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 expression, we will follow the order of operations: first, perform the addition inside the parentheses, then the division. The expression is: (2(1)/(4) + 1(5)/(8)) ÷ 3(7)/(16) Step 1: Convert all mixed numbers to improper fractions. 2(1)/(4) = ((2 × 4) + 1)/(4) = (8 + 1)/(4) = (9)/(4) 1(5)/(8) = ((1 × 8) + 5)/(8) = (8 + 5)/(8) = (13)/(8) 3(7)/(16) = ((3 × 16) + 7)/(16) = (48 + 7)/(16) = (55)/(16) Step 2: Perform the addition inside the parentheses. To add (9)/(4) and (13)/(8), find a common denominator, which is 8. (9)/(4) + (13)/(8) = (9 × 2)/(4 × 2) + (13)/(8) = (18)/(8) + (13)/(8) = (18 + 13)/(8) = (31)/(8) Step 3: Perform the division. Now the expression is (31)/(8) ÷ (55)/(16). To divide by a fraction, multiply by its reciprocal. (31)/(8) ÷ (55)/(16) = (31)/(8) × (16)/(55) Step 4: Multiply the fractions and simplify. (31 × 16)/(8 × 55) Notice that 16 can be divided by 8. (31 × (8 × 2))/(8 × 55) = (31 × 2)/(55) = (62)/(55) The simplified value is (62)/(55). What's next?