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 simplify the given expression, we will first simplify the numerator and the denominator separately, then divide the simplified numerator by the simplified denominator. The expression is: (52)/(3) ÷ 2(7)/(5)6(1)/(3) ÷ 2(7)/(6) Step 1: Convert all mixed numbers to improper fractions. For the numerator: 5(2)/(3) = ((5 × 3) + 2)/(3) = (15 + 2)/(3) = (17)/(3) 2(7)/(5) = ((2 × 5) + 7)/(5) = (10 + 7)/(5) = (17)/(5) For the denominator: 6(1)/(3) = ((6 × 3) + 1)/(3) = (18 + 1)/(3) = (19)/(3) 2(7)/(6) = ((2 × 6) + 7)/(6) = (12 + 7)/(6) = (19)/(6) Step 2: Simplify the numerator. (17)/(3) ÷ (17)/(5) = (17)/(3) × (5)/(17) Cancel out the common factor of 17: = (5)/(3) Step 3: Simplify the denominator. (19)/(3) ÷ (19)/(6) = (19)/(3) × (6)/(19) Cancel out the common factor of 19: = (6)/(3) = 2 Step 4: Divide the simplified numerator by the simplified denominator. The expression now becomes: (5)/(3)2 This is equivalent to (5)/(3) ÷ 2. (5)/(3) ÷ 2 = (5)/(3) × (1)/(2) = (5 × 1)/(3 × 2) = (5)/(6) The simplified value is (5)/(6). What's next?