Here’s a detailed guide on how to multiply \( \frac{6}{18} \) by the reciprocal of \( -\frac{7}{18} \).
Step 1: Understanding Reciprocals
- The reciprocal of a fraction \( \frac{a}{b} \) is obtained by flipping the numerator and denominator, resulting in \( \frac{b}{a} \).
- For \( -\frac{7}{18} \), the reciprocal is \( -\frac{18}{7} \).
Step 2: Setting Up the Multiplication
- We need to multiply \( \frac{6}{18} \) by the reciprocal of \( -\frac{7}{18} \):
\[
\frac{6}{18} \times -\frac{18}{7}
\]
Step 3: Simplifying the Fractions
- Before multiplying, simplify \( \frac{6}{18} \):
- \( \frac{6}{18} = \frac{1}{3} \) (dividing numerator and denominator by 6).
- The expression now looks like:
\[
\frac{1}{3} \times -\frac{18}{7}
\]
Step 4: Performing the Multiplication
- Multiply the numerators and denominators:
\[
\frac{1 \times -18}{3 \times 7} = \frac{-18}{21}
\]
Step 5: Final Simplification
- Simplify \( \frac{-18}{21} \):
- The GCD of 18 and 21 is 3, so divide both by 3:
\[
\frac{-6}{7}
\]
Final Answer
- Thus, the result of multiplying \( \frac{6}{18} \) by the reciprocal of \( -\frac{7}{18} \) is:
\[
\frac{-6}{7}
\]