To solve [tex]\(\frac{1}{5} + \frac{1}{6}\)[/tex], we first need to find a common denominator for the fractions. Here is a detailed, step-by-step solution:
1. Find the Least Common Denominator (LCD):
- The denominators here are 5 and 6.
- The least common multiple (LCM) of 5 and 6 is 30, so 30 is our common denominator.
2. Convert the Fractions:
- We need to convert [tex]\(\frac{1}{5}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex] so they have the same denominator, 30.
- To convert [tex]\(\frac{1}{5}\)[/tex] to a fraction with denominator 30:
[tex]\[
\frac{1}{5} = \frac{1 \times 6}{5 \times 6} = \frac{6}{30}
\][/tex]
- To convert [tex]\(\frac{1}{6}\)[/tex] to a fraction with denominator 30:
[tex]\[
\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}
\][/tex]
3. Add the Fractions:
- Now that both fractions have the same denominator, we can add them:
[tex]\[
\frac{6}{30} + \frac{5}{30} = \frac{6 + 5}{30} = \frac{11}{30}
\][/tex]
4. Convert to Decimal (if required):
- To express [tex]\(\frac{11}{30}\)[/tex] as a decimal, divide the numerator by the denominator:
[tex]\[
\frac{11}{30} \approx 0.36666666666666664
\][/tex]
Hence, [tex]\(\frac{1}{5} + \frac{1}{6} = \frac{11}{30} \approx 0.36666666666666664\)[/tex].
