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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 let's just do the first part first it's pretty straightforward we have two positive numbers let me draw a number line so let me draw a number line and I'll try to focus in so we're gonna start 3 and 1/8 so let's break this zero so you have 1 2 3 and then you have 4 3 and 1/8 is going to be right about there so let me just draw its absolute value so this 3 and 1/8 3 and 1/8 is going to be 3 and 1/8 to the right of 0 so it's going to be exactly that distance from 0 to the right so this right here the length of this arrow you could view it as 3 and 1/8 now whenever I like to deal with fractions especially they have different denominators and and all of that I like to deal with them as improper fraction so it makes the addition in the subtraction and actually the multiplication in the division a lot easier so 3 and 1/8 is the same thing as 8 times 3 is 24 plus 1 is 25 over 8 so this is 25 over 8 which is the same thing as 3 and 1/8 another way to think about it 3 is 24 over 8 and then you add 1/8 to that so you get 25 over 8 so this is our starting point now to that we're going to add 3/4 we are going to add 3/4 so we're going to move another 3/4 we are going to move another 3/4 it's hard drawing these arrows we're going to move another 3/4 to the right so this right here the length of this that we're moving to the right is 3/4 its so plus 3/4 now where does this put us well both of these are positive integers so we can just add them you just have to find a like denominator so we have 25 over 8 we have 25 over 8 plus 3/4 that's the same thing as we need to find a common denominator here the common denominator or the least common multiple of 4 and 8 is 8 this is going to be something over 8 to get from 4 to 8 we multiply by 2 so we have to multiply 3 by 2 as well so you get 6 so 3/4 is the same is six eight six eight we have twenty five eighths and we're adding six eighths to that that gives us twenty five plus six is thirty one over eight so this number right over here this number right over here is thirty one over eight thirty one over eight and it makes sense because thirty-two over eight would be four so it should be a little bit less than four so this number right over here this number right over here is 31 over eight or the length of this arrow the absolute value of that number is 31 over eight a little bit less than a little bit Lesson four if you wanted to write that as a mixed number it would be it would be what three and seven it would be three and seven eighths so that's that right over here this is 31 31 over eight that's that part right over there now to that we want to add a negative 2 and 1/6 so we're going to add a negative number so think about what negative 2 and 1/6 is going to be like so let me do this in a new color do it in pink negative 2 and 1/6 so we're going to subtract or I guess we just say we're going to add a negative 1 we're gonna add a negative 2 and then a negative 1/6 let me draw so negative 2 and 1/6 we could literally draw like this we could literally draw it like this negative 2 and 1/6 we can draw with an arrow that looks something like that so this is negative 2 and 1/6 now there's a couple of ways to think about it you could just say look when you add this arrow this thing that's moving to the left right we could put it over here and you would get straight to negative 2 and 1/6 but we're adding this negative 2 and 1/6 it's the same thing as as subtracting a positive 2 in 1/6 we're moving 2 and 1/6 to the left and we're going to end up we're gonna end up with a number whose absolute value is going to look something like that and it's actually going to be to the right so it's not going to only be its absolute value it's going to be well its absolute value is going to be the number since it's going to be a positive number so let's just think about what it is this value right here which is going to be the answer to our problem is just going to be the difference of 31 over 8 and 2 and 1/6 and it's the positive difference because we're dealing with a positive numbers we just take 31 over 8 and from that we will subtract 2 and 1/6 so let's do this so this orange value is going to be 31 over 831 over 8 minus 2 and 1/6 so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 plus minus 13 over 6 and this is equal to once again we need to get a common denominator over here and looks like 24 will be the common denominator 24 let me make it very clear this 30 what this is the 31 over 8 and this is the 2 and 1/6 this right here is the 2 and 1/6 so 31 over 8 over 24 you have to multiply by 3 to get to the 24 over here so we multiply by 3 on the 31 that gives us 93 and then to go from 6 to 24 you have to multiply by 4 let me do that in another color you have to multiply it by 4 so we have to multiply by 4 up here as well so 4 times 13 let's see 4 times 10 is 40 4 times 3 is 12 so that's 52 so this is going to be equal to 93 minus 52 over 24 and that is so 93 minus 52 3 minus 2 is 1 9 minus 5 is 4 so it is 41 over 41 over 24 and positive and you can see that here just by looking at the number line this right here is 41 over 24 and it should be a little bit less than 2 because 2 would be 48 over 24 so this would be 48 over 24 it makes sense that we're a little bit less than that