Subtracting Fractions with Unlike Denominators Math with Mr J

welcome to math with mr in this video i'm going to cover how to subtract fractions with unlike denominators so let's jump into our examples starting with number one where we have 5 6 minus 3 12 now when we subtract fractions we need common denominator just like when we add fractions for number 1 we have 6 and 12. so we don't have common denominator to start with so we can't subtract quite yet the first thing that we need to do is find common denominator and we can do that by finding the least common multiple between our denominators we want the least because smaller numbers in value are generally easier to work with and this will help cut down on simplifying in the end once we get to our answer as far as why we need common denominator that's topic for another video i'll drop that link down in the description now as you're looking at subtraction problem involving fractions with unlike denominators you may recognize the least common multiple between denominators right away but if not you can always write out your lists of multiples in order to find it so let's start by writing some multiples of both 6 and 12 and see if we can find that least common multiple we'll start with six so i'm going to come to the bottom of the screen where have some extra room to write out these lists and we'll start with six so would suggest writing out four or five multiples for each denominator and see if you can find that least common multiple if not you can always extend the lists until you find that least common multiple so if four or five multiples don't work and you don't see any common multiples extend those lists so the first four multiples of six are now we'll do 12. so the first multiple of 12 is 12. now no need to go on if you find that least common multiple because if you look we have least common multiple of 12. so we are ready to move to the next step which is rename so 12 is going to be our common denominator i'm going to come back up to the original problem underneath and start to write the renamed fractions with that common denominator of 12. so underneath i'll start these fractions with that common denominator of 12 and now we're going to rename we'll start with 5 6. so we're going to rename that fraction with an equivalent fraction with the denominator of 12. so we need to think how do we get the denominator of 6 to equal the denominator of 12 6 times what equals 12 well we know that 6 times 2 equals 12. so whatever we do to the denominator the bottom number we have to do to the numerator the top number in order to keep this fraction equivalent we don't want to change the value of the problem at all so we need to do 5 times 2 to get the renamed numerator 5 times 2 is 10. so 10 12 is equivalent to 5 6. so we renamed with that denominator of 12. now we need to do 3 12 well 3 12 already has denominator of 12 so we don't need to rename we can just bring the 3 down once we rename we can subtract when we subtract fractions we subtract the numerators so 10 minus 3 is 7 and then we keep the denominator of 12 the same so 7 12 is our answer now always look to simplify so can we simplify 7 12 well 7 12 is in simplest form the only common factor between 7 and 12 is 1 so we can't break this down any further as far as simplifying goes so our final simplified answer seven twelfths let's try another one and move on to number two where we have nine tenths minus two fourths so the first thing that we need to do find common denominator so we need that least common multiple between 10 and 4 and that's going to be our common denominator let's go down to the bottom and write out some multiples so we'll start with 10 and we'll write out four multiples to start with so 10 20 30 40. now let's write out four multiples of four and see if we have least common multiple so 4 16. so writing out four multiples for each we don't have match so we need to extend our lists now the multiples of 10 we are already at 40 and the multiples of 4 we're only at 16. so let's extend that one and the next multiple of 4 is 20 and that's going to give us common multiple and specifically the least common multiple so we're going to use 20 for our common denominator let's go back up to the original problem underneath and rename with that common denominator of 20. we'll start with nine-tenths so how do we get that denominator of 10 to equal 20 well 10 times 2 is 20 and whatever we do to the denominator we have to do to the numerator in order to keep this equivalent so 9 times 2 gives us 18 for our renamed numerator so 18 twentieths is equivalent to nine tenths we just have that common denominator of twenty now now we need to do two fourths so how do we get four to equal twenty well we know four times five equals twenty so four times five equals twenty so we need to do the same thing to the numerator in order to get that renamed equivalent fraction with the denominator of twenty so same thing to the numerator 2 times 5 gives us 10. now we're ready to subtract so subtract the numerators the top numbers 18 minus is 8. keep the denominator of 20 and our final answer is eight twentieths now eight twentieths can be simplified there are multiple paths that we can take in order to get this into simplest form but if we use the greatest common factor between 8 and 20 we can simplify it in one step the greatest common factor between 8 and 20 is 4 so let's divide both of these by 4 in order to get our simplified answer so 8 divided by 4 and 20 divided by 4 that's going to give us simplified answer of fifths so two-fifths is our final simplified answer now just to be clear eight twentieths is the correct answer but we were able to simplify that fraction and get simplified answer of two-fifths if you need more help or clarification with simplifying fractions added link to my video about that down in the description as far as subtracting fractions with unlike denominators this was part one do have part two where go through two more examples i'll add that link down in the description as well hope that helped thanks so much for watching until next time peace