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!