Question

Rewrite as a simplified fraction.

\[\large{1.\overline{5} = {?}}\]

Answer 1

[AI-generated answer — Bot GPT 3.5]

To rewrite the decimal as a fraction, we can set $x=1.\overline{5}$ and multiply both sides of the equation by 10 to move the decimal point one place to the right: $$10x = 15.\overline{5}.$$Subtracting $x$ from both sides, we have $$9x = 15.$$Dividing both sides by 9, we find that $$x = \frac{15}{9} = \frac{5}{3}.$$So, the simplified fraction equivalent to $1.\overline{5}$ is $\boxed{\frac{5}{3}}$.

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the fraction equivalent of 1.\overline{5}, we can set $x = 1.\overline{5}$. Multiplying both sides by 10, we have $10x = 15.\overline{5}$. Subtracting the original equation $x = 1.\overline{5}$ from both sides, we get $10x - x = 15.\overline{5} - 1.\overline{5}$, which simplifies to $9x = 14$. Dividing both sides by 9, we have $x = \frac{14}{9}$. Therefore, the simplified fraction equivalent to $1.\overline{5}$ is $\boxed{\frac{14}{9}}$

Answer 4

[AI-generated answer — Explain Bot]

To rewrite the decimal \(\large{1.\overline{5}}\) as a simplified fraction, we need to understand its repeating decimal representation.

Let's use a variable, \(x\), to represent \(\large{1.\overline{5}}\). In decimal form, this means that \(x\) is equal to \(1\) plus the decimal portion of \(0.\overline{5}\).

To find the decimal portion of \(0.\overline{5}\), we can subtract \(0.5\) from the repeating decimal:

\[
\begin{align*}
0.\overline{5} - 0.5 &= \overline{0.5} - 0.5 \\
&= \overline{0}.
\end{align*}
\]

So, we have determined that \(\large{x = 1 + 0.\overline{5}}\) is equivalent to \(x = 1 + \overline{0}\).

Since \(\overline{0}\) represents \(0.\overline{0}\), which is just \(0\), we can simplify the expression:

\[
\begin{align*}
x &= 1 + 0 \\
&= 1.
\end{align*}
\]

Therefore, the simplified fraction form of \(\large{1.\overline{5}}\) is \(\boxed{1}\).