Question Video: Ordering Given Fractions with like Denominators in Descending Order

Video Transcript

Arrange ten nineteenths, fifteen nineteenths, and seven nineteenths in descending order.

When we descend something, we go downwards. And so, when we’re asked to arrange some numbers in descending order, or in this case fractions, we need to put them in order so that their values go downwards. In other words, we put them in order from largest to smallest.

Now, in this problem, we’re given three fractions to put in order: ten nineteenths, fifteen nineteenths, and seven nineteenths. Now, one thing we can see about these fractions is that they all have the same denominator, the same bottom number. Now, we know that the denominator in a fraction shows us the number of equal parts that a whole amount has been split into. So, if we use this bar to represent one whole and then split the whole into 19 equal parts, each part will be worth one nineteenth. And because each fraction shows a number of nineteenths, we can compare them really quickly.

If we were to shade ten nineteenths of this whole amount, we need to shade in 10 out of 19 sections. So this shaded area then represents ten nineteenths. If we were to show fifteen nineteenths, we’d need to color more parts. In fact, we’d need to color another five more parts to show 15 out of 19 parts shaded. But you know, we didn’t really need to draw the diagram to work out that fifteen nineteenths was greater than ten nineteenths. We just needed to look at the fractions.

Because all the fractions show a number of nineteenths, we just need to look at the numerator, which is the top number, and compare those. The fraction with the largest numerator is fifteen nineteenths. Out of our three possible fractions, this is the greatest number of nineteenths that we could have. The next largest numerator — remember, we’re putting these in order from largest to smallest — is 10, ten nineteenths. And so, the second fraction in our order, descending order, is ten nineteenths.

And then, finally, we have a numerator of seven in the fraction seven nineteenths. Seven nineteenths is the smallest of our three fractions. And so because each of our fractions has the same denominator, to put them in order, all we had to do was to compare the numerators. To put the fractions in descending order, we had to start with the largest numerator and go through them until we ended with the smallest numerator.

In descending order, the fractions are fifteen nineteenths, ten nineteenths, and seven nineteenths.