To find the result of adding the fractions \( \frac{3}{4} \) and \( \frac{2}{5} \), we need to follow a systematic approach. Let's break it down step-by-step. ### Step 1: Identify the Denominators The denominators of the fractions are: - For \( \frac{3}{4} \), the denominator is 4. - For \( \frac{2}{5} \), the denominator is 5. ### Step 2: Find the Least Common Denominator (LCD) To add fractions, we need a common denominator. The least common denominator (LCD) is the smallest number that both denominators can divide into without leaving a remainder. - The multiples of 4 are: 4, 8, 12, 16, 20, ... - The multiples of 5 are: 5, 10, 15, 20, ... The smallest common multiple is 20. Therefore, the LCD is 20. ### Step 3: Convert Each Fraction to the Common Denominator Next, we convert each fraction to have the common denominator of 20. 1. **Convert \( \frac{3}{4} \)**: - To convert \( \frac{3}{4} \) to a denominator of 20, we multiply both the numerator and the denominator by 5 (since \( 4 \times 5 = 20 \)): \[ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \] 2. **Convert \( \frac{2}{5} \)**: - To convert \( \frac{2}{5} \) to a denominator of 20, we multiply both the numerator and the denominator by 4 (since \( 5 \times 4 = 20 \)): \[ \frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \] ### Step 4: Add the Converted Fractions Now that both fractions have the same denominator, we can add them: \[ \frac{15}{20} + \frac{8}{20} = \frac{15 + 8}{20} = \frac{23}{20} \] ### Step 5: Final Result The result of adding \( \frac{3}{4} \) and \( \frac{2}{5} \) is: \[ \frac{23}{20} \] ### Conclusion: Correct Option The correct option is **A. \( \frac{23}{20} \)**. ### Explanation of Other Options - **B. \( \frac{17}{20} \)**: This option is incorrect because it does not represent the sum of the two fractions. It may have resulted from an error in the addition or conversion process. - **C. \( \frac{13}{20} \)**: This option is also incorrect. It could be a result of miscalculating the individual fractions or misunderstanding the addition process. - **D. \( \frac{7}{9} \)**: This option is incorrect as it does not relate to the problem at all. It seems to be a random fraction that does not correspond to the addition of \( \frac{3}{4} \) and \( \frac{2}{5} \). ### Revision Summary - To add fractions, find a common denominator (LCD). - Convert each fraction to the common denominator. - Add the numerators while keeping the common denominator. - Simplify if necessary, but in this case, \( \frac{23}{20} \) is already in its simplest form. By following these steps, you can confidently add any fractions together!