Adding Fractions with Unlike Denominators | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to add fractions with unlike denominators so let's jump into our examples starting with number one where we have four-ninths plus one-third now when we add fractions we need a common denominator in other words the bottom numbers need to be the same in order to add for number one we have a nine and a three so obviously we don't have a common denominator to start with so we can't add quite yet so the first thing that we need to do is find a common denominator and we can do that by finding the least common multiple between our denominators now as far as why we need a common denominator that's a topic for another video i'll drop that link down in the description so you may recognize the least common multiple between denominators right away when you see the problem but if not you can always write out your lists of multiples in order to find it let's write out the multiples of nine and three so i'll come to the bottom of the screen where i have some extra room to write out these lists we'll start with nine so nine the first multiples of nine are 9 18 27 36 so i'll write four multiples of nine there i would suggest writing out four or five multiples of each see if you have any common multiples and if not you can always extend your lists so let's do three now and see if we have any common multiples three six nine and it looks like we have a common multiple of 9 and more specifically that's going to be the least common multiple we always want to find the least common multiple smaller numbers in value are generally easier to work with and this will help cut down on simplifying in the end so 9 is going to be our common denominator let's come back up to the original problem and rename these fractions with our common denominator of nine so underneath i'm going to write our common denominator of nine and now we can rename so we'll start with four ninths well four ninths already has a denominator of 9 so we don't need to rename so we can just bring the 4 down as far as 1 3 we need to think 3 times what equals 9. how do we get three to equal nine well we know three times three equals nine now in order to rename we want to have an equivalent fraction we want to keep this equivalent we do not want to change the value of the problem at all so whatever we do to the denominator we have to do to the numerator so 1 times 3 is 3. 3 9 is equivalent to one-third but we have that common denominator of nine now now that both fractions have a common denominator we can add so when we add fractions we add the numerators the top numbers four plus three is seven and then we keep the denominator the same so nine seven ninths is our final answer now it's common practice to simplify fractional answers so we look to see if we can break this fraction down at all are there any common factors between seven and nine besides one can we simplify no the only common factor between seven and nine is one so this is in simplest form and we are done seven ninths is our final answer let's try another one and move on to number two where we have three-tenths plus two-sixths so the first thing that we wanna do we need to find a common denominator so let's write out the multiples of ten and six we'll start with 10 so 10 20 30 40. so we'll write out four multiples for each let's do six now six 12 18 24 so 4 for each and we don't have a common multiple that's okay we can extend our lists now the multiples of 10 we're already at 40 and the multiples of 6 were only at 24 so let's extend that list so after 24 would be 30 and now we have a common multiple and specifically the least common multiple so 30 is going to be our common denominator let's rename our fractions with that denominator of 30. let's start with three tenths so we need to think how do we get ten to equal thirty ten times what equals thirty well ten times three equals thirty we know ten times three equals thirty in order to keep this equivalent whatever we do to the denominator we have to do to the numerator so multiply the numerator by three as well three times three is nine so nine thirtieths is equivalent to three tenths but we have that common denominator of thirty now now we do two sixths so we think how do we get six to equal thirty six times what is thirty well six times five is thirty whatever we do to the denominator we do to the numerator so two times five gives us ten ten thirtieths is equivalent to two sixths now that we found the common denominator we renamed we can add so add the numerators nine plus ten is nineteen keep the denominator of thirty and our final answer is nineteen thirtieths we can check to see if we can simplify but nineteen thirtieths is in simplest form the only common factor between nineteen and thirty is one so we are done so there you have it there's how you add fractions with unlike denominators find a common denominator rename with that common denominator add and then look to see if you can simplify now there is a part two i'll add that link down in the description part two will have two more examples and in one of those examples there's an answer that can be simplified so you can see what that looks like also if you need more help with multiples and least common multiple i'll have a link to that video in the description as well i hope that helped thanks so much for watching until next time peace