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. 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) Substitute these into the expression: (3)/(4) + (12)/(7) ÷ (4)/(7) of (7)/(3)((10)/(7) - (5)/(8)) × (2)/(3) Step 2: Evaluate the numerator. First, calculate "of" (multiplication): (4)/(7) of (7)/(3) = (4)/(7) × (7)/(3) = (4 × 7)/(7 × 3) = (28)/(21) = (4)/(3) Next, perform the division: (12)/(7) ÷ (4)/(3) = (12)/(7) × (3)/(4) = (36)/(28) = (9)/(7) Finally, perform the addition: (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 3: Evaluate the denominator. First, perform the subtraction inside the parentheses: (10)/(7) - (5)/(8) Find a common denominator, which is 7 × 8 = 56: (10 × 8)/(7 × 8) - (5 × 7)/(8 × 7) = (80)/(56) - (35)/(56) = (80 - 35)/(56) = (45)/(56) Next, perform the multiplication: (45)/(56) × (2)/(3) = (45 × 2)/(56 × 3) = (90)/(168) Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 6: (90 ÷ 6)/(168 ÷ 6) = (15)/(28) So, the denominator is (15)/(28). Step 4: Divide the numerator by the denominator. (57)/(28)(15)/(28) = (57)/(28) × (28)/(15) Cancel out the common factor of 28: = (57)/(15) Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3: (57 ÷ 3)/(15 ÷ 3) = (19)/(5) The final answer is (19)/(5). What's next?