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
Here are the solutions to the fraction addition problems: A) Step 1: Find a common denominator for 5 and 3. The least common multiple is 15. (2)/(5) + (4)/(3) = (2 × 3)/(5 × 3) + (4 × 5)/(3 × 5) Step 2: Rewrite the fractions with the common denominator and add them. = (6)/(15) + (20)/(15) = (6 + 20)/(15) = (26)/(15) Step 3: Convert the improper fraction to a mixed number. = 1(11)/(15) The final answer is 1(11)/(15). B) Step 1: Find a common denominator for 2 and 7. The least common multiple is 14. (9)/(2) + (6)/(7) = (9 × 7)/(2 × 7) + (6 × 2)/(7 × 2) Step 2: Rewrite the fractions with the common denominator and add them. = (63)/(14) + (12)/(14) = (63 + 12)/(14) = (75)/(14) Step 3: Convert the improper fraction to a mixed number. = 5(5)/(14) The final answer is 5(5)/(14). C) Step 1: Find a common denominator for 12 and 4. The least common multiple is 12. (8)/(12) + (3)/(4) = (8)/(12) + (3 × 3)/(4 × 3) Step 2: Rewrite the fractions with the common denominator and add them. = (8)/(12) + (9)/(12) = (8 + 9)/(12) = (17)/(12) Step 3: Convert the improper fraction to a mixed number. = 1(5)/(12) The final answer is 1(5)/(12). D) Step 1: Find a common denominator for 8 and 9. The least common multiple is 72. (9)/(8) + (12)/(9) = (9 × 9)/(8 × 9) + (12 × 8)/(9 × 8) Step 2: Rewrite the fractions with the common denominator and add them. = (81)/(72) + (96)/(72) = (81 + 96)/(72) = (177)/(72) Step 3: Convert the improper fraction to a mixed number. = 2(33)/(72) Step 4: Simplify the fractional part by dividing the numerator and denominator by their greatest common divisor, which is 3. = 2(33 ÷ 3)/(72 ÷ 3) = 2(11)/(24) The final answer is 2(11)/(24). E) Step 1: Find a common denominator for 4, 2, and 6. The least common multiple is 12. (3)/(4) + (5)/(2) + (4)/(6) = (3 × 3)/(4 × 3) + (5 × 6)/(2 × 6) + (4 × 2)/(6 × 2) Step 2: Rewrite the fractions with the common denominator and add them. = (9)/(12) + (30)/(12) + (8)/(12) = (9 + 30 + 8)/(12) = (47)/(12) Step 3: Convert the improper fraction to a mixed number. = 3(11)/(12) The final answer is 3(11)/(12). That's 2 down. 3 left today — send the next one.