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 the mixed number and decimal to fractions in the first parenthesis. The mixed number 3 (1)/(5) can be converted to an improper fraction: 3 (1)/(5) = ((3 × 5) + 1)/(5) = (15 + 1)/(5) = (16)/(5) The decimal 0.75 (from 0,75) can be converted to a fraction: 0.75 = (75)/(100) = (3)/(4) So the first parenthesis becomes: ((16)/(5) × (3)/(4)) Step 2: Perform the multiplication in the first parenthesis. (16)/(5) × (3)/(4) = (16 × 3)/(5 × 4) = (48)/(20) Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4: (48)/(20) = (12)/(5) Step 3: Perform the division in the second parenthesis. To divide by a fraction, multiply by its reciprocal: (1)/(5) : (11)/(5) = (1)/(5) × (5)/(11) Now, multiply the fractions: (1)/(5) × (5)/(11) = (1 × 5)/(5 × 11) = (5)/(55) Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5: (5)/(55) = (1)/(11) Step 4: Perform the final addition using the results from Step 2 and Step 3. We need to add (12)/(5) and (1)/(11). To add fractions, find a common denominator. The least common multiple of 5 and 11 is 5 × 11 = 55. Convert (12)/(5) to a fraction with denominator 55: (12)/(5) = (12 × 11)/(5 × 11) = (132)/(55) Convert (1)/(11) to a fraction with denominator 55: (1)/(11) = (1 × 5)/(11 × 5) = (5)/(55) Now, add the fractions: (132)/(55) + (5)/(55) = (132 + 5)/(55) = (137)/(55) The final answer is (137)/(55). That's 2 down. 3 left today — send the next one.