### Video Transcript

Let’s take a look at ordering
rational numbers. But before we do that, I wanna
pause quickly and remind us what rational numbers are. All of the numbers found on this
chart are rational numbers. Rational numbers are positive and
negative numbers that can be written as a fraction. So any number that can be written
in a fraction form is considered a rational number. And without further ado, we’re
gonna talk about ordering rational numbers.

Today we’re gonna focus on numbers
that are already written in fraction form. Here’s an example.

Order these values from least
to greatest. We have sixth-eighths,
two-eighths, five-eighths, three-eighths. What you should’ve noticed
immediately when you saw these values is that they have the same
denominator. And that is good news when it
comes to ordering values from least to greatest.

Since these fractions have the
same denominator, ordering them from least to greatest is as simple as comparing
their numerators. Let’s remember that we’re
working from least to greatest. So we find the smallest
numerator. And that’s gonna be our least
value here, the two-eighths. From there, we’ll have
three-eighths as the next largest value and then five-eighths and, finally, the
greatest value in this set, six-eighths.

Here’s a picture to help you
visualize what’s happening here. Imagine if four people ordered
a personal pizza. And each personal pizza was cut
into eight slices. Since each person’s pizza is
cut into eight slices and the slices are the same size, to find out who ate the
most, we only need to ask who had the most slices of pizza. Two, three, five, and then six
slices.

Here’s our next example.

Order these values from
greatest to least: one-twelfth, one-tenth, one-third, and one-twentieth. Something slightly different is
happening here than in the last example. This time, each of our values
has the same numerator instead of the same denominator. So what does that mean for
us? How can we compare these
values?

Well, we could draw a
picture. Well, we could draw a
picture. If we drew a picture, we would
need to divide the first rectangle into 12 pieces, the second one into 10
pieces, the third one into three pieces, and the fourth one into 20 pieces. It might look something like
this. What we notice here is the more
pieces we divide our whole into, the smaller the pieces get. If we tried to divide one
chocolate bar into 20 pieces, the pieces would be really small. However, if we divided that
same chocolate bar in only three pieces, the pieces are much bigger.

What I’m trying to get you to
see here is when the numerators are the same, fractions with smaller
denominators represent more of the whole. Here we’re trying to move from
greatest to least. One-third is the greatest value
here. Sharing one chocolate bar with
three people is going to work out better for you than sharing one chocolate bar
with 20 people. So after one-third comes
one-tenth and then one-twelfth. And finally, the least value
out of these four is one-twentieth.

Here’s our next example.

Order these values from least
to greatest: eight-halves, eight-fourths, eight-sixths, eight-fifths. So first you notice that they
have the same numerator. This means that the fractions
divided into more pieces, or the ones with the larger denominator, will have a
smaller value. You also remember that this is
true as long as the numerators are the same.

Moving forward, you check that
we’re moving from least to greatest. Since we’re looking for the
fraction that represents the least value, we’re going to try and find the
highest denominator. Here, that’s eight-sixths,
followed by eight-fifths and then eight-fourths and, finally, eight-halves
representing the greatest of these four values.

Here’s our last example.

Order these values from least
to greatest: seven-tenths, six-fourths, four-fifths, and five-halves. Immediately, we notice that
this example is different from all the ones we’ve seen. This time, there’re no common
numerators. There’re also no common
denominators, and this is a problem. We might say this is a problem
of trying to compare apples and oranges. It’s impossible to compare
these in their current state. And therefore, to order them,
we need to find some kind of format for these four values that makes it easier
for us to compare and order them.

And you have a few options. You could try and find the
least common denominator. You could also draw a
picture. You could convert the fractions
to decimals. I’m gonna choose to solve this
one by converting these fractions to decimals. Seven-tenths is one of those
fractions that’s a power of 10, so it converts to 0.7. To convert six-fourths to
decimals, you can divide six by four. That process would look
something like this, leaving you with the answer of 1.5. To convert four-fifths to
decimal format, I first convert this to an equivalent fraction with a base of
10. Eight-tenths is written as 0.8
in decimal format. I’m gonna follow that same
procedure for five-halves. When I do that, I get
twenty-five tenths, which in decimal format is 2.5.

Okay, we’re no longer trying to
compare apples to oranges. Now we have a format that we
can work with. We’re trying to order these
from least to greatest. Seven-tenths is the smallest
value. After that is 0.8 or
four-fifths. Six-fourths comes next. And the greatest of these four
values is five-halves.

Now you’re ready to try some on
your own.