Complete the rational numbers on
the number line.
In this question, we are asked to
complete the rational numbers on the given number line. We can start by noting that there
are four missing rational numbers that we need to find. We can also note that on our number
line, each number is at a regular interval from the last number. So the numbers are increasing or
decreasing by the same amount.
We can see that these are
increments of one-third by noting that the numbers next to zero are positive and
negative one-third. This means that each increment to
the right of zero represents adding one-third and each increment to the left of zero
represents subtracting one-third.
We can use this idea to find each
of the numbers on the number line. First, we note that one of the
numbers is two increments to the right of zero. Since each increment is one-third
and we move two increments to the right, this must be two-thirds. In the same way, we can move to the
left two increments from zero to find negative two-thirds on the number line as
We can follow this same process for
the remaining two numbers. We see that one number is four
increments of one-third to the right of zero, so this is four times one-third. We can write this as
four-thirds. If we followed this same process
for the remaining number, we would see that it is six increments of one-third from
zero, so it is six-thirds. We could then simplify this to get
two. However, we can show that this
value is two by using the number line itself. We can note that every three
increments is equal to one, so six increments will be equal to two.
Hence, the missing rational numbers
on the number line are negative two-thirds, two-thirds, four-thirds, and two.