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) 3(2)/(5) + 2(1)/(6) Step 1: Add the whole numbers. 3 + 2 = 5 Step 2: Add the fractions (2)/(5) + (1)/(6). Find the least common multiple (LCM) of 5 and 6: LCM = 30. (2)/(5) = (2 × 6)/(5 × 6) = (12)/(30) (1)/(6) = (1 × 5)/(6 × 5) = (5)/(30) (12)/(30) + (5)/(30) = (17)/(30) Step 3: Combine the results. Since (17)/(30) < 1, the sum is 5(17)/(30). 5(17)/(30) b) 6(3)/(4) + 9(2)/(3) Step 1: Add the whole numbers. 6 + 9 = 15 Step 2: Add the fractions (3)/(4) + (2)/(3). Find the LCM of 4 and 3: LCM = 12. (3)/(4) = (3 × 3)/(4 × 3) = (9)/(12) (2)/(3) = (2 × 4)/(3 × 4) = (8)/(12) (9)/(12) + (8)/(12) = (17)/(12) Step 3: Convert (17)/(12) to a mixed number. 17 ÷ 12 = 1 remainder 5, since 12 × 1 = 12 and 17 - 12 = 5. So, (17)/(12) = 1(5)/(12). Step 4: Combine the results. 15 + 1(5)/(12) = 16(5)/(12). 16(5)/(12) c) 3(7)/(10) + 6(5)/(4) Step 1: Add the whole numbers. 3 + 6 = 9 Step 2: Add the fractions (7)/(10) + (5)/(4). Find the LCM of 10 and 4: LCM = 20. (7)/(10) = (7 × 2)/(10 × 2) = (14)/(20) (5)/(4) = (5 × 5)/(4 × 5) = (25)/(20) (14)/(20) + (25)/(20) = (39)/(20) Step 3: Convert (39)/(20) to a mixed number. 39 ÷ 20 = 1 remainder 19, since 20 × 1 = 20 and 39 - 20 = 19. So, (39)/(20) = 1(19)/(20). Step 4: Combine the results. 9 + 1(19)/(20) = 10(19)/(20). 10(19)/(20)