Find a whole quantity given the quantity represented by a unit fraction

One third of what is 8? How can we work this out? [][]Well, if we know that 1 third is []8, we can see how we might find 3 thirds, and 3 thirds will be our whole quantity: so if there is 8 in one of our thirds, [][]there will be 8 in our other thirds as well, and that gives us a total of []24. So if you’re told a quantity given by a unit fraction – if you’re told how many you have when you have 1 over something – you can use multiplication to get your answer: so here, we did 8 times 3 to get 24. This is confusing, because usually, when we’re doing something with the denominator, we’re dividing – but because we have a missing number problem, we need to use the inverse operation – so here, because it’s a missing number problem, rather than dividing, we need to multiply.[]
So 1 fifth of what is 6? [][]Well, if we know that 1 fifth is []6, [][][][]then we must have 6 in our other fifths as well, so we have 6 five times, and 6 times 5 is []30.[]
Now, 1 sixth or what is 4? [][]Again, if we know that 1 sixth is []4, [][][][][]then we have 4 in our other sixths as well, and 4 times 6 is []24.[]
So now pause the video, and see if you can find the whole quantities for these questions. For this first question, if you know that 1 quarter of something is 100, []then you need to work out 100 times 4 to find the whole quantity, []so that’s 400. Here, if 1 third is 70, []then you can work out the whole quantity by working out 70 times 3, []so that’s 210. And finally, if 1 fifth is 43, then the whole quantity is 5 fifths, []so you need to work out 43 times 5. [][][]Using column multiplication, we can work out that 43 times 5 is 215, []so that’s our answer.