In this video, we take a look at fractions and the 3 sub-topics. Improper fractions, fractions of numbers and arithmetic. This is a key skill for GCSE maths students!
We cover topics such as converting improper fractions to mixed numbers and vice versa, finding the value of fractions, comparing fractions and more!
Follow along as we show you how to work out a number of AQA GCSE exam questions on Fractions, such as “Work out 1 3/5 divided by ¾” and “a class has 29 students. 16 of the students are girls. What fraction of the students are boys?”
Fractions can be split up into three topics. So we've got improper fractions. This is where our numerator, the number on top is larger than the denominator. The second topic is fractions of numbers. So this could be for example, finding in the fraction of students with blonde hair or something.
And the third topic is arithmetic. So adding monitoring times and dividing fractions together. So let's look at the first topic, improper fractions. This is most often seen in the context of mixed numbers. So for example let's look at 703.
So we could convert this into a mixed number and by mixed number I mean a number that is a mixture of a whole number and a fraction. So it has that kind of format to it. And so in this example all we're doing is we're basically in seven divided by three, right? So we want to find how many threes go into seven. Well, there are two whole threes in seven so we can put a two there and then what's left over we've got a couple of remainder.
One because t three because are six we want seven and so we've got a remainder of one. So that one is still divided by that three. Another way to think of it is that two is also essentially six thirds, isn't it? That's what's giving us that too. And because we need seven thirds in total, we've got this six thirds we need to add on an extra third and likewise we can go back the other way as well.
We can be given a mixed number and we can go back the other way. So we could think of that too as six thirds. Add on sixths with that one third and we can get back to that seven thirds again. So we can flip between the two types of fractions. Next up is fractions of numbers.
So if we just look at this example, a fifth of 40 well, on the calculator we would need to do 40 times a fifth or a fifth times 40 and 40 times a fifth. Well, we can think of this as actually 40 over one times one over five. And when we time structures together we'll do it in a second. With arithmetic, what we do is we do top times top and bottom times bottom. So we end up doing 40 times one which is 40 and we do one times five which is five and so 40 over one times one of five gives us 45th and this is basically 40 divided by five.
So that's the takeaway there. We can either find times by fifth or we can look at this and we're basically doing 40 divided by five and they're the exact same thing, right? They're kind of interchangeable ways of thinking about the same problem. And with arithmetic well, just for a second I'm going to write this as five over one and as I did that, I'm going to write this as 40 over one. Because what we can see instantly when we start to tackle division is we can either divide by five over one, like we're doing here, or we can times by one over five and then the exact same thing.
So if we can do multiplication with fractions, we can actually do division because we just flip that fraction around and we're able to turn that division question into a multiplication question.
So whenever we have just two more example, let's say we've got five 6th divided by two 7th. Well, this is the exact same as five six times seven over T. And again, when we have this same problem, we just do top times top, bottom times bottom, we get 35. So that's division taken care of, that's multiplication taken care of. Adding and minusing is slightly trickier.
We have to make sure we have the same denominator. So let's do, let's stick with this. Let's do five six plus two 7th. In this case I can't add 6th and 7th together. They're two separate things.
So what we need to do is we need to turn these two fractions into two new fractions that have the same denominator. So I need to have the same number here as I have here on the bottom of my two fractions and I have two different numbers on top. Well, the trick we can do is we can take this whole fraction and we can times it by seven by that denominator. And what we end up with is we end up with five times seven on the top, which is 35 and we end up with six times seven on the bottom, which is 42. The next thing we do is we take this whole fraction and we times it by this denominator.
We times it by six. So we do that and what we end up with is the exact same number on the bottom because again we're doing six times seven to get a new denominator, which again is 42 and we do six times two on the top to get twelve because whenever we do the bottom we have to be to the top. And what we can see now is we've got the same number on the bottom. So now we're doing 35 42 plus 1240 tooths. That's the correct question we end up with and that would be our final answer.
So that's how we add and minus thing is the exact same. Again, we need to have that same denominator. Let's go on and look at some exam style questions. So we'll go back to our subject one and do a practise question on this. Submitting one and three fifths divided by three quarters.
Well, I don't want to do one and three fifths. I want to convert this into an improper fraction. So at the moment this is a mixed number and I'm going to write this as one plus three five. There's a kind of an imaginary plus sign between these two that we don't normally right, but it is there because we are just combining these two numbers together, this number and this fraction. And I'm also going to write this one as one over one where you'll see your one in a second.
Because what we end up having now is a fraction plus a fraction. Well, we now have to do that, right? We just need to times this whole fraction by this denominator and then we times this whole fraction by this denominator. Well, one times five is going to be five, one times five is going to be five and this whole fraction times one is just going to stay the same, right? One times anything, it's just itself.
And so we can now work out the total value of this five fifths plus three five is going to give us eight five. And this question then becomes eight. Five divided by three quarters.
Well, we've seen that we don't really want to do a division, we'd much rather do a multiplication. So what we can do is we can flip the top and bottom around and turn it into a multiplication. So this becomes eight thirds times four thirds and we just do top times top, bottom times bottom. Eight times four gives us 32 and five times three gives us 15. That's what I'm saying.
Moving on to summit number two fractions of numbers. If a class has 29 students and 16 of them are girls, what fraction of students are boys? So we're going to assume that all the non girls are going to be boys. So we're going to say if it's dying off in 29 and we're subtracting the 16 girls, we're going to be left with 13 boys. And as a fraction of the total, well, that's just 13 out of moving on to the final topic, a recordic, we'll do an adding one first.
So one third plus one 12th. Well, as we've seen before, we need to make sure that these two numbers are two denominators of the same number. We can't just add thirds and twelve together because they're different things. And what we can do is if we're smart about this, rather than times in this whole fraction by this denominator and this whole fraction by this denominator, we can take a shortcut and we can just times this first fraction by the top and the bottom by four. And what that's going to give us is four on top and twelve on the bottom.
And we've all of a sudden we've got into our t same denominators. Yeah, we could have done the old method, we would have ended up with 1236 plus 336, but it's just slightly quicker swing and 412 plus 112 is going to give us 512. Right. Final question, three quarters times one five. Three over four times one over five.
We just need top times top, bottom times bottom. We get three over 20 and it is really simple as that. Timely fractions is counter intuitively the nicest one to do. And that is the end of all fractions.
Book a lesson with this tutor
A young, gifted tutor who uses his engineering experience to ignite your curiosity in Maths. A straight 'A' student, he knows exactly how you need to learn to help you ace your exams.