To find a common denominator for the fractions [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{3}{9}\)[/tex], you need to determine the least common multiple (LCM) of their denominators.
1. Identify the denominators of the fractions:
- For [tex]\(\frac{1}{4}\)[/tex], the denominator is 4.
- For [tex]\(\frac{3}{9}\)[/tex], the denominator is 9.
2. Determine the LCM of 4 and 9. The LCM is the smallest positive integer that is divisible by both 4 and 9.
3. By finding the LCM, we determine that the smallest positive integer divisible by both 4 and 9 is 36.
4. Therefore, the common denominator for [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{3}{9}\)[/tex] is [tex]\(36\)[/tex].
Hence, the answer is [tex]\(36\)[/tex].
