To write equivalent fractions for $\frac{3}{4}$ and $\frac{1}{6}$ using a common denominator, follow these steps:

1. Find the Least Common Denominator (LCD):

   • The denominators are 4 and 6.
   • The least common multiple (LCM) of 4 and 6 is 12.
   • So, the least common denominator is 12.

2. Convert $\frac{3}{4}$ to an equivalent fraction with a denominator of 12:

   • Multiply both the numerator and the denominator of $\frac{3}{4}$ by 3 (since $4 \times 3 = 12$): $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

3. Convert $\frac{1}{6}$ to an equivalent fraction with a denominator of 12:

   • Multiply both the numerator and the denominator of $\frac{1}{6}$ by 2 (since $6 \times 2 = 12$): $\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$

So, the equivalent fractions with a common denominator are: $\frac{9}{12} \quad \text{and} \quad \frac{2}{12}$

Would you like more details on this process, or do you have any questions?

Here are five related questions to consider:

1. How do you find the least common denominator of two or more fractions?
2. Can you add or subtract fractions with different denominators without converting them?
3. What is the benefit of using the least common denominator instead of any common denominator?
4. How would you convert improper fractions to mixed numbers?
5. Can you simplify the fraction $\frac{9}{12}$? If so, what is the simplified form?

Tip: When finding the least common denominator, list the multiples of each denominator to easily identify the smallest one they share.