Certainly!
To solve the problem, we need to divide the fraction [tex]\(-\frac{7}{8}\)[/tex] by the fraction [tex]\(-\frac{3}{4}\)[/tex].
Here are the steps to find the quotient:
1. Identify the fractions involved:
- Dividend = [tex]\(-\frac{7}{8}\)[/tex]
- Divisor = [tex]\(-\frac{3}{4}\)[/tex]
2. Division of fractions: To divide one fraction by another, multiply the first fraction (dividend) by the reciprocal of the second fraction (divisor).
The reciprocal of [tex]\(-\frac{3}{4}\)[/tex] is [tex]\(-\frac{4}{3}\)[/tex].
3. Set up the multiplication:
[tex]\[
\frac{-7}{8} \div \frac{-3}{4} = \frac{-7}{8} \times \frac{-4}{3}
\][/tex]
4. Multiply the numerators and the denominators:
[tex]\[
\frac{-7 \times -4}{8 \times 3} = \frac{28}{24}
\][/tex]
5. Simplify the resulting fraction: Simplify [tex]\(\frac{28}{24}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 28 and 24 is 4.
[tex]\[
\frac{28 \div 4}{24 \div 4} = \frac{7}{6}
\][/tex]
6. Convert to a mixed number if needed: The quotient [tex]\(\frac{7}{6}\)[/tex] can be written as a mixed number.
[tex]\(\frac{7}{6} = 1 \frac{1}{6}\)[/tex]
Therefore, the quotient of [tex]\(\frac{\frac{-7}{8}}{\frac{-3}{4}}\)[/tex] is:
[tex]\[
1 \frac{1}{6}
\][/tex]
So, the correct answer is [tex]\(1 \frac{1}{6}\)[/tex].
