This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Convert all mixed numbers to improper fractions. For the numerator: 4(1)/(4) = (4 × 4 + 1)/(4) = (17)/(4) 3(1)/(2) = (3 × 2 + 1)/(2) = (7)/(2) 3(1)/(8) = (3 × 8 + 1)/(8) = (25)/(8) For the denominator: 3(2)/(5) = (3 × 5 + 2)/(5) = (17)/(5) 1(1)/(4) = (1 × 4 + 1)/(4) = (5)/(4) 2(5)/(6) = (2 × 6 + 5)/(6) = (17)/(6) Step 2: Evaluate the numerator. (17)/(4) - (7)/(2) + (25)/(8) Find a common denominator, which is 8. (17 × 2)/(4 × 2) - (7 × 4)/(2 × 4) + (25)/(8) = (34)/(8) - (28)/(8) + (25)/(8) (34 - 28 + 25)/(8) = (6 + 25)/(8) = (31)/(8) Step 3: Evaluate the denominator. The expression is 3(2)/(5) of 1(1)/(4) ÷ 2(5)/(6). "of" means multiplication. (17)/(5) × (5)/(4) ÷ (17)/(6) First, perform the multiplication: (17)/(5) × (5)/(4) = (17 × 5)/(5 × 4) = (17)/(4) Next, perform the division. To divide by a fraction, multiply by its reciprocal: (17)/(4) ÷ (17)/(6) = (17)/(4) × (6)/(17) (17 × 6)/(4 × 17) = (6)/(4) = (3)/(2) Step 4: Divide the numerator by the denominator. (31)/(8)(3)/(2) = (31)/(8) ÷ (3)/(2) Multiply by the reciprocal of the denominator: (31)/(8) × (2)/(3) = (31 × 2)/(8 × 3) Simplify by canceling out a factor of 2: (31 × 1)/(4 × 3) = (31)/(12) Convert the improper fraction to a mixed number: (31)/(12) = 2(7)/(12) The final answer is 2(7)/(12).