Question Video: Finding a Rational Number with a Given Condition on the Number Line | Nagwa Question Video: Finding a Rational Number with a Given Condition on the Number Line | Nagwa

Question Video: Finding a Rational Number with a Given Condition on the Number Line Mathematics • First Year of Preparatory School

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Find the rational number that lies one-third of the way from the smaller number between −(1/2) and −1(1/2).

02:20

Video Transcript

Find the rational number that lies one-third of the way from the smaller number between negative one-half and negative one and one-half.

In this question, we are asked to find the rational number that lies between negative one-half and negative one and one-half that lies one-third of the way from the smaller of these numbers to the larger of these numbers.

To answer this question, we can start by sketching both numbers on a number line to help us determine which is the smaller number and how far is one-third of the distance. To do this, we first rewrite negative one and one-half as negative three-halves. Since both numbers are multiples of one-half, we can count in halves to the left of zero to represent negative one-half and negative three-halves on the number line. We count to the left since both numbers are negative. We obtain the following sketch. We can see that negative three-halves is the smaller of the two numbers. And we can also note that the distance on the number line between the two values is one, since we have to travel two intervals of one-half to travel between them.

One-third of the distance between the numbers is one over three, which is one-third. So we want to travel an interval of one-third along the number line from negative three-halves. There are many ways of doing this. Since we have a number line, we will do this calculation on the number line. We can note that splitting halves into thirds will give us sixths, since two times three is six. So, we will split the number line into sixths. We can then note that adding one-third is the same as adding two-sixths. So we need to move two increments of one-sixth to the right of negative three over two. This gives us negative seven-sixths.

Hence, negative seven-sixths lies one-third of the way from negative one and one-half to negative one-half.

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