Equivalent fraction visually

so what I want you to do is pause this video and think about what fraction the red part represents in each of these I guess each of these shapes or what fraction of the whole does the red part represent and I also want you to plot it out on a number line to plot that fraction as a number on a number line so let's go through each of these so in this pie right over here we have one two three four five equal sections and one of those five equal sections is shaded in so we could say that one-fifth of this pie is shaded in now over here we have one two three four five six seven eight nine 10 equal sections and two of them are shaded in so we could say that two tenths are shaded in and then finally right over here once again we have 1 2 3 4 5 6 7 8 9 10 equal sections 10 equal sections and two of them are shaded in red so in this situation the red of the red slices represent two tenths of the whole and if we were to try to plot this on a number line so right over here we do a quick one right over here let me see let me do it like this make a big number line here and let's take the section between 0 & 1 that's what we want to focus on and I'm going to divide it into five equal sections so one two three four five equal sections and then that gets us to one so this right over here one fifth that would be one out of the 5 equal sections so that would get us right over there so this would be this would be one-fifth now what I want to do let me copy and paste this same number line since I've already drawn it so copy and paste it so let me put it right over here but now I'm going to divide it into ten equal sections so if we take let's see let me divide it into ten equal sections on the top one so one two three four five six seven eight nine ten so I've divided it into 10 equal sections and I want to figure out where 2/10 goes so I'm going to go two of those equal sections so one two so once again I've got to that exact same point so this 1/5 I could also represent as two over ten so I could represent this as two over ten this point right over here and you might be saying hey wait but that means that those are the same number they're the exact same point on the number line and if you said that you would be absolutely correct 1/5 is equal to 2/10 they represent the exact same number and it makes sense even when you visually look at them as a fraction of these pies here going from this this slice to this slice if you were to just if you were to just divide all of these slices into two if you just divide all of these slices into two you see that you have the exact same fraction you have the exact same fraction shaded in as this one right over here they've become identical I didn't shade in anything else I'd haven't taken any of the red away I haven't added any of the red I just divided all of those all of those pieces of pie into two and so you see that the exact same part of the whole pie shaded in and here it's not quite as obvious but if you imagined taking this dividing it into two and then splitting them up so that they look like this you still have the same part of the circle you still have the same part of the circle shaded in red so it makes complete sense that they represent the same number on the number line that this number right over here it's not only 1/5 it also is 2/10 1/5 is equal to 2/10