### Video Transcript

Arrange the numbers on the cards in
DESCENDING order. One and five-eighths, two and
one-sixths, one and five-sevenths, and one and two-fifths.

Now the first thing to do is to
think about what does descending mean. Well, you descend down the stairs;
it’s going down. So we’re starting at the biggest
thing and we’re ending up at the smallest thing.

So let’s create some slots for our
answers; the largest is gonna go first and the smallest is gonna go last. Now the first number is one and
something, the second number is two and something — so that’s obviously bigger than
the first card — the third is one and something, and the fourth is one and
something. So card number two here seems to
have the biggest number. Two is bigger than one; so that’s
definitely the biggest number. Now the other three cards are all
one and something. So we need to look at the something
— the fractions that go with the one, that are added onto the one — and see which is
the largest and which is the smallest.

Well, five-eighths is over a half
because four-eighths would be a half; so five-eighths is greater than a half. And five-sevenths, well three and a
half sevenths would be a half, even though we shouldn’t mix fractions within
fractions, but five-sevenths is bigger than three and a half sevenths. So five-sevenths is also bigger
than a half. Well, that hasn’t got us very far
so far. But let’s look at the last fraction
and one and two-fifths. For two-fifths, two and a half
fifths would be a half. So two-fifths is less than a
half. So the first card is one and more
than a half; the third card is one and more than a half. But the last card, the fourth card,
is one and less than a half. So of those three, that must be the
smallest card. So one and two-fifths is the
smallest.

So now we got to evaluate these two
things here: five-eighths or five-sevenths. Which is bigger and which is
smaller? And to compare five-eighths and
five-sevenths, we’re gonna take two identical circular cakes and cut them up into
either eight pieces or seven pieces. Now if we were going to be sharing
the same cake out between eight people, each person is gonna get a little bit less
than they will get if we were sharing it out with seven people.

So five of the smaller pieces has
got to be smaller than five of the larger pieces. So this means that one and
five-eighths is smaller than one and five-sevenths. So there’s our answer: the largest
number is two and a sixth, the next largest number is one and five-sevenths, the
next largest number is one and five-eighths, and the smallest number is one and
two-fifths.