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
Here's the step-by-step solution to simplify the expression: The problem is to simplify 8(2)/(3) ÷ (23(2)/(5) OF 3(1)/(4) - 22). We will follow the BODMAS/PEMDAS order of operations. Step 1: Convert all mixed numbers to improper fractions. 8(2)/(3) = (8 × 3 + 2)/(3) = (24 + 2)/(3) = (26)/(3) 23(2)/(5) = (23 × 5 + 2)/(5) = (115 + 2)/(5) = (117)/(5) 3(1)/(4) = (3 × 4 + 1)/(4) = (12 + 1)/(4) = (13)/(4) The expression becomes: (26)/(3) ÷ ((117)/(5) OF (13)/(4) - 22) Step 2: Perform the "OF" operation, which means multiplication, inside the parenthesis. (117)/(5) × (13)/(4) = (117 × 13)/(5 × 4) = (1521)/(20) The expression now is: (26)/(3) ÷ ((1521)/(20) - 22) Step 3: Perform the subtraction inside the parenthesis. To subtract 22 from (1521)/(20), we convert 22 to a fraction with a denominator of 20. 22 = (22 × 20)/(20) = (440)/(20) Now subtract: (1521)/(20) - (440)/(20) = (1521 - 440)/(20) = (1081)/(20) The expression now is: (26)/(3) ÷ (1081)/(20) Step 4: Perform the division. To divide by a fraction, multiply by its reciprocal. (26)/(3) ÷ (1081)/(20) = (26)/(3) × (20)/(1081) Multiply the numerators and the denominators: (26 × 20)/(3 × 1081) = (520)/(3243) The fraction (520)/(3243) cannot be simplified further as there are no common factors between the numerator and the denominator (520 = 2^3 × 5 × 13 and 3243 = 3 × 23 × 47). The final answer is (520)/(3243). That's 2 down. 3 left today — send the next one.