in today's video we're going to look at how you add and subtract fractions and there are really two key points you need to know the first is that you have to have a common denominator which means that the numbers on the bottom of your fractions need to be the same and the second is that you only add or subtract the numerators which are the numbers on top so in this sum here where we're trying to add three quarters and one third the first thing we need to do is find a common denominator which means that we need to make these two denominators the same number the best way to do this is to find their lowest common multiple or lcm which is the smallest multiple that they both have in common and so in this case that's going to be 12. now that we have the lcm we can rewrite the equation but with both of our denominators as the number 12 then because we've changed the denominators of our fractions we're gonna have to figure out what the new numerators will be to get from four to twelve we've effectively multiplied it by three so we're also going gonna have to multiply the numerator of three by three as well to get nine this means that we've changed the three quarters into nine twelfths but that's absolutely fine because they're both exactly the same value three-quarters is just a more simplified version then for this other one to get from three to twelve we've multiplied it by four so we also need to multiply the one by four to get a new numerator of four and again because we multiplied the numerator and the denominator by the same number one third and four twelfths both have exactly the same value now that we've done the tricky part of getting a common denominator all we have left is the easy part of adding the numerators together so 9 plus 4 which gives us 13. and because we don't change the denominator it'll be 13 over 12 and then it's always good to double check if your fraction can be simplified but 13 over 12 can't be so we leave that as our final answer now let's take a look at this subtraction question where we've got to subtract two-fifths from five-thirds like before the first step is to find a common denominator which we do by finding the lowest common multiple of three and five which is fifteen so we go ahead and rewrite our fractions with 15 on the bottom and figure out what the new numerators will be to get 15 we have to multiply 3 by 5 so we also have to multiply 5 by 5 to get 25 and to get from 5 to 15 we've multiplied by 3 so we also multiply 2 by 3 to get 6. then lastly as we only subtract the numerators we do 25 take away 6 to get 19 over 15. and again we can't simplify that at all so we leave that as our final answer in case you didn't notice five thirds is an improper fraction because the numerator is bigger than the denominator but this doesn't matter at all when you're adding or subtracting fractions we just treat it like any other fraction if we'd been given it in a mixed number form though so one and two-thirds then we'd have needed to convert it into its improper fraction form first let's have a go at a couple more examples so in this first one we're trying to add two and three quarters which is a mixed number to five 12. the first step is to convert two and three quarters to its improper fraction form which we do by multiplying the two by the denominator of four to get eight and then adding that 8 to the numerator of 3 so that we get rid of the 2 and just have 11 over 4. next we need to find a common denominator so we find the lowest common multiple of 4 and 12 which is 12 and then rewrite the question to get from 4 to 12 we have to multiply by 3 so we also multiply the 11 by 3 to get 33 over 12. 5 12 already has a denominator of 12 though so we don't need to do anything to that one and we can just rewrite 5 over 12. then last we just add the numerators together so 33 plus 5 giving us 38 over 12 which we can simplify down to 19 over 6. in this last one we're doing five-sixths minus four over fifteen the lowest common multiple of six and fifteen is thirty to get from six to thirty we have to multiply by 5 so we also multiply the 5 by 5 to get 25 to get from 15 to 30 we multiply by 2 so we also multiply 4 by 2 to get 8. then by subtracting the numerators we get 25 minus 8 to end up with 17 over 30. anyways that's everything for this video so if you had any thoughts then please do let us know down in the comments and cheers for watching