[Music] welcome to math with mr j [Music] in this video i'm going to cover how to simplify a mixed number and if you know how to simplify a fraction you're going to know how to simplify a mixed number because all we do is simplify the fractional part of a mixed number and leave the whole number alone so let's jump into our examples and see exactly what i mean by that so for number one we have 4 and 10 15. so remember when we simplify a fraction we are looking for common factors that we can divide both the numerator and denominator by we want to break the fraction down to the lowest numbers in value that we possibly can now when the only common factor between the numerator and denominator is 1 we are in simplest form so again we only simplify the fractional part of a mixed number and we leave the whole number so 10 15 what are some common factors of 10 and 15 what can we divide 10 and 15 by well 5 so let's divide the 10 and the 15 by 5 and this is going to equal 4 and well 10 divided by 5 is 2. fifteen divided by five is three two thirds the only common factor between two and three is one so this is in simplest form four and two 3. now if you're unsure about factors and how to find factors or what they are i do have a video on simplifying fractions where we list all the factors for the numerator and denominator and then go from there i'll drop that link down in the description if you need more practice with simplifying fractions let's move on to number two where we have seven and twelve twentieths so we need to think of common factors between twelve and twenty what can we divide both twelve and twenty by well four let's divide them both by four and this is going to give us 7 12 divided by 4 is 3 and 20 divided by 4 is 5. so we get 7 and three fifths the only common factor between three and five is one so the fractional part is in simplest form now for number two there is more than one path that we can take to get to simplest form so let's do this again but using a different common factor so 4 is the greatest common factor between 12 and 20. so we were able to simplify in one step but maybe you are thinking that 2 is a common factor between 12 and 20. they are both even which is correct so let's divide both of them by 2 and see what happens this will give us 7 and well 12 divided by 2 is 6. 20 divided by 2 is 10 so we have 7 and 6 10 which is different than our seven and three-fifths but we still have a common factor other than one six and ten have a common factor of two so we can divide by two again we end up with seven and six divided by two is three ten divided by two is five the only common factor between three and five is one so we are in simplest form seven and three-fifths so two different paths there but the same exact answer both are correct when we divided by four we divided by the greatest common factor between 12 and 20 and we were able to simplify in one step the bottom one where we started by dividing by 2 we divided by something less than the greatest common factor so simplifying took more than one step which again is perfectly okay we got to the same answer either way so there you have it there's how you simplify a mixed number you only need to simplify the fractional part of the mixed number you leave the whole number alone so if you're able to simplify fractions you're able to simplify mixed numbers if you're looking for more help with simplifying fractions i added links to more videos down in the description i hope that helped thanks so much for watching until next time peace you