# Video: Finding a Rational Number with a Given Condition in the Number line

Find the rational number that lies at one-third of the way from the smaller number between −6/7 and 6/7.

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### Video Transcript

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

Let’s firstly consider the number line between our two values negative six-sevenths and six-sevenths. Both of these values are a distance of six-sevenths away from zero. When adding two fractions with the same denominator, the denominator remains the same. Therefore, six-sevenths plus six-sevenths is equal to twelve sevenths.

We can therefore say that the difference between six-sevenths and negative six-sevenths is twelve sevenths. In this question, we’re asked to find the number that is one-third of the way from the smaller number. Dividing twelve sevenths by three gives us four-sevenths. This means that the number we’re looking for is four-sevenths greater than negative six-sevenths.

Negative six-sevenths plus four-sevenths is equal to negative two-sevenths as negative six plus four equals negative two. The rational number that lies at one-third of the way from the smaller number between negative six-sevenths and six-seventh is negative two-sevenths.