15. [-/1 Points] DETAILS MY NOTES TGEIALG6 1.2.091. Perform the operation and, if possible, simplify. Need Help? Read It Watch It \( \div \frac{4}{27} \) SUBMIT ANSWER

It looks like the operation you need to perform involves dividing by the fraction \(\frac{4}{27}\). However, the first part of the operation (the dividend) seems to be missing from your question. To help you understand how to perform and simplify such operations, I'll provide a general explanation. ### **Dividing by a Fraction** When you divide by a fraction, it's equivalent to multiplying by its **reciprocal**. The reciprocal of a fraction is created by swapping its numerator and denominator. **General Rule:** \[ a \div \frac{b}{c} = a \times \frac{c}{b} \] ### **Step-by-Step Example** Let's say you need to perform the following operation: \[ \frac{2}{3} \div \frac{4}{27} \] **Step 1: Identify the Reciprocal of the Divisor** The divisor here is \(\frac{4}{27}\), so its reciprocal is \(\frac{27}{4}\). **Step 2: Multiply the Dividend by the Reciprocal of the Divisor** \[ \frac{2}{3} \times \frac{27}{4} \] **Step 3: Multiply the Numerators and the Denominators** \[ \frac{2 \times 27}{3 \times 4} = \frac{54}{12} \] **Step 4: Simplify the Fraction** \[ \frac{54}{12} = \frac{9}{2} \quad \text{(by dividing both numerator and denominator by 6)} \] ### **Final Answer** \[ \frac{9}{2} \] ### **Summary** - **Divide by a fraction** by **multiplying by its reciprocal**. - **Simplify** the resulting fraction if possible. If you provide the complete operation, I'd be happy to help you solve it specifically!