Converting yards into inches

we're asked how many inches are in four and a half yards let me write that down four and 1/2 yards now whenever we're dealing with fractions and we're going to multiply and divide by fractions it really complicates the issue to have a mixed number so right from the get-go I want to turn this into an improper fraction let me do it in over here in the top right 4 and 1/2 written as an improper fraction is equal to what we're still going to have 2 as a denominator so 2 times 4 is 8 so 8 halves is the same thing as 4 right let me rewrite this this 4 just as a bit of review 4 is the same thing as 8 over 2 that's the same thing as 4 and then you have that plus plus 1/2 that is going to give you 9 halves the quick way to do it 2 times 4 is 8 8 plus 1 is 9 so 4 and a half is the same thing as 9 halves so 4 and 1/2 yards is the same thing as let me write it over here 9 over 2 9 over 2 yards now we want to convert this into inches now just so we can take this in baby steps maybe we convert this into feet first and then once we have it in feet then we can convert it into inches so to convert it into feet we just have to remember that there are three feet for every one yard so let me write that down there are there are three feet there are 3 feet per yard and if we were to multiply 9 halves yards times 3 feet this yard would be in the numerator and be divided by this yard and they would cancel out and we just be left with feet so we know we have to multiply by 3 you could say this is 3 feet for every one yard if it makes it simpler just 3 feet per yard and another way to think about it is however many yards you have you're going to have more feet right there are 3 feet per yard so if I have 1 yard I'm gonna have 3 feet if I'm gonna have 2 yards I'm gonna have 6 feet so you should think about it in your head ok well yeah multiplying by 3 so that also makes sense so if we multiply by 3 right over here the nine times three is twenty-seven over two over two times let me write it out let me take it step by step not skipping any steps so this is equal to 9 over 2 times 3 over 1 times 3 over 1 yards this yards right here I'll do it in orange yards times feet per yards feet per yard times in this purple feet per yard the yards cancel out and you are left with 9 times 3 is equal to 27 27 over 2 27 over 2 feet so we figured out 4 and 1/2 yards is 27 over 2 feet and that makes sense because we should have more feet than yards and actually this should be 3 times more so everything makes sense this 27 over 2 is 3 times 9 over 2 so now we have 27 over 2 feet feet and now we want to convert this to inches and we just have to remember they're 12 inches per yard and we're going to want to multiply by 12 because however many inches we have area however many feet we have we're gonna have 12 times as many inches if we have one foot we're gonna have 12 inches 2 feet 24 inches 27 over 2 feet we're going to multiply it by 12 to get the number of inches so this is going to be times 12 and we'll make sure the the dimensions work out 12 inches 12 inches per foot and the feet on the foot day this is just the plural and the singular of the same word it's the same dimension this will cancel out so this will be if we just rearrange the multiplication view it as everything is getting multiplied and when you just multiply a bunch of things order doesn't matter so this is equal to 27 over 2 times 12 times 12 feet I'm just swapping the order feet times inches inches / feet or foot just the singular of the same word the feet and the foot cancel out they're the same unit and you have 27 times 12 divided by 2 inches and what we could do here is that our final answer is going to be our final answer is going to be 27 times 12 over 2 inches and before we multiply the 27 times 12 and then divide by 2 you immediately see well I can just divide 12 by 2 and 2 by 2 and it makes our computation simpler 12 divided by 2 is 6 2 divided by 2 is 1 so it becomes 27 times 6 inches and let's figure out what that is 27 27 times 6 7 times 6 is 42 2 times 6 is 12 plus 4 is 16 so it's equal to this is equal to 162 162 inches which makes sense 4 and 1/2 yards that gets us to this number right here 27 divided by 2 is 13 and 1/2 feet you multiply that by 12 that makes sense you're gonna have a bunch of inches 162 inches