Locate the following rational numbers on the number line.
(a) $\frac{7}{- 8}$
(b) $- (\frac{3}{- 5})$

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Solution

We find we can firstly convert the rational numbers into their equivalent forms and then plot on the number line.

(a) $\frac{7}{- 8} = \frac{- 7}{8}$ , which is a negative rational number lying between -1 and 0. So we can divide the line between -1 and 0 into 8 equal parts.
Now mark the seventh division to the left of 0 to get $\frac{- 7}{8}$ .

(b) $- (\frac{3}{- 5}) = \frac{- (3)}{- (- 5)} = \frac{- 3}{5}$ , which is a negative rational number lying between -1 and 0. So we can divide the line between -1 and 0 into 5 equal parts.
Now mark the third division to the left of 0 to get $\frac{- 3}{5}$ .

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