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you're having a movie marathon each movie lasts about 1 and 3/4 hours if you want to watch three movies how long will your movie marathon last you can use the number line below to help you find your answer so each movie less 1 and 3/4 1 and 3/4 hours long so let's say the first movie so let's say the first movie happens to be Star Wars which I probably would include in any movie marathon so it's going to be 1 in 3/4 hours long so this is a see this is 1 1 and then we're going to have 3/4 more so each of these are fourth because we have four sections between 1 and 2 1 2 3 4 so we're going to watch 3/4 it's 1 2 3 so that's how long my first movie is and then my second movie is going to be another 1 and 3/4 so 1 is 4/4 so 1 2 3 4 and then we have another 3/4 1 2 3 and just as the way I said that 4/4 and 3/4 is 7/4 so 1 in 3/4 that's the same thing as 7/4 and you see that over here when I did the 1 and 3/4 in blue I actually marked off 7/4 same thing here here in magenta and now let's do it in green so Gandhi is actually a good bit longer than 1 and 3/4 but it's a good movie so I put it here just because one of my favorite and so let's do another one in 3/4 hours so or we could view that is 4/4 plus 3/4 hours or seven four it's one two three four five six seven so that gets us that gets us to five so this point right over here is 5 and 1/4 it's ours let's see if we got that same if we get the same result when we do it when we do it mathematically I guess this is mathematical as well but every movie lasts 1 and 3/4 hours we already said that one in 3/4 is the same thing as 1 plus 3/4 is the same thing 1 is the same thing as 4/4 so it's 4/4 plus 3/4 which is the same thing as 7/4 and another way to convert this mixed number into an improper fraction you say hey look four times one is four and that's really where you're getting the four fourths from plus three seven seven forts now we're going to we're going to do seven fourths of an hour three times so we're going to multiply seven fourths seven fourths times three times three now there's several ways that you could think about this you could literally view this as having seven three seven forts and adding them together so seven fourths plus seven fourths plus seven fourths which would be equal to 21 over four and if you wanted to convert this into a mixed number 21 over 4 is the same thing as well 4 goes into 20 evenly so you could call this 20 over 4 plus 1 over 4 and 20 over 4 is the same thing as 5 so it's five and one five and 1/4 which is exactly what we saw here another way of thinking about it you could say 7/4 and then we can multiply it by 3 over 1 times 3 over one just to make it clear that we're multiplying the numerators and multiplying the denominators so in the numerator I'm going to have 7 plus 7 plus 7 that's 7 times 3 and the denominator gonna have 4 times 1 which is just 4 well this is just 7 times 3 over 4 or 21 over 4 which we've already seen is 5 and 1/4