Question Video: Completing the Rational Numbers on a Given Number Line Mathematics • 6th Grade

Complete the rational numbers on the number line.


Video Transcript

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 shown.

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.

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