To solve the problem [tex]\( \frac{1}{4} + \frac{3}{8} \)[/tex], we need to add the two fractions and reduce the sum to its lowest terms. Here is a detailed step-by-step solution:
1. Identify the denominators:
- The denominators are 4 and 8.
2. Find the least common denominator (LCD):
- The least common denominator of 4 and 8 is 8.
3. Convert the fractions to have the same denominator:
- To convert [tex]\( \frac{1}{4} \)[/tex] to a fraction with a denominator of 8, multiply both the numerator and the denominator by 2:
[tex]\[
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
\][/tex]
- The second fraction, [tex]\( \frac{3}{8} \)[/tex], already has the denominator of 8.
4. Add the fractions:
- Now that we have like denominators, we can add the fractions:
[tex]\[
\frac{2}{8} + \frac{3}{8} = \frac{2 + 3}{8} = \frac{5}{8}
\][/tex]
5. Simplify the result (if needed):
- In this case, the fraction [tex]\( \frac{5}{8} \)[/tex] is already in its simplest form because the numerator and denominator share no common factors other than 1.
Therefore, the reduced form of [tex]\( \frac{1}{4} + \frac{3}{8} \)[/tex] is [tex]\( \frac{5}{8} \)[/tex], and the correct answer is:
[tex]\[
\boxed{\frac{5}{8}}
\][/tex]
