7 5/12 - (1 5/8 + 2 1/24)=

To solve the expression \( 7 \frac{5}{12} - (1 \frac{5}{8} + 2 \frac{1}{24}) \), we will first convert all mixed numbers to improper fractions, calculate the sum inside the parentheses, and then perform the subtraction. 1. Convert \( 7 \frac{5}{12} \) to an improper fraction: \[ 7 \frac{5}{12} = \frac{7 \times 12 + 5}{12} = \frac{84 + 5}{12} = \frac{89}{12} \] 2. Convert \( 1 \frac{5}{8} \) to an improper fraction: \[ 1 \frac{5}{8} = \frac{1 \times 8 + 5}{8} = \frac{8 + 5}{8} = \frac{13}{8} \] 3. Convert \( 2 \frac{1}{24} \) to an improper fraction: \[ 2 \frac{1}{24} = \frac{2 \times 24 + 1}{24} = \frac{48 + 1}{24} = \frac{49}{24} \] 4. Now, calculate \( 1 \frac{5}{8} + 2 \frac{1}{24} \): First, find a common denominator for \( \frac{13}{8} \) and \( \frac{49}{24} \). The least common multiple of 8 and 24 is 24. Convert \( \frac{13}{8} \) to have a denominator of 24: \[ \frac{13}{8} = \frac{13 \times 3}{8 \times 3} = \frac{39}{24} \] Now add: \[ \frac{39}{24} + \frac{49}{24} = \frac{39 + 49}{24} = \frac{88}{24} \] Simplifying \( \frac{88}{24} \): \[ \frac{88 \div 8}{24 \div 8} = \frac{11}{3} \] 5. Now substitute back into the original expression: \[ 7 \frac{5}{12} - (1 \frac{5}{8} + 2 \frac{1}{24}) = \frac{89}{12} - \frac{11}{3} \] Convert \( \frac{11}{3} \) to a fraction with a denominator of 12: \[ \frac{11}{3} = \frac{11 \times 4}{3 \times 4} = \frac{44}{12} \] 6. Now perform the subtraction: \[ \frac{89}{12} - \frac{44}{12} = \frac{89 - 44}{12} = \frac{45}{12} \] Simplifying \( \frac{45}{12} \): \[ \frac{45 \div 3}{12 \div 3} = \frac{15}{4} \] 7. Convert \( \frac{15}{4} \) back to a mixed number: \[ 15 \div 4 = 3 \text{ R } 3 \quad \Rightarrow \quad 3 \frac{3}{4} \] Thus, the final answer is: \[ 3 \frac{3}{4} \]