How to Add Negative Fractions | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to add negative fractions and this is going to take our knowledge of adding positive fractions and adding positive and negative integers so something to keep in mind as we go through our examples let's jump into number one where we have negative three-fifths plus one-third now the first thing that we need to do when adding fractions we need to find a common denominator so that bottom number we have a five and a three so we need to find the least common multiple between those two denominators and that's going to be our least common denominator now you may be able to figure out what that least common multiple between our denominators is without writing out the multiples i'm going to write out the multiples for a quick refresher in case you need it so five and three the multiples of five i'm going to do the first five so 5 10 15 20 [Music] and then the first five multiples of three and we're looking for a match here 9 12 15. so we want the least common multiple so the smallest in value that they have in common well that's going to be 15. so that's our common denominator so we are going to use 15 for our least common denominator and now we need to rename our fractions with that denominator so equivalent fractions with that denominator of 15. so let's start with negative three-fifths so how do we get five our denominator there to equal fifteen well multiply it by three five times three is fifteen now whatever we do to the bottom we must do to the top in order to keep this equivalent so negative 3 times 3 is negative 9. so negative 9 15 is our renamed equivalent fraction with that denominator of 15. let's do one third we know three times five is fifteen so whatever we do to the bottom we do to the top one times five is 5. so 5 15 is our renamed equivalent fraction for 1 3. now we have a common denominator so we are able to add now just like when we add positive fractions we are going to add our numerators so negative 9 plus a positive 5. that gives us negative 4. so that's our numerator and then keep our denominator of 15 the same always check to see if you can simplify your answer the only common factor between our numerator and denominator is one so we are in simplest form and we are done so negative four fifteenths let's move on to number two where we have negative six tenths plus negative two eighths so the first thing that we need to do find a common denominator and we're going to find the least common denominator by finding the least common multiple between 10 and 8. and we're going to start with 10 so let's write out the first five multiples of 10. so 10 20 30 40 50. and then let's write out four or five multiples of eight and see if we have any common multiple so 8 16 24 32 40. so 40 is a common multiple and that happens to be the least common multiple so that's going to be our least common denominator so let's rewrite these fractions using our least common denominator of 40. so again we're going to find equivalent fractions here with that denominator of 40. so let's start with negative 6 tenths we need to think how do we get 10 to equal 40 and then apply that to our numerator so we get an equivalent fraction well we know 10 times 4 is 40 so let's do that to the top in order to keep this equivalent so negative 6 times 4 is negative 24. now let's do negative 2 8. how do we get 8 to equal 40 well we multiply it by 5. so let's do that to the top to keep this equivalent negative 2 times 5 is negative 10. now we have our fractions renamed with that least common denominator of 40. so we are now able to add let's add our numerators so negative 24 plus negative 10 equals negative 34. so that is our numerator and then our denominator is 40. so we have negative 34 40ths now we do have a common factor of 2 between our numerator and denominator so we can simplify let's divide both of these by 2 to get our answer in simplest form so negative 34 divided by 2 is negative 17 and then 40 divided by 2 is 20. so our simplified answer is negative 17 twentieths now one more thing i do want to mention is how to write out negative fractions there are different ways we can write the negative sign with the numerator in front of the fraction or with the denominator so keep in mind there are different ways to write out negative fractions now i go into more detail in another video i drop that link down in the description so there you have it there's how you add negative fractions i hope that helped thanks so much for watching until next time peace you