### Video Transcript

Arrange the elements in the set one
and two-thirds, negative one-eighth, one and one-ninth, and negative one-half in
descending order.

Descending order is from greatest
to least. And so we notice about all of these
values that they do not have a common denominator. But if we think about them in terms
of the number line, we know that negative one-half needs to go to the left of zero
and one and two-thirds needs to go to the right of zero. At this point, we’ll need to
compare negative one-half and negative one-eighth and one and one-ninth and one and
two-thirds.

Starting with the negatives, we
have negative one-half and negative one-eighth. If we multiply the numerator and
the denominator by four, for negative one-half, it becomes negative four over
eight. Now, because these values are
negative, we need to be very careful how we compare them. Negative one-eighth will be closer
to zero on a number line than negative four-eighths. So they belong on the number line
like this. If we’re going in descending order,
from greatest to least, negative one-eighth would belong on the list before negative
one-half.

But now we need to compare the two
positive values. One and one-ninth and one and
two-thirds both have the whole-number portion of one. And that means to compare them,
we’ll simply need to compare their fractions. These two fractions do not have a
common denominator. But if we multiply two-thirds by
three in the numerator and the denominator, this mixed number becomes one and
six-ninths. One and six-ninths is larger than
one and one-ninth. And so we could place them on our
number line like this. And we’re ready to write them in
descending order.

Descending order is greatest to
least. We want to again write it in the
set notation, so we’ll open the brackets. The largest of the values is one
and two-thirds, then one and one-ninth, then negative one-eighth, and negative
one-half. We’ll close the brackets. And we’ve rearranged this set into
descending order.