(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 \( 1: 5 \)

To tackle these ratio problems, it's important to understand the basic concept of ratios. A ratio compares two or more quantities, showing their relative sizes. To divide a number in a certain ratio, you first add the parts of the ratio together and then allocate portions according to those parts. Here are the answers to your divisions: 1. \( 45 \) in the ratio \( 2: 3 \) results in \( 18 \) and \( 27 \). 2. \( 56 \) in the ratio \( 3: 4 \) leads to \( 24 \) and \( 32 \). 3. \( 112 \) in the ratio \( 5: 3 \) divides into \( 70 \) and \( 42 \). 4. \( 162 \) in the ratio \( 2: 7 \) gives \( 36 \) and \( 126 \). 5. \( 220 \) in the ratio \( 9: 11 \) divides into \( 99 \) and \( 121 \). 6. \( 675 \) in the ratio \( 2: 5 \) yields \( 225 \) and \( 450 \). 7. \( 780 \) in the ratio \( 2: 3: 5 \) would give \( 130 \), \( 195 \), and \( 455 \). 8. \( 806 \) in the ratio \( 1: 5 \) results in \( 134 \) and \( 672 \). To make dividing in ratios less intimidating, a common mistake people make is forgetting to add the parts of the ratio together before assigning values. Always remember: add the total parts first to find out how much each part is worth. Then, engage in a fun practice by using ratios in recipes; it’s a delicious way to understand their practical application!