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.
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Example: 1(2)/(3) + (3)/(2) This shows the general method: convert mixed numbers to improper fractions, find LCD, add, and convert back to mixed. The same steps apply to a), b), and c). Step 1: Convert mixed number to improper fraction. 1(2)/(3) = (1 × 3 + 2)/(3) = (5)/(3) Second fraction: (3)/(2) Step 2: Find LCD of 3 and 2: 6. (5)/(3) = (5 × 2)/(3 × 2) = (10)/(6) (3)/(2) = (3 × 3)/(2 × 3) = (9)/(6) Step 3: Add numerators. (10)/(6) + (9)/(6) = (19)/(6) Step 4: Convert to mixed number. 19 ÷ 6 = 3 remainder 1, so 3(1)/(6) Final answer: 3(1)/(6) a) 5(2)/(3) + (9)/(3) Using the same method (denominators match, so LCD = 3). Step 1: Convert mixed number. 5(2)/(3) = (5 × 3 + 2)/(3) = (17)/(3) Second fraction: (9)/(3) Step 2: LCD is 3 (no conversion needed). Step 3: Add numerators. (17)/(3) + (9)/(3) = (26)/(3) Step 4: Convert to mixed number. 26 ÷ 3 = 8 remainder 2, so 8(2)/(3) Final answer: 8(2)/(3) b) 6(3)/(5) + (9)/(5) Using the same method (denominators match, so LCD = 5). Step 1: Convert mixed number. 6(3)/(5) = (6 × 5 + 3)/(5) = (33)/(5) Second fraction: (9)/(5) Step 2: LCD is 5 (no conversion needed). Step 3: Add numerators. (33)/(5) + (9)/(5) = (42)/(5) Step 4: Convert to mixed number. 42 ÷ 5 = 8 remainder 2, so 8(2)/(5) Final answer: 8(2)/(5) c) 3(7)/(10) + 6(4)/(5) Using the same method as the example (LCD needed). Step 1: Convert both to improper fractions. 3(7)/(10) = (3 × 10 + 7)/(10) = (37)/(10) 6(4)/(5) = (6 × 5 + 4)/(5) = (34)/(5) Step 2: LCD of 10 and 5: 10. (37)/(10) (already) (34)/(5) = (34 × 2)/(5 × 2) = (68)/(10) Step 3: Add numerators. (37)/(10) + (68)/(10) = (105)/(10) Step 4: Convert to mixed number (or simplify first). (105)/(10) = (21)/(2) 21 ÷ 2 = 10 remainder 1, so 10(1)/(2) Final answer: 10(1)/(2)