How To Add Signed Fractions

we have negative 3/4minus 7/6 minus 3/6. and there's manyways to do this. but it immediatelyjumps out at me that these last two numbershave a 6 in the denominator. so i'm going to worryabout these first.

How To Add Signed Fractions, i'm going to view this asnegative 7/6 minus 3/6. so if we have negative7/6 minus 3/6, that's going to be the samething as negative 7 minus 3 over 6.

and of course, wehave this negative 3/4 out front thatwe're going to add to whatever we get over here. so this is these two termsthat i'm adding together. negative 7 minus3 is negative 10. so it's negative 10 over 6. and then i'm going to haveto add that to negative 3/4. and now i have to worry aboutfinding a common denominator. let me write that sothey have a similar size.

so now i have to worry aboutfinding a common denominator. what is the smallest number thatis a multiple of both 4 and 6? well, it might jump outat you that it's 12. you can literally just gothrough the multiples of 4. or you could look atthe prime factorization of both of these numbers. and what's thesmallest number that has all of the primefactors of both of these? so you need two 2s, andyou need a 2 and a 3.

so if you have two 2s and a3, that's 4 times 3 is 12. so let's rewrite thisas something over 12 plus something over 12. well, to get yourdenominator from 4 to 12, you have to multiply by 3. so let's multiply ournumerator by 3 as well. so if we multiplynegative 3 times 3, you're going to have negative 9. and to get yourdenominator from 6 to 12,

you have to multiply by 2. so let's multiply ournumerator by 2 as well so that we don't change thevalue of the fraction. so that's goingto be negative 20. and now we're ready to add. our common denominator is 12. and so this is going to benegative 9 plus negative 20, or we could even writethat as minus 20, over 12, which is equal to--and we deserve a drum roll now.

this is negative 29 over 12. and 29 is a primenumber, so it's not going to share any commonfactors other than 1 with 12. so we also have this inthe most simplified form.