Sure, let's rewrite the fractions [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] with a least common denominator.
1. Identify the Denominators:
The denominators of the fractions [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] are 4 and 6, respectively.
2. Find the Least Common Multiple (LCM) of the Denominators:
The least common multiple of 4 and 6 is the smallest number that is a multiple of both. In this case, the LCM of 4 and 6 is 12.
3. Rewrite Each Fraction with the Least Common Denominator:
- For [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
\][/tex]
- For [tex]\(\frac{5}{6}\)[/tex]:
[tex]\[
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
\][/tex]
So, the fractions [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] rewritten with a least common denominator of 12 are [tex]\(\frac{3}{12}\)[/tex] and [tex]\(\frac{10}{12}\)[/tex].
Therefore, the answer is:
[tex]\[
\boxed{\frac{3}{12} \text{ and } \frac{10}{12}}
\][/tex]
