\( 5 \frac{1}{2} \) Inches \( +\frac{3}{8} \) Inches \( +\frac{7}{16} \) Inches

To solve the problem, we need to add the three measurements together: \( 5 \frac{1}{2} \) inches, \( \frac{3}{8} \) inches, and \( \frac{7}{16} \) inches. ### Step 1: Convert the mixed number to an improper fraction First, we convert \( 5 \frac{1}{2} \) to an improper fraction. \[ 5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \] ### Step 2: Find a common denominator Next, we need to find a common denominator for the fractions \( \frac{11}{2} \), \( \frac{3}{8} \), and \( \frac{7}{16} \). The denominators are 2, 8, and 16. The least common multiple (LCM) of these numbers is 16. ### Step 3: Convert each fraction to have the common denominator Now we convert each fraction: 1. Convert \( \frac{11}{2} \) to a denominator of 16: \[ \frac{11}{2} = \frac{11 \times 8}{2 \times 8} = \frac{88}{16} \] 2. \( \frac{3}{8} \) to a denominator of 16: \[ \frac{3}{8} = \frac{3 \times 2}{8 \times 2} = \frac{6}{16} \] 3. \( \frac{7}{16} \) is already in terms of 16. ### Step 4: Add the fractions Now we can add the fractions together: \[ \frac{88}{16} + \frac{6}{16} + \frac{7}{16} = \frac{88 + 6 + 7}{16} = \frac{101}{16} \] ### Step 5: Convert back to a mixed number Finally, we convert \( \frac{101}{16} \) back to a mixed number: \[ 101 \div 16 = 6 \quad \text{(remainder 5)} \] So, \( \frac{101}{16} = 6 \frac{5}{16} \). ### Final Answer The sum of \( 5 \frac{1}{2} \) inches, \( \frac{3}{8} \) inches, and \( \frac{7}{16} \) inches is: \[ 6 \frac{5}{16} \text{ inches} \]