Question

Write the decimal as a fraction or mixed number.

$\mathbf{-}\mathbf{1}\mathbf{.}\overline{\mathbf{36}}$

Short answer

The fraction is $-\frac{15}{11}$.

Step-by-step solution

Step 1. Given information

Consider, the decimal $-1.\overline{36}$ provided in question.

Step 2. Calculation

Consider $-1·\overline{36}=-1+\left(-0·\overline{36}\right)$

But $-0·\overline{36}=-\frac{36}{99}$

Therefore,

$\begin{array}{c}-1\cdot \overline{36}=-1+\left(\frac{-36}{99}\right)\\ =\frac{\left(-1\times 99\right)+\left(-36\right)}{99}\\ =\frac{-135}{99}\\ =\frac{-15}{11}\end{array}$

Hence, $\text{-1}·\overline{36}=\frac{-15}{11}$

Thus, the fraction number that can be formed is $\frac{-15}{11}$.