![]() Or the smaller side, or the point, pointing to the smaller number. So we want the larger side or the opening on the larger number. So how do we write the symbol? Well we always want to open So we see that both 10/7 and 5/3 are between one and two, but which one of these is actually larger? Well we see 5/3 is further to the right on the number line than 10/7. So this is 1/7, this isĢ/7, 3/7, 4/7, 5/7, 6/7, this is 7/7, I could write that down, this is, one is the same thing as 7/7, 8/7, 9/7, 10/7 right over here. ![]() It would be sqrt (26 34 13) which can be simplified to 23 32 sqrt (13) 72sqrt (13). To split the part of the number line between zero and one or between each whole number So for your example of 67392, find the prime factorization then take the square root. And if we were to go over here, two would be the same thing as 6/3. This is 4/3, and then this right over here is going to be 5/3. So this is 1/3, this isĢ/3, this is 3/3, which is, of course, the same thing as one. So I'm marking off all of the- I'm marking off all of the thirds. Sections, one, two, and three, you see that right over here. And then the space from one to two is split into three equal The space from zero to one is split into three equal You see right over here, this is 1/3, this is 2/3, the thirdsĪre being marked off in blue right over here. We have zero, one, two and, first, I divide the number line into thirds. That, I'm going to plot each of these on a number line and I encourage you to pause this video and try to do the sameīefore I work it out. So which of these is going to be larger? And to help us with And a whole here wouldīe 7/7, this is 10/7. So you cannot say that.The fraction 5/3 to 10/7 or which- if we can figure out which one of these fractions is larger. ![]() Over here is not equal in size to this part right But remember, it needsĬlear looking at this that this part right Say, well, I've got 5 parts, and then I've shaded in 1. This right over here isġ/5 of the entire pie. Of pie-looking thing, this circle-looking thing, we Right over here represents 1/3 of the whole. Red part represent? And so I encourage youįor this rectangle, we have 3 equal parts, and Triangle as a whole, what fraction does this Red part represent? If you view this yellow Purple thing, the whole, what fraction does thisīlue part the whole, what fraction does this Or a piece of paper write down if you consider this Right now is pause the video, and either in your head Square right over here that I'm shading in red This one to show you it does not have to be And then if I were toĭivide each of those into 2 equal parts, I Of those into 2 equal parts to get me 4 equal parts. This whole, in this case, the whole is this You could view this asġ of the 4 equal parts, or you could view thisĪs a whole divided by 4 would get you exactly this much. Have shaded in red? Well, it is 1 out of theĤ equal parts, right? I've shaded in 1 out ofġ/4 of the whole. So with one cut like that, I'veĭivided it into 2 equal parts, and then with another Now, what I'm going to do isĭivide this into 4 equal parts. But first, we'll thinkĪbout the most fundamental. Talk about in this video is the idea of a fraction. So how big is the smaller triangle? Using the same ways of calculations we get that the area of the small triangle is approximetly 0,05 cm squared. So we know the whole triangle is approximetly 0,435 cm squared large. We can find the height using the pythagorean theorem, which tells us that the heigth will be approximetly 0,87 cm or to be exact the half of the square root of 3. Don't worry if you don't understand right now. So how big is the whole triangle? The formula for area of any triangle is half of base times it's heigth also known as bh/2. So what is the area of that small triangle compared to the whole shape? Let's do some calculations: Let's say each side of the whole triangle is excatly 1 cm (you can also use inches or no units as well if that helps). How many triangles would you need? The answer is excatly 8 - meaning that the small triangle is just a 1/8th. Let's leave calculations aside - when we look at the small triangle and the whole triangle, we have to ask ourselves: "How many times would that small triangle fit into the whole?" Try imagining having infinite amount of these small triangle to play with and your goal is to build a copy of the whole triangle. Therefore we might think that the area of each part is 1/4th of the whole triangle as well, but unfortunately we're looking for equal area not equal parts of a side. Looking at the video we can see that one of the sides is devided into four 1/4ths. Equilateral means the triangle has all the sides of the same length and all the angles of the same size. I'm gonna assume that that triangle is equilateral. ![]() What a great question! Let's go think about it using geometry.
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