To find the sum of the fractions \( \frac{3}{8} + \frac{1}{4} \), we need to follow a systematic approach 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. In this case, we have: - The first fraction \( \frac{3}{8} \) has a denominator of 8. - The second fraction \( \frac{1}{4} \) has a denominator of 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: \[ \frac{3}{8} + \frac{2}{8} = \frac{3 + 2}{8} = \frac{5}{8} \] ### Step 4: Final Answer The sum of the fractions \( \frac{3}{8} + \frac{1}{4} \) is \( \frac{5}{8} \). ### Explanation of Options Now, let's review the options provided: - **A. \( \frac{5}{8} \)**: This is the correct answer, as we calculated. - **B. \( \frac{7}{8} \)**: This is incorrect. It may arise from a miscalculation, possibly by incorrectly adding the numerators or misinterpreting the fractions. - **C. \( \frac{1}{2} \)**: This is also incorrect. \( \frac{1}{2} \) is equivalent to \( \frac{4}{8} \), which is less than \( \frac{5}{8} \). - **D. \( \frac{3}{4} \)**: This is incorrect as well. \( \frac{3}{4} \) is equivalent to \( \frac{6}{8} \), which is greater than \( \frac{5}{8} \). ### Common Pitfalls - **Not finding a common denominator**: Always ensure that fractions have the same denominator before adding. - **Incorrectly converting fractions**: When changing the denominator, remember to multiply both the numerator and denominator by the same number. - **Adding numerators without considering the denominators**: Ensure that you only add the numerators after confirming the denominators are the same. ### Revision Summary - To add fractions, find a common denominator. - Convert fractions to have the same denominator if necessary. - Add the numerators and keep the common denominator. - Double-check your work to avoid common mistakes. The correct answer to the question is **A. \( \frac{5}{8} \)**.