Of course! Let's simplify and evaluate the fraction [tex]\(\frac{-13}{-117}\)[/tex] step by step:
1. Identify the negative signs:
- Both the numerator and the denominator are negative. When a negative number is divided by another negative number, the result is positive. Therefore, [tex]\(\frac{-13}{-117} = \frac{13}{117}\)[/tex].
2. Simplify the fraction:
- To simplify [tex]\(\frac{13}{117}\)[/tex], we need to identify the greatest common divisor (GCD) of 13 and 117.
- The GCD of 13 and 117 is 13 because 13 is a prime number, and 117 is divisible by 13. Let's divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{13}{117} = \frac{13 \div 13}{117 \div 13} = \frac{1}{9}
\][/tex]
3. Evaluate the fraction:
- Now that we have simplified the fraction to [tex]\(\frac{1}{9}\)[/tex], we need to calculate its decimal form.
- The decimal form of [tex]\(\frac{1}{9}\)[/tex] is a repeating decimal, specifically:
[tex]\[
\frac{1}{9} = 0.1111111111111111\ldots
\][/tex]
So, the decimal representation of the fraction [tex]\(\frac{-13}{-117}\)[/tex] is [tex]\(0.1111111111111111\)[/tex].
Thus, the solution to the fraction [tex]\(\frac{-13}{-117}\)[/tex] is [tex]\(\boxed{0.1111111111111111}\)[/tex].
