To find the sum of the fractions \( \frac{3}{8} \) and \( \frac{1}{4} \), we need to follow a series of steps to ensure we add them correctly. Let's break it down step-by-step. ### Step 1: Identify a Common Denominator Fractions can only be added directly if they have the same denominator. The denominators in our fractions are 8 and 4. - The denominator of \( \frac{3}{8} \) is 8. - The denominator of \( \frac{1}{4} \) is 4. To add these fractions, we need a common denominator. The least common multiple (LCM) of 8 and 4 is 8. This means we can keep \( \frac{3}{8} \) as it is, but we need to convert \( \frac{1}{4} \) to have a denominator of 8. ### Step 2: Convert \( \frac{1}{4} \) to a Fraction with a Denominator of 8 To convert \( \frac{1}{4} \) to a fraction with a denominator of 8, we can multiply both the numerator and the denominator by 2: \[ \frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8} \] ### Step 3: Add the Fractions Now that both fractions have the same denominator, we can add them: \[ \frac{3}{8} + \frac{2}{8} = \frac{3 + 2}{8} = \frac{5}{8} \] ### Conclusion The sum of \( \frac{3}{8} \) and \( \frac{1}{4} \) is \( \frac{5}{8} \). ### Explanation of the Options Now, let's evaluate the options provided: - **A. \( \frac{5}{8} \)**: This is the correct answer, as we calculated above. - **B. \( \frac{7}{8} \)**: This option is incorrect. It suggests that the sum is greater than \( \frac{5}{8} \), which is not possible since both fractions being added are less than 1. - **C. \( \frac{1}{2} \)**: This option is also incorrect. \( \frac{1}{2} \) is equivalent to \( \frac{4}{8} \), which is less than the sum we calculated. - **D. \( \frac{3}{4} \)**: This option is incorrect as well. \( \frac{3}{4} \) is equivalent to \( \frac{6}{8} \), which is greater than \( \frac{5}{8} \). ### Summary of Key Points - To add fractions, ensure they have a common denominator. - Convert fractions as necessary to achieve this common denominator. - Add the numerators while keeping the common denominator. - The correct answer to the sum of \( \frac{3}{8} \) and \( \frac{1}{4} \) is \( \frac{5}{8} \). This thorough approach ensures that you understand not just the answer, but the reasoning behind it, which is crucial for mastering fraction addition in mathematics.