Video: GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 7

GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 7

04:09

Video Transcript

Francesco and Emilia share their sweets in the ratio six to seven. Part a) What fraction of the sweets does Amelia receive? Michaela and Lubna share some tomatoes. Lubna receives three-fifths of the tomatoes. Part b) Write down the ratio for the number of tomatoes that Lubna receives to the number of tomatoes Michaela receives.

So we’re gonna start with part a and we’re looking at Francesco and Amelia and the sweets that they share in the ratio six to seven. Because Francesco was written first and then Amelia, we know that the six from our ratio — so the six parts — will actually refer to Francesco and the seven parts will refer to Amelia.

The first thing I want to do is actually calculate the total parts. So how many parts are there with Francesco? Six parts and Amelia, seven parts of our ratio. So to work this out, what we’re gonna do is we’re gonna do six add seven which is gonna give us an answer of 13. So we know that there are 13 parts in total.

Now, if we look at what we’re trying to answer, what we’re trying to do is actually find out what fraction of the sweets does Amelia receive. Well, we’ve already said that the seven parts actually relates to Amelia. So we want to know what fraction of the total number of sweets is seven parts.

Well, Amelia is actually going to receive seven parts cause we’ve already established that out of or we can say seven over then 13 because actually 13 is the total number of parts. So therefore, we can say that Amelia is going to receive seven thirteenths of the sweets.

But what we can do is just double-check this is correct because actually we’ve never looked at Francesco. Well, we said Amelia gets seven thirteenths. So therefore, Francesco would have six thirteenths because it says Francesco has six parts and six out of the 13 total parts.

Now, what we can do is actually add these together. So we can have six thirteenths cause that’s Francesco’s fraction of the sweets added to seven thirteenths because that’s Amelia’s fraction of the sweets. Well, now, if we’re gonna add those two fractions, they have the same denominator. So all we need to do is add the numerators. Well, when we do that, we get thirteen thirteenths which is such the same as one. So that’s all the sweets. So yes, our answer is correct.

Okay, so great, we can now move on to part b. Well, for part b, we’re actually told that Michaela and Lubna share some tomatoes and Lubna receives three-fifths of these tomatoes. Well, if we actually think about three-fifths and what it means, if we’ve got three-fifths of tomatoes, that means that Lubna is actually getting three parts out of total of five parts of our tomatoes.

So therefore, we can actually say that Michaela is going to get the remaining parts, so the other parts out of five. And we actually can work that out by subtracting three from five because we said Lubna had three of the five parts. So that means Michaela is gonna have five minus three of the five parts, which means that Michaela is gonna have two parts of what the tomatoes were actually split into.

Okay, great, so now, we know that Lubna is gonna have three of the five parts, Michaela is gonna have two of the five parts. So now, what we need to do is actually write down the ratio of the number of tomatoes that Lubna receives to the number of tomatoes that Michaela receives.

It’s very important that this is written this way round because this will determine how our ratio actually looks. And that’s because if Lubna’s written first, that means in our ratio, we’ve got to have L first or Lubna first and then we’ve got Michaela.

And then as we said, Lubna has three of the five parts, Michaela has two of the five parts. So therefore, we can say that the ratio of the number of tomatoes that Lubna receives to the number of tomatoes Michaela receives is three to two.

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