Arrange the numbers on the cards in descending order. One and one-quarter, one and two-thirds, five-eighths, and one-third.
Here we have four cards. And we’re asked to arrange the numbers on these cards in descending order. When something descends, it goes down. And so descending order means arranging the numbers in the cards from largest to smallest value.
Now if we stopped to take a look at the values on our cards, we can see that we have two different types of number. Our last two cards are fractions, and our first two cards are mixed numbers. In other words, they contain a whole number and a fraction parts.
Now we can see just by looking at our first two numbers they’re both greater than one. We know this because the whole number part of the fractions is one: one and a quarter, one and two-thirds. On the fractions on our second two cards, we can see that these values are less than one. This is because the numerators or their top numbers are less than the denominators or the bottom numbers. So five-eighths is five out of eight, which is less than one. And one-third is one out of three, and that’s also less than one. So what have we found out so far?
The largest two cards are going to be the first two cards that we can see. And the smallest two cards are the second two cards that we can see. So we just need to put each pair of cards in order.
To begin with, let’s look at our first pair. Which is larger, one and a quarter or one and two-thirds? Well, both numbers have one as their whole number, which we’ve explained already. So, really, we just need to compare one-quarter with two-thirds. We can use fraction strips to find the answer. Here’s what one-quarter would look like. And here’s how we might show two-thirds. Two-thirds is clearly greater than one-quarter. And so we can say, out of our two number cards, one and two-thirds is greater than one and a quarter. And so we can now order our first two number cards. One and two-thirds has the greatest value and then one and a quarter.
Now we need to put our final two cards in order. We know that these come after the first two because they’re fractions worth less than one. But which is greater, five-eighths or one-third? We might know the answer already. But just to check, let’s use a bar model again. We know that four-eighths are the same as a half. So five-eighths are just greater than one-half. But one-third has a value less than one-half. So if we put our final two number cards in order from largest to smallest, we must start with five-eighths and then put one-third last.
We’ve used our knowledge of mixed numbers and fractions to put the numbers in the cards in descending order. These numbers, from largest to smallest, are one and two-thirds, one and a quarter, five-eighths, and one-third.