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.