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Current time:0:00Total duration:5:06

let's think about what it means to multiply 2 over 3 or 2/3 times 4/5 times 4/5 in a previous video we've already seen how we can actually compute this this is going to be equal to in the numerator we just multiply the numerators so it's going to be 2 times 4 2 times 4 and in the denominator or we just multiply the denominator so it's going to be 3 times 5 3 times 5 and so the numerator is going to be 8 and the denominator is going to be 15 and this is about as simple as we can make it 8 and 15 don't have any factors common to each other other than 1 so this is what it is it's 8:15 so but why does that actually make sense and to think about it well we'll think of 2 ways of visualizing it so let's draw 2/3 so let's draw 2/3 I'll draw it relatively big so I'm going to draw 2/3 and I'm going to take 4/5 of it so 2/3 make it pretty big 2/3 2/3 just like this so this is 1/3 and then this would be 2/3 check it a little bit better job making those equal or at least closer to being looking equal so there you go I have thirds let me do it one more time so here I have drawn thirds 2/3 represents two of them it represents two of them and you one way to think about this is this is 2/3 times 4/5 is 4/5 of this 2/3 so how do we how do we divide this 2/3 into fifths well what if we divided each of these sections into five so let's do that so let's divide each into 5 1 2 3 4 5 1 2 3 4 5 and I can even divide this into 5 if I want one two two three four five and we want to take four-fifths of this section here so how many fifths do we have here we have one two three four five six seven eight nine ten and we got to be careful these really aren't fifths these are actually 15s because the hole is this thing over here so I should really say how many fifteenth's do we have and that's that's where we get this number from but you see you have 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 where did that come from I had 3 I had thirds and then I took each of those thirds and I split them into fifths so then I had five times as many sections 3 times 5 is 15 but now we want 4/5 of this right over here so we have this is 1015 s'right over here notice that's the same thing as 2/3 now if we want to take 4/5 of that 4/5 of if you have 10 of something that's going to be 8 of them so we're going to take eight of them so one two three four five six seven eight we took eight of the 15 so that is 815 you could have thought it the exact about it the other way around you could have started with fifths so let me draw it that way so let me draw a hole so this is a hole and let me draw it let me cut it into five equal pieces or as close as I can draw five equal pieces one two three four five 4/5 we're going to we're going to shade in four of them it's four of the five equal pieces three four and now we want to take 2/3 of that well how can we do that well let's split each of these five into three pieces so now we have essentially 15 again so one two three four five six seven eight nine ten 11 12 13 14 15 and we want to take 2/3 of this yellow area we're not taking 2/3 of the whole section we're taking 2/3 of the four so how many 15s do we have here we have 1 2 3 4 5 6 7 8 9 10 11 12 so if you have 12 of something and you want to take 2/3 of that you're going to be taking 8 of it so you're going to be taking 1 2 3 4 5 6 7 8 or 8 of the 15 s now so either way you get to the same result you're one way you're thinking of taking 4/5 of 2/3 another way you could think of it is you're taking 2/3 of 4/5