To find the result of adding the fractions \( \frac{3}{4} \) and \( \frac{2}{5} \), we need to follow a series of steps to ensure we perform the addition correctly. Let's go through this step-by-step. ### Step 1: Find a Common Denominator When adding fractions, we need to have a common denominator. The denominators in our fractions are 4 and 5. The least common multiple (LCM) of 4 and 5 is 20. This will be our common denominator. ### Step 2: Convert Each Fraction Next, we need to convert each fraction to have this common denominator of 20. 1. **Convert \( \frac{3}{4} \)**: - To convert \( \frac{3}{4} \) to a fraction with a denominator of 20, we can 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 fraction with a denominator of 20, we can 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 3: 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 4: Simplify if Necessary In this case, \( \frac{23}{20} \) is already in its simplest form. It is an improper fraction, which means the numerator is greater than the denominator. If needed, it can also be expressed as a mixed number: \[ \frac{23}{20} = 1 \frac{3}{20} \] ### Conclusion The result of adding \( \frac{3}{4} \) and \( \frac{2}{5} \) is \( \frac{23}{20} \). ### Explanation of Options - **Option A: \( \frac{7}{20} \)** - This is incorrect because it does not represent the sum of the two fractions. It seems to be a miscalculation. - **Option B: \( \frac{23}{20} \)** - This is the correct answer, as shown in our calculations. - **Option C: \( \frac{13}{20} \)** - This is also incorrect. It may arise from an incorrect addition or misunderstanding of the common denominator. - **Option D: \( \frac{1}{5} \)** - This is incorrect as it is far less than the sum of the two fractions and does not relate to the problem. ### Revision Summary - To add fractions, find a common denominator. - Convert each fraction to have the common denominator. - Add the numerators while keeping the common denominator. - Simplify the result if necessary. The correct answer is **B: \( \frac{23}{20} \)**.