To find the result of adding the fractions \( \frac{3}{8} \) and \( \frac{1}{4} \), we need to follow a series of steps to ensure we perform the addition 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: \[ \frac{3}{8} + \frac{2}{8} = \frac{3 + 2}{8} = \frac{5}{8} \] ### Step 4: Final Result The result of adding \( \frac{3}{8} \) and \( \frac{1}{4} \) is \( \frac{5}{8} \). ### Explanation of the Correct Option The correct option is **A. \( \frac{5}{8} \)**. This is the result we obtained after ensuring both fractions had a common denominator and then performing the addition. ### Explanation of Why Other Options Are Incorrect - **B. \( \frac{7}{8} \)**: This option suggests that the sum is larger than \( \frac{5}{8} \). If we had added \( \frac{3}{8} \) and \( \frac{4}{8} \) (which is \( \frac{1}{2} \)), we would get \( \frac{7}{8} \). However, we only added \( \frac{2}{8} \), not \( \frac{4}{8} \). - **C. \( \frac{1}{2} \)**: This option is equivalent to \( \frac{4}{8} \). The sum of \( \frac{3}{8} \) and \( \frac{2}{8} \) is greater than \( \frac{1}{2} \), so this option is incorrect. - **D. \( \frac{3}{4} \)**: This option is equivalent to \( \frac{6}{8} \). Again, since \( \frac{5}{8} \) is less than \( \frac{3}{4} \), this option is also incorrect. ### Common Pitfalls - **Not finding a common denominator**: This is a common mistake when adding fractions. Always ensure the denominators are the same before proceeding. - **Incorrectly converting fractions**: When changing the denominator, remember to multiply both the numerator and denominator by the same number. - **Adding numerators without adjusting 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. - Simplify the result if possible. By following these steps, you can confidently add fractions and avoid common mistakes!