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 problems: 1. Problem 1: (2)/(7) + (3)/(7) - (2)/(7) Step 1: Combine the numerators since the denominators are the same. (2+3-2)/(7) Step 2: Perform the arithmetic in the numerator. (5-2)/(7) = (3)/(7) The simplified answer is (3)/(7). 2. Problem 2: (2)/(9) + (4)/(9) - (7)/(9) Step 1: Combine the numerators. (2+4-7)/(9) Step 2: Perform the arithmetic in the numerator. (6-7)/(9) = (-1)/(9) The simplified answer is -(1)/(9). 3. Problem 3: (7)/(12) - (5)/(12) - (3)/(12) + (8)/(12) Step 1: Combine the numerators. (7-5-3+8)/(12) Step 2: Perform the arithmetic in the numerator from left to right. (2-3+8)/(12) = (-1+8)/(12) = (7)/(12) The simplified answer is (7)/(12). 4. Problem 4: (8)/(10) + (7)/(10) - (9)/(10) Step 1: Combine the numerators. (8+7-9)/(10) Step 2: Perform the arithmetic in the numerator. (15-9)/(10) = (6)/(10) Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2. (6 ÷ 2)/(10 ÷ 2) = (3)/(5) The simplified answer is (3)/(5). 5. Problem 5: (12)/(15) - (7)/(15) - (5)/(15) + (11)/(15) Step 1: Combine the numerators. (12-7-5+11)/(15) Step 2: Perform the arithmetic in the numerator from left to right. (5-5+11)/(15) = (0+11)/(15) = (11)/(15) The simplified answer is (11)/(15). 6. Problem 6: (9)/(8) - (5)/(8) - (3)/(8) + (10)/(8) Step 1: Combine the numerators. (9-5-3+10)/(8) Step 2: Perform the arithmetic in the numerator from left to right. (4-3+10)/(8) = (1+10)/(8) = (11)/(8) The simplified answer is (11)/(8). 7. Problem 7: (7)/(9) - (1)/(9) Step 1: Combine the numerators. (7-1)/(9) Step 2: Perform the arithmetic in the numerator. (6)/(9) Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3. (6 ÷ 3)/(9 ÷ 3) = (2)/(3) The simplified answer is (2)/(3). 8. Problem 8: (10)/(15) - (8)/(15) + (7)/(15) - (4)/(15) Step 1: Combine the numerators. (10-8+7-4)/(15) Step 2: Perform the arithmetic in the numerator from left to right. (2+7-4)/(15) = (9-4)/(15) = (5)/(15) Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5. (5 ÷ 5)/(15 ÷ 5) = (1)/(3) The simplified answer is (1)/(3). 3 done, 2 left today. You're making progress.