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 follow the order of operations (BODMAS/PEMDAS): Brackets, Orders (powers/roots), Division/Multiplication (from left to right), Addition/Subtraction (from left to right). "Of" means multiplication. First, convert all mixed numbers to improper fractions: 1(5)/(7) = (1 × 7 + 5)/(7) = (12)/(7) 2(1)/(3) = (2 × 3 + 1)/(3) = (7)/(3) 1(3)/(7) = (1 × 7 + 3)/(7) = (10)/(7) 2(2)/(3) = (2 × 3 + 2)/(3) = (8)/(3) Substitute these into the expression: (3)/(4) + (12)/(7) ÷ (4)/(7) of (7)/(3)((10)/(7) - (5)/(8)) × (8)/(3) Step 1: Evaluate the numerator. The numerator is (3)/(4) + (12)/(7) ÷ (4)/(7) of (7)/(3). First, calculate the "of" part: (4)/(7) of (7)/(3) = (4)/(7) × (7)/(3) = (4 × 7)/(7 × 3) = (4)/(3) Now the numerator becomes: (3)/(4) + (12)/(7) ÷ (4)/(3) Next, perform the division: (12)/(7) ÷ (4)/(3) = (12)/(7) × (3)/(4) = (12 × 3)/(7 × 4) = (3 × 4 × 3)/(7 × 4) = (9)/(7) Now the numerator becomes: (3)/(4) + (9)/(7) Perform the addition by finding a common denominator (28): (3)/(4) + (9)/(7) = (3 × 7)/(4 × 7) + (9 × 4)/(7 × 4) = (21)/(28) + (36)/(28) = (21 + 36)/(28) = (57)/(28) So, the numerator is (57)/(28). Step 2: Evaluate the denominator. The denominator is ((10)/(7) - (5)/(8)) × (8)/(3). First, calculate the expression inside the brackets by finding a common denominator (56): (10)/(7) - (5)/(8) = (10 × 8)/(7 × 8) - (5 × 7)/(8 × 7) = (80)/(56) - (35)/(56) = (80 - 35)/(56) = (45)/(56) Now the denominator becomes: (45)/(56) × (8)/(3) Perform the multiplication: (45)/(56) × (8)/(3) = (45 × 8)/(56 × 3) = ((15 × 3) × 8)/((7 × 8) × 3) = (15)/(7) So, the denominator is (15)/(7). Step 3: Divide the numerator by the denominator. (57)/(28)(15)/(7) = (57)/(28) ÷ (15)/(7) To divide by a fraction, multiply by its reciprocal: (57)/(28) × (7)/(15) Simplify before multiplying: (57)/(4 × 7) × (7)/(15) = (57)/(4 × 15) Both 57 and 15 are divisible by 3: 57 ÷ 3 = 19 and 15 ÷ 3 = 5. (19)/(4 × 5) = (19)/(20) The final answer is (19)/(20).