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
a) Step 1: Convert the mixed number to an improper fraction. 1 (2)/(3) = (1 × 3 + 2)/(3) = (5)/(3) Step 2: Add the fractions. (5)/(3) + (5)/(2) Step 3: Find the least common denominator (LCD), which is 6. (5)/(3) = (5 × 2)/(3 × 2) = (10)/(6) (5)/(2) = (5 × 3)/(2 × 3) = (15)/(6) Step 4: Add the numerators. (10 + 15)/(6) = (25)/(6) Step 5: Convert to a mixed number. (25)/(6) = 4 (1)/(6) Final answer: 4 (1)/(6) 4 (1)/(6) b) Step 1: Convert the mixed number to an improper fraction. 6 (3)/(5) = (6 × 5 + 3)/(5) = (33)/(5) Step 2: Add the fractions. (33)/(5) + (9)/(8) Step 3: Find the least common denominator (LCD), which is 40. (33)/(5) = (33 × 8)/(5 × 8) = (264)/(40) (9)/(8) = (9 × 5)/(8 × 5) = (45)/(40) Step 4: Add the numerators. (264 + 45)/(40) = (309)/(40) Step 5: Convert to a mixed number. (309)/(40) = 7 (29)/(40) Final answer: 7 (29)/(40) 7 (29)/(40) c) Step 1: Convert the mixed numbers to improper fractions. 3 (7)/(10) = (3 × 10 + 7)/(10) = (37)/(10) 6 (5)/(4) = (6 × 4 + 5)/(4) = (29)/(4) Step 2: Add the fractions. (37)/(10) + (29)/(4) Step 3: Find the least common denominator (LCD), which is 20. (37)/(10) = (37 × 2)/(10 × 2) = (74)/(20) (29)/(4) = (29 × 5)/(4 × 5) = (145)/(20) Step 4: Add the numerators. (74 + 145)/(20) = (219)/(20) Step 5: Convert to a mixed number. (219)/(20) = 10 (19)/(20) Final answer: 10 (19)/(20) 10 (19)/(20)