To divide two fractions, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is created by swapping its numerator and denominator. Let's go through the steps to solve \(\frac{5}{3} \div \frac{30}{12}\).

### Step-by-step Solution

1. **Write down the division of fractions:**
   \[
   \frac{5}{3} \div \frac{30}{12}
   \]

2. **Find the reciprocal of the second fraction:**
   The reciprocal of \(\frac{30}{12}\) is \(\frac{12}{30}\).

3. **Convert the division into multiplication:**
   \[
   \frac{5}{3} \times \frac{12}{30}
   \]

4. **Multiply the fractions:**
   \[
   \frac{5 \times 12}{3 \times 30}
   \]

5. **Calculate the multiplication:**
   \[
   \frac{60}{90}
   \]

6. **Simplify the fraction:**
   To simplify \(\frac{60}{90}\), find the greatest common divisor (GCD) of 60 and 90, which is 30. Divide both the numerator and the denominator by 30:
   \[
   \frac{60 \div 30}{90 \div 30} = \frac{2}{3}
   \]

### Final Answer

\[
\frac{5}{3} \div \frac{30}{12} = \frac{2}{3}
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How do you multiply two fractions?
2. What is the reciprocal of a fraction, and how is it used in division?
3. How do you simplify a fraction?
4. Can the division of two fractions result in a whole number?
5. What is the difference between dividing fractions and multiplying fractions?

**Tip:** Always simplify fractions at the end of your calculations to get the answer in its simplest form!

Learn how to divide fractions \(\frac{5}{3}\) by \(\frac{30}{12}\) using the reciprocal method with a step-by-step solution. This problem covers the division of fractions, reciprocal of fractions, and simplification techniques. Suitable for students in Grades 6-8.

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