in a game each card is either a black circle white circle black triangle or white triangle and as you can tell there are two different colors we have have white and we have black and then we also have two types of shape we have circles and we have triangles so and this works similar to like a normal deck of cards except much more simple because there's fewer suits and things like that but we can say that the number of black shapes to White shapes is 3 to five so this means that for every three black shapes there should be five white shapes now don't forget those shapes can either be circles or triangles as well so these three black shapes they could be two circles and one triangle they could be one Circle and it could be anything right and the number of cards with a circle to the number of cards with a triangle is 2 to 7 now I am a big fan of kind of drawing things out but in this case you might realize that you can't actually draw this out for a very special reason for example if I say three black shapes I'm just going to color in the black shapes um um again I don't know what kind of shapes they will be other than the color and then we have five whites let's just draw five two 3 4 five the problem is I can't actually make them with the correct number of shapes because if you look here it says the number of cards with a circle is two for every seven triangles but the thing is that adds up to a total of nine and this adds up to a total of eight so I can't actually visualize this just yet because we're talking about a different total so in my opinion the best thing to do is to make the totals the same so we're going to look for the lowest common multiple between 8 and 9 which is 72 so Times by 9 * by 8 so we've got the black to white we've times the ratio by 9 so instead of 3 it's going to be 3 * 9 which is 27 and instead of 5 it's going to be 5 * 9 which is 45 and then for circles to triangles we have 2 * 9 for circles which is 18 and we have 7 * 8 for the um triangles which gives me 56 now they have the same total and I can now simp uh I can now draw this out if I wanted to obviously the problem here is drawing out 72 shapes is a bit boring but if you look both these add up to 72 they have the same total I actually don't really care about drawing them out in this case because if you look it says express the total number of cards with a black shape as a fraction of the triangles so in other words I want the number of black shapes over the number of triangles well how many black shapes do I have well I have 27 black ones and I have 56 triangles that's your answer now I know what some of you are probably thinking how do I know that there's 72 cards in the back because technically I could have also made this 144 that's a common multiple if you make this 144 and I want you to check this just in case you'd have to make all of these twice as big if I make the top and bottom of this fraction twice as big it will still simplifi down to 27 over 56 so it doesn't actually matter that this isn't the total number of cards this might not be the total number of cards this is the minimum number of cards but because we're talking about a fraction we're talking about a proportion it doesn't matter if I double it for example let's say half of my Suites are red okay half of them are red I could have one red suite and two blue Suites but I could also have two red Suites and four blue Suites and still get the same fraction when I simplify because don't forget fractions are all about proportion so in this case I don't really care about the total number of cards even though it says that I'm actually working out a proportion and that's a slightly tricky thing with this question it was answered really really badly which is why I've called it a grade n question because remember those grade n questions are just the final 10% of the marks which a lot of it comes from problem solving rather than actual topics but it's only a three mark question and if you look at what I've done I've done it very quickly I've times them by 9 and 8 and then just made a fraction but again it's the problem solving so whenever you do anything with maths you need to think about what it's trying to tell you and what the point is what does this 3 to five mean what does this 2 to7 mean what is it and what does this question actually mean in terms of proportion is it a number is it a percentage what is it and I hope that helps I'm going to do a few more videos like this where they're very short they're very contained and I'll link you to videos which which explain in more detail what the topic is but it's all about the problem solving so without further Ado I'll see you in the next one