400 people are asked if they like football. Three-fifths of the people say yes. Of those who like football, 60 percent regularly watch football games. Part a) Complete the frequency tree. Part b) What fraction of the 400 people regularly watch football games? Assume that the people who do not like football do not watch football regularly.
So what we need to do first is use the information from the question to complete the
frequency tree. So first of all, we’re told that three-fifths of the people say yes they like
football. Well, to find three-fifths of 400, what we do is, first of all, we divide by the
denominator and then we multiply by the numerator.
You could do it the other way around. So you can multiply by the numerator then divide by the denominator. But I’m gonna do it the first method because that will be easier for this value.
So we have 400 divided by five. And this is gonna be 80. And the reason that it’s 80 is because if we have 40 divided by five, it’s eight. So then we’ve got an extra zero. Alternatively, you could’ve used the bus stop method. Then we see how many fives go into four, which is zero. So then we carry the four. And we see how many fives go into 40, which is, as we said, eight. And then we’ve got how many fives go into zero, which is just zero. So we get our 80.
Okay, great, so we’ve divided by the denominator, so divided by five. Now we need to multiply by the numerator, so multiply by three. And when we multiply by three, we’re gonna get 80 multiplied by three, which is equal
to 240. And that’s because if we do three multiplied by eight, it’s 24, cause it’s eight, 16,
24. And then we add the zero. So therefore, we have 240 people who like football.
So now we’ve written that into our frequency tree. Now we can fill in the value below, which is the number of people who do not like
football. Well, 240 and this number must sum to 400. So therefore, to find out what this number, so the number who do not like football,
is, we’re gonna take 240 away from 400.
So to do that, first of all, we set up a column subtraction. So you’ve got zero minus zero, which is just zero. Then we’ve got zero minus four, which we can’t do. So we’re gonna have to borrow from the four in the hundreds column. So then we’ve got 10 minus four, because we’ve borrowed as I said from the hundreds
column. And 10 minus four is six. And then finally we have three minus two, which is 160. So therefore, we can say that 160 people do not like football.
So we filled in the first two parts of our frequency tree. Now let’s move on to the next part. So now what we’re trying to do is see how many people of those who like football
regularly watch football games. Well, we’re told that 60 percent do. So therefore, what we want to do is find out 60 percent of 240.
Well, if we think about it as 100 percent is 240, then to find 10 percent, cause
that’s what we want to do first and then we’ll be able to find 60 percent, what we
do is we divide each side by 10. So we have 10 percent is equal to 24.
And now from here, there’re two ways to find out what 60 percent is. The first is to multiply 24 by six, because 10 percent when multiplied by six gives
us 60 percent. And to do that, what we’ve got is 24 multiplied by six set up here in a column
multiplication. So we’re gonna start with six multiplied by four, which is 24. So we’re gonna carry the two. And then we’ve got six multiplied by two, which is 12. Well, 12 add two is 14. So we get 144, which is gonna give us that 60 percent is equal to 144.
Now I said there’s another method. So I’ll quickly show you that. Well, to use the other method, what we do is we’d find 50 percent. And we do that by halving 240. So 240 divided by two is 120. That’s because 24 divided by two is 12. And then we’ve got the extra zero. And then all we need to do is add on 10 percent, because if you’ve got 50 percent,
you add on 10 percent to make 60 percent. So we do 120 plus 24 because that’s how much 10 percent was. And we get our 144.
So this is a nice method if you’re bit unconfident when dealing with
multiplication. So we can now fill that in on our frequency tree. So we know that 144 people regularly watch football.
So now what we need to do is work out the final place on our frequency tree. This is the number of people who like football but do not watch football
regularly. And we know that this value plus 144 must sum to 240. So I’ve set up another column subtraction. So we got 240 minus 144. So we do zero minus four. We can’t do. So we’re gonna borrow from the tens column. So when we do that, we get 10 minus four. So then we do 10 minus four, which is six.
So then we move on. And we’ve got three minus four. Well, we can’t do that. So we’re gonna have to borrow from the hundreds column. When we do that, we’ve now got 13 minus four, which is nine. And then, finally, we have one minus one, which is zero. So we now know that the number of people who like football but do not regularly watch
football is 96. And we’ve completed the frequency tree.
So now what we’re gonna do is move on to part b. What fraction of the 400 people regularly watch football games? Well, to work this out, we’re gonna have the number of people who regularly watch
football games divided by the number of people there are in total, which is going to
be 144 over 400. And remembering that we know that it’s 144 people who regularly watch football
because we’re told to assume that the people who do not like football do not watch
So now we can simplify our fraction by dividing the numerator and denominator by
two. So when we do that, we get 72 over 200. And we just see how we did the numerator. So if we do 144 divided by two or set it up with the bus stop method, well, twos into
one don’t go. So we just get zero then carry the one. Then twos into 14 go seven times, remainder zero. And then, finally, twos into four go twice. And that’s how we got our 72.
Okay, great, so now we can simplify this even further because we can divide the
numerator and denominator again by two. So then we get 36 over 100. And we can divide the numerator again using the bus stop method. And we’d have got 36. So now if we take a look, we got 36 over 100. Or both of these values have four as a factor. So then we get nine over 25. And that’s because nine multiplied by four is 36 and 25 multiplied by four is
100. So therefore, we can say that the fraction of the 400 people who regularly watch
football games is nine over 25.