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: (5 - 2)/(7)6 (1)/(3) ÷ 2 (5)/(6) Step 1: Simplify the numerator. 5 - (2)/(7) = (5 × 7)/(7) - (2)/(7) = (35)/(7) - (2)/(7) = (35 - 2)/(7) = (33)/(7) Step 2: Convert the mixed numbers in the denominator to improper fractions. 6 (1)/(3) = ((6 × 3) + 1)/(3) = (18 + 1)/(3) = (19)/(3) 2 (5)/(6) = ((2 × 6) + 5)/(6) = (12 + 5)/(6) = (17)/(6) Step 3: Perform the division in the denominator. (19)/(3) ÷ (17)/(6) = (19)/(3) × (6)/(17) = (19 × 6)/(3 × 17) = (19 × (3 × 2))/(3 × 17) Cancel out the common factor of 3: = (19 × 2)/(17) = (38)/(17) Step 4: Divide the simplified numerator by the simplified denominator. The expression now becomes: (33)/(7)(38)/(17) = (33)/(7) ÷ (38)/(17) To divide by a fraction, multiply by its reciprocal: = (33)/(7) × (17)/(38) Step 5: Multiply the fractions to get the final result. = (33 × 17)/(7 × 38) = (561)/(266) The fraction (561)/(266) cannot be simplified further as there are no common factors between the numerator and the denominator. The simplified value is (561)/(266). That's 3 down. 2 left today — send the next one.