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 your math problems: Exercise 1. To solve 7(2)/(5) + 8(4)/(3): Step 1: Convert the mixed numbers to improper fractions. 7(2)/(5) = (7 × 5 + 2)/(5) = (37)/(5) 8(4)/(3) = (8 × 3 + 4)/(3) = (28)/(3) Step 2: Find a common denominator, which is 15. (37)/(5) = (37 × 3)/(5 × 3) = (111)/(15) (28)/(3) = (28 × 5)/(3 × 5) = (140)/(15) Step 3: Add the fractions. (111)/(15) + (140)/(15) = (111 + 140)/(15) = (251)/(15) Step 4: Convert the improper fraction back to a mixed number. (251)/(15) = 16(11)/(15) The answer is 16(11)/(15). 2. To solve 2(5)/(9) + 7(1)/(3): Step 1: Convert the mixed numbers to improper fractions. 2(5)/(9) = (2 × 9 + 5)/(9) = (23)/(9) 7(1)/(3) = (7 × 3 + 1)/(3) = (22)/(3) Step 2: Find a common denominator, which is 9. (22)/(3) = (22 × 3)/(3 × 3) = (66)/(9) Step 3: Add the fractions. (23)/(9) + (66)/(9) = (23 + 66)/(9) = (89)/(9) Step 4: Convert the improper fraction back to a mixed number. (89)/(9) = 9(8)/(9) The answer is 9(8)/(9). 3. To solve 9(3)/(5) + 5(3)/(4): Step 1: Convert the mixed numbers to improper fractions. 9(3)/(5) = (9 × 5 + 3)/(5) = (48)/(5) 5(3)/(4) = (5 × 4 + 3)/(4) = (23)/(4) Step 2: Find a common denominator, which is 20. (48)/(5) = (48 × 4)/(5 × 4) = (192)/(20) (23)/(4) = (23 × 5)/(4 × 5) = (115)/(20) Step 3: Add the fractions. (192)/(20) + (115)/(20) = (192 + 115)/(20) = (307)/(20) Step 4: Convert the improper fraction back to a mixed number. (307)/(20) = 15(7)/(20) The answer is 15(7)/(20). Home Work 1. To solve 2(3)/(5) - 1(1)/(2): Step 1: Convert the mixed numbers to improper fractions. 2(3)/(5) = (2 × 5 + 3)/(5) = (13)/(5) 1(1)/(2) = (1 × 2 + 1)/(2) = (3)/(2) Step 2: Find a common denominator, which is 10. (13)/(5) = (13 × 2)/(5 × 2) = (26)/(10) (3)/(2) = (3 × 5)/(2 × 5) = (15)/(10) Step 3: Subtract the fractions. (26)/(10) - (15)/(10) = (26 - 15)/(10) = (11)/(10) Step 4: Convert the improper fraction back to a mixed number. (11)/(10) = 1(1)/(10) The answer is 1(1)/(10). 2. To solve 9(3)/(6) - 7(3)/(5): Step 1: Simplify the first mixed number and convert both to improper fractions. 9(3)/(6) = 9(1)/(2) = (9 × 2 + 1)/(2) = (19)/(2) 7(3)/(5) = (7 × 5 + 3)/(5) = (38)/(5) Step 2: Find a common denominator, which is 10. (19)/(2) = (19 × 5)/(2 × 5) = (95)/(10) (38)/(5) = (38 × 2)/(5 × 2) = (76)/(10) Step 3: Subtract the fractions. (95)/(10) - (76)/(10) = (95 - 76)/(10) = (19)/(10) Step 4: Convert the improper fraction back to a mixed number. (19)/(10) = 1(9)/(10) The answer is 1(9)/(10). 3. To solve 3(3)/(5) - 2(2)/(3): Step 1: Convert the mixed numbers to improper fractions. 3(3)/(5) = (3 × 5 + 3)/(5) = (18)/(5) 2(2)/(3) = (2 × 3 + 2)/(3) = (8)/(3) Step 2: Find a common denominator, which is 15. (18)/(5) = (18 × 3)/(5 × 3) = (54)/(15) ✂️ _That answer was long and got cut off. Reply continue and I'll finish it._