How to Subtract Negative Fractions | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to subtract negative fractions now this is going to combine knowledge of subtracting positive fractions and subtracting positive and negative integers so we are going to combine those two things when we subtract negative fractions so something to keep in mind let's jump into our examples starting with number one where we have negative three-fourths minus one-sixth now just like when we subtract positive fractions we need a common denominator so the least common denominator between four and six is going to be the least common multiple between four and six now we may be able to think what that least common multiple uh will be without writing out our lists of multiples for four and six but just as a refresher i will write out the multiples so let's start with four and again we're looking for the least common multiple so the smallest multiple in value that they share here so we can count up by fours 4 8 12 16 20. now those multiples go on forever so we can just write the first five and see if we have any in common if not we can always extend our lists so 6 12 18 24 30. so we are looking for the least common multiple so the smallest multiple and value that they share and that is going to be 12. so that's the least common multiple and therefore it's going to be our least common denominator so 12 here and now we need to rename our fractions with that common denominator of 12. now these are going to be equivalent fractions so we are not changing the value of the problem at all let's start with negative three-fourths so how do we get 4 to equal 12 well 4 times 3 is 12. so whatever we do to the bottom we have to do to the top in order to keep this equivalent so negative 3 times 3 is negative 9. negative 9 12 is equivalent to negative 3 4 but we renamed it with that common denominator of 12. now we need to do 1 6. so how do we get 6 to equal 12 well multiply it by 2. whatever we do to the bottom we need to do to the top to keep it equivalent 1 times 2 is 2. so now we have our common denominator of 12 and we have our fractions renamed with that common denominator of 12. so we are able to subtract now just like when we subtract positive and negative integers we can add the opposite so let's add the opposite well the opposite of positive 2 12 is negative 2 12 now we can add our numerators negative 9 plus negative 2 is negative 11 and we keep our denominator of 12. always check to see if you can simplify your answer well the only common factor between our numerator and denominator is one so we are in simplest form and our final answer is negative 11 12. let's move on to number two where we have negative 5 15 minus negative 9 10 now again the first thing that we need to do we need to find a common denominator and the least common denominator is going to be our least common multiple so let's find the least common multiple between 15 and 10. we'll start by writing out the multiples of 15. so 15 30. now you may notice that 30 is going to be a multiple of 10 as well so there would be no reason to continue our lists if you either know the least common multiple off the bat and you can think of it or if you find it while you're writing out your lists again there would be no reason to continue on if you recognize that i'm going to continue going and write out four multiples of each and then kind of go from there so this would be 45 and then 60. so let's write out our multiples of 10 here so 10 20 30 like we talked about 40. so 30 is going to be our least common multiple so i wrote out four multiples each for 15 and 10 and then looked for the least common multiple again like we talked about with number one if you do not see a least common multiple as you write out your lists you can always extend your list my suggestion write four or five multiples and then go from there so our least common multiple and therefore our least common denominator is going to be 30. now let's rename how do we get 15 to equal 30 well multiply it by 2. do the same thing to the top negative 5 times 2 is negative 10. how do we get 10 to equal 30 let's do negative nine-tenths well multiply by three do the same thing to the top to keep it equivalent negative nine times three negative 27. now that we have our common denominator of 30 and our fractions renamed we have equivalent fractions there remember we're not changing the value of anything these are equivalent we are ready to subtract again just like when we subtract positive and negative integers we can add the opposite so the opposite of a negative 27 30 would be a positive twenty-seven thirtieths so let's add a negative ten plus a positive twenty-seven equals a positive seventeen and we keep our denominator of 30 the same now the only common factor between 17 and 30 is one so this is in simplest form and we are done seventeen thirtieths now there is one more thing i do want to mention and it's about subtracting a negative so for example number two we started with negative five fifteenths and we subtracted negative nine tenths we ended up for our answer with 17 thirtieths so we increased in value even though this was a subtraction problem now that's because when you subtract a negative you actually increase in value you can think of it as subtracting or taking away debt which is a good positive thing so again when you subtract a negative you are going to increase in value that's something to think about and keep in mind when working with negatives so there you have it there's how you subtract negative fractions i hope that helped thanks so much for watching until next time peace you