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 numbers to improper fractions. The expression is (1)/(2) + 2(1)/(3) + 4(1)/(4). Convert 2(1)/(3): 2(1)/(3) = ((2 × 3) + 1)/(3) = (6 + 1)/(3) = (7)/(3) Convert 4(1)/(4): 4(1)/(4) = ((4 × 4) + 1)/(4) = (16 + 1)/(4) = (17)/(4) The expression becomes: (1)/(2) + (7)/(3) + (17)/(4) Step 2: Find the least common multiple (LCM) of the denominators. The denominators are 2, 3, and 4. Multiples of 2: 2, 4, 6, 8, 10, 12, ... Multiples of 3: 3, 6, 9, 12, ... Multiples of 4: 4, 8, 12, ... The LCM of 2, 3, and 4 is 12. Step 3: Convert each fraction to an equivalent fraction with a denominator of 12. For (1)/(2): (1)/(2) = (1 × 6)/(2 × 6) = (6)/(12) For (7)/(3): (7)/(3) = (7 × 4)/(3 × 4) = (28)/(12) For (17)/(4): (17)/(4) = (17 × 3)/(4 × 3) = (51)/(12) Step 4: Add the fractions. (6)/(12) + (28)/(12) + (51)/(12) = (6 + 28 + 51)/(12) = (34 + 51)/(12) = (85)/(12) Step 5: Convert the improper fraction back to a mixed number. Divide 85 by 12: 85 ÷ 12 = 7 with a remainder of 85 - (12 × 7) = 85 - 84 = 1. So, (85)/(12) = 7(1)/(12). The sum is 7(1)/(12). That's 2 down. 3 left today — send the next one.