We are asked to plot the fractions 2/3, -2/3,
7/3, and -9/3 on the number line.
Then write any improper fractions as mixed
numbers.
Notice for all of the fractions, the denominators
are 3.
Because of this, we will cut each length equal
to 1 unit into 3 equally sized parts or lengths.
Looking at the number line, the distance between
0 and 1 is equal to 1 unit.
We will now cut this length into 3 equally
sized parts or lengths.
The smaller lengths are now equal to 1/3 of
a unit.
We will do this for each length equal to 1
unit, which is the distance between 1 and
2, 2 and 3, 0 and -1, -1 and -2, and -2 and
-3.
Now the length between tick marks is equal
to 1/3 of a unit and we can plot the 4 fractions.
Positive 2/3 is located 2/3 of a unit to the
right of 0.
Starting at 0 and counting to the right by
1/3's, we have 0, 1/3, 2/3.
We can also think of 2/3 as 2 copies of 1/3.
-2/3 is located 2/3 of a unit to the left
of 0.
Starting at 0 and moving left, we count by
-1/3's.
We have 0, -1/3, -2/3.
Be can view -2/3 as 2 copies of -1/3.
Notice how these 2 fractions are the same
distance from zero, which is why they are
called opposites.
The next fraction is 7/3, which is located
7/3 of a unit to the right of 0.
Starting at 0, moving to the right we count
by 1/3's.
We have 1/3, 2/3, 3/3 which equals 1, 4/3,
5/3, 6/3 which is equal to 2, and 7/3.
We can view 7/3 as 7 copies of 1/3.
And finally we have -9/3, which is located
9/3 of a unit to the left of 0.
Starting at 0 moving to the left, we count
by -1/3's.
Here we know we have -2/3, then -3/3 which
is equal to -1, -4/3, -5/6, -6/3 which is
equal to -2, -7/3, -8/3, and finally -9/3.
Notice how -9/3 is equal to -3.
For the second part of this question, we're
asked to write any improper fractions as mixed
numbers.
An improper fraction is a fraction where the
numerator is greater than or equal to the
denominator.
Notice 7/3 and -9/3 are improper fractions.
Notice that 7/3 is greater than 2 and less
than 3.
If we start at 2 and count by 1/3, we have
2 and then 2 1/3.
2 1/3 is the mixed number for the improper
fraction 7/3.
Then looking at -9/3, notice how we can see
-9/3 is equal to -3.
I hope you found this helpful.
