Adding and Subtracting Mixed Numbers 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 and subtract mixed numbers and we have one example each that we're going to go through together in order to get this down so let's jump into number one where we have five and two sevenths plus three and a half now before i start i wanna mention that if you're able to add and subtract fractions with unlike denominators you'll be able to do these types of problems there's just a couple of extra steps but you'll be good to go so let's start with number one and the first thing i like to do is line these up vertically so up and down so five and two sevenths plus 3 and a half now the first thing we want to do we need to see do we have a common denominator between our fractions so can we add our fractions right away no we don't have a common denominator so we need to find one and rename so we have a seven and a two so the least common denominator for a seven and a two is going to be 14. so let's rename here we'll put an equal sign and we have five and how many fourteenths and then three and how many fourteenths well we know 7 times 2 gives us 14 so we need to do the same thing to the top we're doing the same exact thing we do when we add fractions we just have a whole number in front so 2 times 2 do the same exact thing to the top 2 times 2 is 4. so 2 7 is equivalent to 4 14. so we renamed with that common denominator least common denominator of 14. so let's do it to the half here we know that 2 times 7 is 14 so do the same exact thing to the top to keep it equivalent 1 times 7 is 7 and this is addition so now once we have that common denominator and we renamed we're able to add or subtract so let's add our fractions first 4 plus 7 is 11 and this is 14 and then we add our whole numbers so 5 plus 3 is 8. so once you get to that point check to see if you can simplify the fractional part so do we have any common factors between the 11 and 14 while the only common factor is one so this is in simplest form our final answer is 8 and 11 14. let's move to number two where we have subtraction and subtraction is the same exact thing that we just did but instead of adding we're going to subtract so let's line up vertically up and down so 7 and 11 12 minus 2 and 3 4. so do we have a common denominator between our two fractions are we able to subtract right away no so we need to find a common denominator and the least common denominator between a twelve and a four is going to be twelve so let's rename so we have seven and how many twelfths and two and how many twelfths well seven and eleven twelfths already has a denominator of twelve so we don't need to rename so let's transfer our 11 over now we do need to rename the three fourths so we know four times 3 is 12 do the same thing to the top to get an equivalent fraction here so 3 times 3 is 9. so 3 4 is equivalent to 9 12 and both fractions have a common denominator now so we are able to subtract so to recap we didn't have a common denominator so we were not able to subtract so we found one we renamed and now we're ready to subtract so eleven minus nine gives us two and we have twelfths now do the whole numbers so seven minus two is five and we get to five and 2 12. now before we finish we always look to see if we can simplify the fractional part and we can because we have a common factor other than 1 between our numerator 2 and our denominator 12 a common factor of 2 between both of those so let's divide both by 2 to simplify here and we get 5 and one sixth and one-sixth is in simplest form the only common factor between one and six is one so we are done the final answer to number two is five and one-sixth so there you have it there's how you add and subtract mixed numbers i hope that helped thanks so much for watching until next time peace