To divide the fraction \(\frac{1}{8}\) by the fraction \(\frac{-1}{6}\), we can follow these steps:
1. Understand the Problem:
To divide one fraction by another, you multiply the first fraction by the reciprocal (or multiplicative inverse) of the second fraction.
2. Reciprocal of the Second Fraction:
The reciprocal of \(\frac{-1}{6}\) is \(\frac{-6}{1}\). This means we convert the division into a multiplication problem.
3. Set Up the Multiplication:
Instead of \(\frac{1}{8} \div \frac{-1}{6}\), we rewrite it as \(\frac{1}{8} \times \frac{-6}{1}\).
4. Perform the Multiplication:
To multiply the fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{1 \times -6}{8 \times 1} = \frac{-6}{8}
\][/tex]
5. Simplify the Result:
Simplify the fraction \(\frac{-6}{8}\):
[tex]\[
\frac{-6}{8} = \frac{-6 \div 2}{8 \div 2} = \frac{-3}{4}
\][/tex]
6. Convert to Decimal:
Finally, convert the simplified fraction to a decimal for better readability:
[tex]\[
\frac{-3}{4} = -0.75
\][/tex]
Therefore, the result of the division [tex]\(\frac{1}{8} \div \frac{-1}{6}\)[/tex] is [tex]\(-0.75\)[/tex].
