(b) (1) Divide 45 in the ratio \( 2: 3 \). (2) Divide 56 in the ratio \( 3: 4 \). (3) Divide 112 in the ratio \( 5: 3 \). (4) Divide 162 in the ratio \( 2: 7 \) (5) Divide 220 in the ratio \( 9: 11 \). (6) Divide 675 in the ratio 2 : (7) Divide 780 in the ratio \( 2: 3: 5 \). (8) Divide 806 in the ratio \( 1: 5 \)

Let's solve each part step by step. ### (1) Divide 45 in the ratio \( 2: 3 \) To divide a number in a given ratio, we first find the total parts of the ratio. Here, the total parts are \( 2 + 3 = 5 \). Now, we can find the value of each part: \[ \text{Value of each part} = \frac{45}{5} = 9 \] Now, we can find the two parts: - First part: \( 2 \times 9 = 18 \) - Second part: \( 3 \times 9 = 27 \) So, \( 45 \) divided in the ratio \( 2:3 \) gives \( 18 \) and \( 27 \). ### (2) Divide 56 in the ratio \( 3: 4 \) Total parts = \( 3 + 4 = 7 \). Value of each part: \[ \text{Value of each part} = \frac{56}{7} = 8 \] Now, the two parts: - First part: \( 3 \times 8 = 24 \) - Second part: \( 4 \times 8 = 32 \) So, \( 56 \) divided in the ratio \( 3:4 \) gives \( 24 \) and \( 32 \). ### (3) Divide 112 in the ratio \( 5: 3 \) Total parts = \( 5 + 3 = 8 \). Value of each part: \[ \text{Value of each part} = \frac{112}{8} = 14 \] Now, the two parts: - First part: \( 5 \times 14 = 70 \) - Second part: \( 3 \times 14 = 42 \) So, \( 112 \) divided in the ratio \( 5:3 \) gives \( 70 \) and \( 42 \). ### (4) Divide 162 in the ratio \( 2: 7 \) Total parts = \( 2 + 7 = 9 \). Value of each part: \[ \text{Value of each part} = \frac{162}{9} = 18 \] Now, the two parts: - First part: \( 2 \times 18 = 36 \) - Second part: \( 7 \times 18 = 126 \) So, \( 162 \) divided in the ratio \( 2:7 \) gives \( 36 \) and \( 126 \). ### (5) Divide 220 in the ratio \( 9: 11 \) Total parts = \( 9 + 11 = 20 \). Value of each part: \[ \text{Value of each part} = \frac{220}{20} = 11 \] Now, the two parts: - First part: \( 9 \times 11 = 99 \) - Second part: \( 11 \times 11 = 121 \) So, \( 220 \) divided in the ratio \( 9:11 \) gives \( 99 \) and \( 121 \). ### (6) Divide 675 in the ratio \( 2:1 \) Total parts = \( 2 + 1 = 3 \). Value of each part: \[ \text{Value of each part} = \frac{675}{3} = 225 \] Now, the two parts: - First part: \( 2 \times 225 = 450 \) - Second part: \( 1 \times 225 = 225 \) So, \( 675 \) divided in the ratio \( 2:1 \) gives \( 450 \) and \( 225 \). ### (7) Divide 780 in the ratio \( 2:3:5 \) Total parts = \( 2 + 3 + 5 = 10 \). Value of each part: \[ \text{Value of each part} = \frac{780}{10} = 78 \] Now, the three parts: - First part: \( 2 \times 78 = 156 \) - Second part: \( 3 \times 78 = 234 \) - Third part: \( 5 \times 78 = 390 \) So, \( 780 \) divided in the ratio \( 2:3:5 \) gives \( 156 \), \( 234 \), and \( 390 \). ### (8) Divide 806 in the ratio \( 1:5 \) Total parts = \( 1 + 5 = 6 \). Value of each part: \[ \text{Value of each part} = \frac{806}{6} \approx 134.33 \] Now, the two parts: - First part: \( 1 \times 134.33 \approx 134.33 \) - Second part: \( 5 \times 134.33 \approx 671.67 \) So, \( 806 \) divided in the ratio \( 1:5 \) gives approximately \( 134.33 \) and \( 671.67 \). ### Summary of Results: 1. \( 45 \) in the ratio \( 2:3 \) gives \( 18 \) and \( 27 \). 2. \( 56 \) in the ratio \( 3:4 \) gives \( 24 \) and \( 32 \). 3. \( 112 \) in the ratio \( 5:3 \) gives \( 70 \) and \( 42 \). 4. \( 162 \) in the ratio \( 2:7 \) gives \( 36 \) and \( 126 \). 5. \( 220 \) in the ratio \( 9:11 \) gives \( 99 \) and \( 121 \). 6. \( 675 \) in the ratio \( 2:1 \) gives \( 450 \) and \( 225 \). 7. \( 780 \) in the ratio \( 2:3:5 \) gives \( 156 \), \( 234 \), and \( 390 \). 8. \( 806 \) in the ratio \( 1:5 \) gives approximately \( 134.33 \) and \( 671.67 \).