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
To evaluate the expression, we will first convert all mixed numbers to improper fractions, then perform the multiplication in the numerator and the subtraction in the denominator, and finally divide the resulting fractions. Step 1: Convert mixed numbers to improper fractions. 2(7)/(8) = ((2 × 8) + 7)/(8) = (16 + 7)/(8) = (23)/(8) 1(1)/(5) = ((1 × 5) + 1)/(5) = (5 + 1)/(5) = (6)/(5) 2(1)/(4) = ((2 × 4) + 1)/(4) = (8 + 1)/(4) = (9)/(4) The expression becomes: (23)/(8) × (6)/(5)8 - (9)/(4) Step 2: Calculate the numerator. (23)/(8) × (6)/(5) = (23 × 6)/(8 × 5) = (138)/(40) Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2: (138 ÷ 2)/(40 ÷ 2) = (69)/(20) Step 3: Calculate the denominator. 8 - (9)/(4) = (8)/(1) - (9)/(4) Find a common denominator, which is 4: (8 × 4)/(1 × 4) - (9)/(4) = (32)/(4) - (9)/(4) = (32 - 9)/(4) = (23)/(4) Step 4: Divide the numerator by the denominator. Now we have: (69)/(20)(23)/(4) To divide by a fraction, multiply by its reciprocal: (69)/(20) × (4)/(23) We can simplify by canceling out common factors. Divide 4 in the numerator and 20 in the denominator by 4: (69)/(5 × 4) × (4)/(23) = (69)/(5 × 23) Since 69 = 3 × 23, we can simplify further: (3 × 23)/(5 × 23) = (3)/(5) The final answer is (3)/(5). 3 done, 2 left today. You're making progress.