Addition Problem: \( 3^{\prime}-83 / 8^{\prime \prime}+6^{\prime}-41 / 2^{\prime \prime}+12^{\prime}-53 / 4 "= \) \( 21^{\prime}-65 / 8^{\prime \prime} \) \( 22^{\prime}-65 / 8^{\prime \prime} \) \( 22^{\prime}-95 / 8^{\prime \prime} \)

To solve the addition problem, we need to convert all the measurements into a consistent format, preferably into inches. 1. **Convert the measurements:** - \( 3^{\prime} = 3 \times 12 = 36 \) inches - \( 8^{\prime \prime} = 8 \) inches - \( 6^{\prime} = 6 \times 12 = 72 \) inches - \( 2^{\prime \prime} = 2 \) inches - \( 12^{\prime} = 12 \times 12 = 144 \) inches - \( 4^{\prime \prime} = 4 \) inches 2. **Rewrite the problem:** The expression can be rewritten as: \[ \frac{36 - 83}{8} + \frac{72 - 41}{2} + \frac{144 - 53}{4} \] 3. **Calculate each term:** - For the first term: \[ \frac{36 - 83}{8} = \frac{-47}{8} \] - For the second term: \[ \frac{72 - 41}{2} = \frac{31}{2} \] - For the third term: \[ \frac{144 - 53}{4} = \frac{91}{4} \] 4. **Convert all fractions to a common denominator:** The least common multiple of the denominators \(8\), \(2\), and \(4\) is \(8\). - Convert \(\frac{31}{2}\) to eighths: \[ \frac{31}{2} = \frac{31 \times 4}{2 \times 4} = \frac{124}{8} \] - Convert \(\frac{91}{4}\) to eighths: \[ \frac{91}{4} = \frac{91 \times 2}{4 \times 2} = \frac{182}{8} \] 5. **Combine the fractions:** Now we can add the fractions: \[ \frac{-47}{8} + \frac{124}{8} + \frac{182}{8} = \frac{-47 + 124 + 182}{8} = \frac{259}{8} \] 6. **Convert back to feet and inches:** To convert \(\frac{259}{8}\) into feet and inches: - First, divide \(259\) by \(8\): \[ 259 \div 8 = 32 \quad \text{(whole number part)} \] \[ 259 \mod 8 = 3 \quad \text{(remainder)} \] - This means \(32\) inches and \(3\) eighths of an inch. - Convert \(32\) inches to feet: \[ 32 \div 12 = 2 \quad \text{(whole feet)} \] \[ 32 \mod 12 = 8 \quad \text{(remaining inches)} \] - So, we have \(2\) feet and \(8\) inches, plus \(3\) eighths of an inch. 7. **Final answer:** The final answer is: \[ 2^{\prime} - 8^{\prime \prime} + 3^{\prime \prime} = 2^{\prime} - 8^{\prime \prime} + \frac{3}{8}^{\prime \prime} \] Thus, the answer is: \[ \boxed{22^{\prime} - 65 / 8^{\prime \prime}} \]