In this video, we're going to look at two types of fractions, improper fractions and mixed numbers, and we'll see how to convert between the two of them. An improper fraction is one in which the numerator is bigger than the denominator, like in 8 over 5. In order to show an improper fraction, like 8 fifths of this donut shape, we'd first have to split this shape. into five equal pieces so that we get fifths and then take eight of them.
So this here is effectively eight fifths of the donut. Or if we wanted to show seven thirds we'd split the donut into three so that we get thirds and then need four extra pieces so that we had seven of these thirds in total. You can also write these fractions as mixed numbers. which is where you say how many holes you have and what fraction you have left. So for this 8 fifths example, we effectively have one hole and three fifths left.
So as a mixed number, we just write 1 and 3 over 5. And for our 7 thirds example, we can make two holes and then we have this 1 third left by itself. so we write it as 2 and 1 third. In your exam, you could be asked to leave your answer in either form, or sometimes you might have to convert from one form to another. To convert an improper fraction, like 9 over 4, into a mixed number, we just divide the numerator by the denominator. So 9 divided by 4, which is 2 remainder 1. and so the mixed number form would be 2 wholes and 1 over 4, because that remainder of 1 was never actually divided by 4, so it's still a fraction.
Or if we wanted to convert 23 over 6, we're to just do 23 divided by 6, which is 3 remainder 5, so the mixed number form would be 3 and 5 sixths. We can also do the opposite and go from a mixed number to an improper fraction. For this we multiply the whole number by the denominator so 2 times 7 which is 14. Next we take the 4 7ths part of the fraction and we add our 14 to the numerator so our fraction becomes 4 plus 14 all over 7. which we can simplify to 18 over 7. So the improper fraction form of 2 and 4 sevenths is 18 over 7. Let's try one more.
So the first thing we do here is multiply the 3 by the 5 to get 15. Then we take the 3 fifths and we add the 15 to the numerator to get 15 plus 3 all over 5. which we just simplify to 18 over 5, which must be our answer, because that is an improper fraction. Anyway, that's everything for this video, so hope you found it helpful. If you did, then share it with your friends, and we'll see you next time.