Certainly! Let's start with the problem of adding the fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex]. We'll go through the process step by step:
1. Find the common denominator: The denominators of the fractions are 5 and 6. The least common multiple (LCM) of 5 and 6 is 30. Therefore, our common denominator is 30.
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[
\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}
\][/tex]
- For [tex]\(\frac{1}{6}\)[/tex]:
[tex]\[
\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}
\][/tex]
3. Add the fractions:
- Sum the numerators while keeping the common denominator:
[tex]\[
\frac{18}{30} + \frac{5}{30} = \frac{18 + 5}{30} = \frac{23}{30}
\][/tex]
4. Simplify the fraction, if possible: The fraction [tex]\(\frac{23}{30}\)[/tex] is already in its simplest form because 23 and 30 have no common factors other than 1.
Therefore, the final simplified result of adding [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex] is [tex]\(\frac{23}{30}\)[/tex].
