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: Evaluate the first term: (-(13)/(4) × (5)/(6)). Multiply the numerators and the denominators: -(13)/(4) × (5)/(6) = -(13 × 5)/(4 × 6) = -(65)/(24) Step 2: Evaluate the second term: ((9)/(2) ÷ (3)/(4)). To divide by a fraction, multiply by its reciprocal: (9)/(2) ÷ (3)/(4) = (9)/(2) × (4)/(3) Simplify before multiplying: (9)/(3) × (4)/(2) = 3 × 2 = 6 Step 3: Evaluate the third term: ((5)/(8) × (-6)/(15)). Multiply the numerators and the denominators. Simplify by canceling common factors: (5)/(8) × (-6)/(15) = (5)/(15) × (-6)/(8) = (1)/(3) × (-3)/(4) = -(1 × 3)/(3 × 4) = -(1)/(4) Step 4: Combine the results from Step 1, Step 2, and Step 3. The original expression becomes: -(65)/(24) - 6 + (-(1)/(4)) -(65)/(24) - 6 - (1)/(4) To combine these, find a common denominator, which is 24. Convert 6 to a fraction with denominator 24: 6 = (6 × 24)/(1 × 24) = (144)/(24) Convert -(1)/(4) to a fraction with denominator 24: -(1)/(4) = -(1 × 6)/(4 × 6) = -(6)/(24) Now substitute these back into the expression: -(65)/(24) - (144)/(24) - (6)/(24) Combine the numerators: (-65 - 144 - 6)/(24) = (-209 - 6)/(24) = (-215)/(24) The final answer is -(215)/(24). 3 done, 2 left today. You're making progress.