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
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.