How to Simplify Fractions (Part 2) | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to simplify a fraction and this is part two so if you need part one that link is down in the description and then you can come back to part two if you're ready for part two let's jump into number one where we have 18 thirtieths so when it comes to simplifying fractions remember we are looking to get the smallest numbers in value that we can for our numerator and denominator the simplest lowest numbers we do this by finding common factors between our numerator and denominator and then dividing them by that common factor that way we break this fraction down to those lowest simplest numbers we talked about so in part one we listed the factors for our numerators and denominators you want to get to the point where you do not need to do that so for part two we are not going to list the factors so for eighteen thirtieths here we need to start by thinking are there any common factors between eighteen and 30. while they are both even so we can divide them both by two and start breaking the fraction down that way now let's try to think of a larger common factor in value other than two that way it's going to take less steps to simplify you want to find the largest factors in value that you can and if you use the greatest common factor you will simplify in one step so for example 18 and 30 here well i know that we can divide 18 by 6 6 is a factor of 18 and 6 is also a factor of 30. let's divide both of these by 6. 6 is actually the greatest common factor so let's divide this by 6 and this by 6. and we get well 18 divided by 6 is 3 and 30 divided by 6 is 5. now the only common factor between 3 and 5 is 1 so this is in simplest form 6 is the greatest common factor between 18 and 30 so we were able to simplify in one step now let's actually do number one again and take a different path to get to the simplest form so let me rewrite eighteen thirtieths and we mentioned that they were both even so we have a common factor of 2 let's divide both of them by 2 and see what happens so divide by the common factor of 2 18 divided by 2 is 9 30 divided by 2 is 15. 9 15 is different than three fifths but 9 and 15 have a common factor of three so we can divide both of those by three because the only common factor isn't one yet when the only common factor is one that's when we're done so nine divided by three is three fifteen divided by three is five so we get three fifths that way as well now let's actually do that one other way so eighteen thirtieths now another common factor of 18 and 30 is 3 so let's see what happens if we divide by 3 first the common factor of 3 so we will divide both of these by 3 and we get 18 divided by 3 is 6 30 divided by 3 is 10 so 6 tenths well that's different than three fifths but we still have a common factor other than one 6 and 10 they're both even so they have a common factor of 2. let's divide both of these by 2 here and we get 6 divided by 2 is 3 and then 10 divided by 2 is 5. so we got three-fifths that way as well so you can see that there are sometimes different paths that we can take in order to simplify a fraction so something to keep in mind but again if you use the greatest common factor you will simplify a fraction in one step now the more you do of these and become more familiar with simplifying fractions and really fractions in general the better you will become at simplifying fractions let's move on to number two where we have 42 forty-ninths now we need to think are there any common factors between 42 and 49 other than 1 that we can divide both these numbers by in order to simplify this fraction or is the only common factor 1 and we are already in simplest form so what we can do now we can take a look at one of our numbers and think of its factors once we start thinking of factors we can see if any will be common factors so for example let's start with 42 here we know that 1 and 42 are factors of 42 are there any other factors well we know 6 times 7 equals 42 so 6 and 7 are factors of 42 let's compare that information to 49 well 49 we know 7 times 7 equals 49 we know 7 is a factor of 49 as well so 7 is a common factor between 42 and 49. let's see if we can think of any other factors that may be larger in value well 3 and 14 are factors of 42 but they are not factors of 49 so let's use 7 and go from there if you have a common factor you can just start there and start breaking the fraction down get to the next fraction and then see if you can continue simplifying or if the only common factor is 1 and you are in simplest form so again let's choose 7 here so we will divide both by 7. 42 divided by 7 is 6 49 divided by seven is seven so we have a six and a seven now the only common factor between six and seven is one so this is in simplest form and 7 happens to be the greatest common factor between 42 and 49 so we were able to simplify in one step so there you have it there's how you simplify a fraction part two i hope that helped thanks so much for watching until next time peace