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we're asked how many inches are in four and a half yards and we'll do it a couple of ways one we could just say how many inches are in four yards and how many inches are and a half a yard and this is really four plus one half yards or we can convert this into an improper fraction first and then convert but before I even do that let's just think about how many inches there are in a yard so if I have one yard if I have one yard we know that there are we know that there are three feet we know that there are three feet for every one yard right and when you say wait why do you why am i multiplying by three instead of saying there's one yard for every three feet and the easiest way to think about it is you what you're going to have a larger value over here and you're also you're also going to want to have these units right over here cancel out so yard is cancelling out with yard so you have one yard is equal to is equal to three feet which is kind of what we already knew I'm just showing you how the dimensions cancel out and how many inches are there per foot well we know that there are 12 inches there are 12 inches for every 1 foot and same logic over here inches is a smaller unit of measurement so it makes sense that we're multiplying by 12 3 feet is going to be more inches we're multiplying by 12 and also these units cancel out foot in the numerator foot in the denominator 3 times 12 divided by 1 is equal to 36 36 inches so you might have already known it but this is nice to have the dimensions cancel out like this we know that one yard is equal to 36 36 inches or there are 36 inches for every one yard and so that we can now either break this down or we could turn this into an improper fraction first I'll just break it down into 4 yards plus 1/2 yards so we could say that this is 4 yards so 4 yards is going to be equal to well let's just multiply it times 36 inches 36 inches for every one yard the yards cancel out 4 times 36 is 120 plus 24 so that's 144 so this is equal to 144 144 inches that's just the 4 yards and then if we do the half yards if we do the half yards so one half of a I guess I just say one half yard once again times thirty six inches per yard the yards cancel out one half times 36 is going to be equal to 18 inches 18 inches so 4 and 1/2 yards the same thing as 4 yards plus one half yards which is the same thing as 144 inches plus 18 inches which is going to give us let's just add it up over here on the right 144 plus 18 4 plus 8 is 12 4 plus 1 is 5 you have this one up here so it's 6 and then we have a 1 so when you add them all together you get 162 inches the other way to do this would have been to convert this into an improper fraction and then multiply by the unit so let's do it that way if I have 4 and 1/2 of anything really so let me write 4 and a half trying to find a suitable color so if I have 4 and a half this is the same thing this is the same thing 4 is the same thing as 8 halves this is the same thing so let me write it this way 4 and 1/2 the same thing as 4 plus 1/2 which is the same thing as 4 if we want to have a same denominator as this 2 over here or is it just 1/2 over here this is the same thing as 8 over 2 or you could say 4 over 1 is the same thing as 8 over 2 if we won't have a common denominator so 8 over 2 plus 1 over 2 actually let me write it that way just so you really understand what we're doing 4 is the same thing as 4 over 1 so it's 4 over 1 plus 1/2 if we want to find a common denominator it's 2 so 4 over 1 is the same thing as 8 over 2 plus 1/2 which is equal to 9 halves now I did it this way which takes longer just so you really understand how we converted it why it makes hopefully conceptually how why it just makes intuitive sense why 4 and 1/2 is the same thing as 9 halves but if you want a simple process for it you could just say look 4 times 2 is 8 8 plus 1 is 9 and that gives you that 9 right over there so 9 halves so we have 9 1/2 yards that we want to convert to inches so we have 9 half yards that we want to convert to inches same process times 36 inches times 36 inches per yards yard in the numerator yard in the denominator we are left with 9 over 2 times 36 times we could say times 36 over 1 if we like times 36 over 1 36 inches for every 1 yard 36 or the number 36 really is the same as 36 over 1 and then we're left with just inches in our units we're just left with inches and over here there's several ways that we can simplify it probably the easiest way to simplify it is we can divide both of our numerator and our denominator by 2 so let me write it this way I don't want to skip step so we have 9 times 36 over 2 times 1 or over 2 inches and we can divide the numerator and the denominator by 2 to simplify it they're both divisible by 2 36 divided by 2 is 18 2 divided by 2 is 1 so we're really just left with 9 times 18 inches and you just we can just multiply 9 times 18 let me do it over here 18 times 9 8 times 9 is 72 1 times 9 is 9 plus 7 is 100 or it's 16 so we get 162 inches so all of this simplifies to 162 inches and we are done