 Let us learn about adding and subtracting mixed fractions What is a mixed fraction? For example? Something like this is a mixed fraction So it has this whole part and a fraction part as well. Let's take an example to perform Addition first addition is a simpler operation among addition and subtraction. So let's say we have three volts and 5 by 8 and if you want to add it to two holes 1 by 3 How are we going to do this a very simple way to do that is to combine? the whole part first and once you decide to combine the whole part write it separately and then put another plus sign and Then add the fraction part right together and I am showing it in the purple color So you will have 5 by 8 plus 1 by 3 Because you cannot directly add these fractions here since the denominators are not equal You will have to make the denominators equal. So let's do this operation on the right separately I'll just quickly show you how we can do that. So we have 5 by 8 plus 1 by 3 So if you cross multiply you get 5 times 3 here in the numerator of the first fraction And then you also multiply the denominator by 3 plus we do 1 times 8 and in the denominator we have 8 times 3 again and This is basically 15 plus 8 divided by 24 and this is equal to 23 divided by 24 And so you have the result here and you have already combined the whole part, which is 5 So what we have is this result and we can write it together as 5 volts 23 by 24 And this is how you have added the mixed fraction There could have been a case where this fraction would have been greater than one say for example If in the numerator of the second mixed fraction We had 2 and so the operation in here would have changed And so I am just changing 1 to 2 everywhere And so we would have had 15 plus 16 here and in the numerator we would have got 31 So in the result we would have got 5 holes and the fraction as 31 by 24 and we can write 31 by 24 as 1 hole and 7 by 24 So you would add this 5 with 1 hole there and you would have got 6 holes 7 by 24 Now another very interesting way to do Addition or subtraction is to convert any even Mixed fraction into an improper fraction where the numerator is greater than the denominator So what we do is we multiply the whole part by denominator And then we add the numerator to it And we get a new numerator We keep the denominator as is We can do the same thing here then multiplying 9 with 2 And then adding 7 to get the new numerator and writing the same denominator We get 5 by 3 plus 25 by 9 And if we multiply the first fraction by 3 numerator and denominator to get 9 as a denominator We get 15 by 9 plus 25 by 9 And this gives us 40 by 9 and then we divide 40 by 9 We get 4 holes and the remainder is 4 And the denominator is 9 and this is how we can add Mixed fraction by converting them into improper fractions as well Now let's see how we can do subtraction So let's say we have 3 holes 2 by 3 minus 1 hole 1 by 2 Now the safest method of subtraction of mixed fraction according to me is to convert them into improper fractions But let's see how else we can do that. You need to look at the whole parts first See if the left hand side is greater than the right hand side and we indeed see that 3 is greater than 1 So we can safely subtract these two then put a plus sign and perform the subtraction of fraction parts So let me just write it in different color. So whatever we see here 2 by 3 and 1 by 2 We keep it here. So 2 by 3 Minus 1 by 2 the result of the first part is 2 and then we have 2 by 3 minus 1 by 2 And if we cross multiply and perform the subtraction We get 2 plus 4 minus 3 divided by 6 which is 1 by 6 And then we can safely write this result as 2 holes 1 by 6 note that 2 by 3 was also greater than 1 by 2 In this case And that's why we could separately write the subtraction of whole parts as well as fraction part But the things would have changed if the fraction part on the left hand side was less than the fraction part on the right hand side And in that case the best way to perform subtraction is to convert them into improper fractions So let's say we had 4 1 by 2 minus 3 4 by 5 And in that case you can see that the fraction on the left hand side is less than the fraction on the right hand side If you don't know how to see whether which one is greater you can quickly do cross multiplication and see the numerator So 5 here and 8 here so fraction on the right hand side has to be greater The best way to do this is to convert these in the improper fractions So multiplying 4 with 2 And adding 1 in the numerator and writing the new numerator with denominator 2 Minus same thing here 3 times 5 plus 4 divided by 5 as a denominator and we get 9 over 2 minus 19 over 5 and now we multiply the left hand side by 5 in the numerator and denominator And for the other fraction we multiply both numerator and denominator by 2 And so we get 45 divided by 10 minus 38 divided by 10 and this gives us 7 divided by 10 and there is no whole part here and this is how we got our result