Calculate \( \begin{array}{ll}\text { a) } 1 \frac{1}{2}: 3 & \text { b) } \frac{3}{4}: \frac{7}{16}: \frac{12}{32} \\ \text { c) } 2 \mathrm{~mm}: 10 \mathrm{~km} & \text { d) } 50 \text { toea }: \mathrm{K} 5.40 \\ \text { e) } 6 \mathrm{k}: \mathrm{k} & \\ \text { f) A pot contains } 5.4 \mathrm{~kg} \text { of greens, } 200 \mathrm{~g} \text { of lamp } \\ \text { flaps, and } 2.5 \mathrm{~kg} \text { of chicken. Find the ratio of the } \\ \text { weight of chicken to the combine weight of the } \\ \text { greens and lamb flaps. }\end{array} \)

**a)** Express \(1\frac{1}{2}\) as an improper fraction: \[ 1\frac{1}{2} = \frac{3}{2} \] Then, \[ \frac{3}{2} : 3 = \frac{3}{2} \div 3 = \frac{3}{2} \times \frac{1}{3} = \frac{3}{6} = \frac{1}{2} \] **b)** We are given the ratio: \[ \frac{3}{4} : \frac{7}{16} : \frac{12}{32} \] First, simplify \(\frac{12}{32}\): \[ \frac{12}{32} = \frac{12 \div 4}{32 \div 4} = \frac{3}{8} \] Now the ratio becomes: \[ \frac{3}{4} : \frac{7}{16} : \frac{3}{8} \] To compare easily, convert all fractions to have a common denominator, say 16: \[ \frac{3}{4} = \frac{12}{16}, \quad \frac{7}{16} = \frac{7}{16}, \quad \frac{3}{8} = \frac{6}{16} \] Thus, \[ \frac{12}{16} : \frac{7}{16} : \frac{6}{16} = 12 : 7 : 6 \] **c)** We have: \[ 2\,\text{mm} : 10\,\text{km} \] Convert kilometers to millimeters. Recall that: \[ 1\, \text{km} = 1\,000\,000\, \text{mm} \] Thus, \[ 10\, \text{km} = 10 \times 1\,000\,000\, \text{mm} = 10\,000\,000\, \text{mm} \] The ratio becomes: \[ 2 : 10\,000\,000 \] Dividing both numbers by 2 gives: \[ 1 : 5\,000\,000 \] **d)** The ratio given is: \[ 50\,\text{toea} : K5.40 \] Write the ratio as: \[ 50 : 5.40 \] Multiply both terms by 10 to eliminate the decimal: \[ 500 : 54 \] Divide both numbers by 2: \[ 250 : 27 \] **e)** The ratio is: \[ 6k : k \] Since \(k\) is common (and assumed nonzero), cancel \(k\) to get: \[ 6:1 \] **f)** The pot contains: - Greens: \(5.4\,\text{kg}\) - Lamb flaps: \(200\,\text{g}\) - Chicken: \(2.5\,\text{kg}\) First, convert \(200\,\text{g}\) to kilograms: \[ 200\,\text{g} = 0.2\,\text{kg} \] Combined weight of greens and lamb flaps: \[ 5.4\,\text{kg} + 0.2\,\text{kg} = 5.6\,\text{kg} \] Now, the ratio of the weight of chicken to the combined weight is: \[ 2.5 : 5.6 \] Multiply both by 10 to eliminate decimals: \[ 25 : 56 \] Thus, the final ratios are: - a) \(\frac{1}{2}\) - b) \(12:7:6\) - c) \(1:5\,000\,000\) - d) \(250:27\) - e) \(6:1\) - f) \(25:56\)