A bottle can hold three-tenths of a litre of oil. How many bottles are needed to store twelve litres of oil?
So let’s try visualising the problem. We’ve got lots of little bottles containing three-tenths of a litre each. When I add all those volumes together, I get an answer of twelve. So the question is how many bottles do I need to make a total of twelve litres. So the question really becomes “how many times does three-tenths go into twelve?” And to answer that question, we need to do the calculation twelve divided by three-tenths.
Now for some reason, as soon as we start introducing fractions, these questions seem a lot more complicated. But let’s imagine a similar problem. The bottle can hold five litres. How many bottles are needed to store ten litres? Well, clearly the answer is two. I’ve got five litres plus five litres make ten litres, but the calculation there- so the calculation how many times does five go into ten can be worked out using ten divided by five, and the answer is obviously two. So imagining a simpler version of the old problem can help you to identify the calculation that you need to make.
So how are we gonna tackle this problem? We’ve got a whole number twelve divided by a fraction — three-tenths. Well maybe you’ll find it easier if you convert twelve into a fraction. So twelve is an equivalent to twelve over one. Now we’ve got a fraction divided by a fraction. And there’s a very simple rule that we need to follow in order to do fraction division: dividing fractions is easy as pie; flip the second and multiply. So twelve over one divided by three over ten is the same as twelve over one. So flipping the second becomes ten over three. And instead of doing division, we’re gonna do multiplication. So the equivalent calculation is twelve over one times ten over three.
Now with fraction multiplications, we can look at the numbers on the numerator on the top and we can look at the numbers on the denominators on the bottom and see if we got any common factors that will enable us to cancel. And three is a common factor of twelve and three; three divided by three is one and twelve divided by three is four. So this calculation becomes four over one times ten over one, which is forty over one. Now obviously, we don’t need the over one; that’s just a whole number forty. So we need forty bottles.
Now if that’s the right answer, if we do the calculation forty times three-tenths, we expect to get an answer of twelve. So let’s try that out. So the calculation is forty times three-tenths and we’re hoping that the answer is gonna be twelve. Well, forty is the same as forty over one. So if I write forty over one times three over ten, I’ve got a fraction calculation. And again I can do some cancelling, ten is going to ten once and ten is going to forty four times. So that becomes four over one times three over one, which is in fact twelve over one or just twelve. So yup, it looks like our answer is correct. We need forty bottles in order to store twelve litres of oil.