To find the result of adding the fractions \( \frac{3}{4} \) and \( \frac{1}{2} \), 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 4 (from \( \frac{3}{4} \)) and 2 (from \( \frac{1}{2} \)). To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 4 and 2 is 4. This means we can convert \( \frac{1}{2} \) into a fraction with a denominator of 4. ### Step 2: Convert \( \frac{1}{2} \) to a Fraction with a Denominator of 4 To convert \( \frac{1}{2} \) to a fraction with a denominator of 4, we can multiply both the numerator and the denominator by 2: \[ \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \] ### Step 3: Add the Fractions Now that both fractions have the same denominator, we can add them: \[ \frac{3}{4} + \frac{2}{4} = \frac{3 + 2}{4} = \frac{5}{4} \] ### Step 4: Final Result The result of adding \( \frac{3}{4} \) and \( \frac{1}{2} \) is \( \frac{5}{4} \). ### Explanation of the Correct Option The correct answer is **B. \( \frac{5}{4} \)**. This fraction is an improper fraction, which means the numerator is greater than the denominator. It can also be expressed as a mixed number: \( 1 \frac{1}{4} \). ### Why the Other Options are Incorrect - **A. \( \frac{1}{4} \)**: This option is incorrect because it does not represent the sum of \( \frac{3}{4} \) and \( \frac{1}{2} \). It is much smaller than the actual sum. - **C. \( \frac{2}{4} \)**: This option simplifies to \( \frac{1}{2} \), which is also incorrect. It represents only one of the fractions, not their sum. - **D. \( \frac{3}{2} \)**: This option is incorrect as well. While it is a valid fraction, it does not represent the sum of \( \frac{3}{4} \) and \( \frac{1}{2} \). The correct sum is \( \frac{5}{4} \), which is less than \( \frac{3}{2} \). ### Summary of Key Points - To add fractions, ensure they have a common denominator. - Convert fractions as necessary to achieve a common denominator. - Add the numerators while keeping the common denominator. - The final answer can be simplified or expressed as a mixed number if needed. By following these steps, you can confidently add fractions and understand the reasoning behind the operations.