Question

Write a rational number in fraction form that is equivalent to -1.\overline{5}

Answer 1

Answer:

$\dfrac{-14}{9}$.

Step-by-step explanation:

The given number is $-1.\overline{5}$.

We need to find a rational number in fraction form that is equivalent to given number.

Let $x=-1.\overline{5}$

$x=-1.555...$     ...(1)

Multiply both sides by 10.

$10x=-15.555...$  ...(2)

Subtracting (1) from (2), we get

$10x-x=-15.555...-(-1.555...)$

$9x=-14$

Divide both sides by 9.

$x=\dfrac{-14}{9}$

Therefore, the required rational number is $\dfrac{-14}{9}$.