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
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.