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
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
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
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
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.