1. **State the problem:** Calculate the value of $$B = \frac{\frac{1}{4} + \frac{3}{2} - \frac{5}{3}}{\frac{41}{24} - \frac{7}{8} \div \frac{3}{5}}$$ 2. **Recall the order of operations:** - Perform division and multiplication before addition and subtraction. - When dividing fractions, multiply by the reciprocal. 3. **Calculate the numerator:** $$\frac{1}{4} + \frac{3}{2} - \frac{5}{3}$$ Find a common denominator, which is 12: $$\frac{1}{4} = \frac{3}{12}, \quad \frac{3}{2} = \frac{18}{12}, \quad \frac{5}{3} = \frac{20}{12}$$ Sum and subtract: $$3/12 + 18/12 - 20/12 = (3 + 18 - 20)/12 = 1/12$$ 4. **Calculate the denominator:** $$\frac{41}{24} - \frac{7}{8} \div \frac{3}{5}$$ First, divide $\frac{7}{8} \div \frac{3}{5}$: $$\frac{7}{8} \times \frac{5}{3} = \frac{35}{24}$$ Now subtract: $$\frac{41}{24} - \frac{35}{24} = \frac{6}{24} = \frac{1}{4}$$ 5. **Combine numerator and denominator:** $$B = \frac{\frac{1}{12}}{\frac{1}{4}} = \frac{1}{12} \times \frac{4}{1} = \frac{4}{12} = \frac{1}{3}$$ **Final answer:** $$B = \frac{1}{3}$$