YERCISE 4 You may use a calculator in this exercise. Express the following as a ratio in its simplest form: \( \begin{array}{llll}\text { (1) } 18 \text { to } 12 & \text { (2) } 24 \text { to } 32 & \text { (3) } 15 \text { to } 25\end{array} \) \( \begin{array}{lll}\text { (4) } 30 \text { to } 20 & \text { (5) } 9 \text { to } 15 \text { to } 21 & \text { (6) } 1000 \text { to } 10 \text { to } 100 \\ \text { (7) } 1,6 \text { to } 1 & \text { (11) } 0,36 \text { to } 0,06 & \text { (9) } 0,01 \text { to } 0,00001 \\ \text { (10) } 2,4 \text { to } 0,8 \text { to } 0,16 & \text { (1) } 1,5 \mathrm{~m} & \text { (12) } 6 \mathrm{~kg} \text { to } 600 \mathrm{~g} \text { to } 3000 \mathrm{~g} \\ \text { (13) } 48 \text { seconds to } 1 \text { minute } & \text { (14) } 3 \frac{1}{7} \text { to } \frac{11}{14} & \text { (15) } 2 x^{2} y \text { to } 6 x y^{2}\end{array} \)

To express the given ratios in their simplest form, we will follow these steps: 1. **Identify the two quantities in each ratio.** 2. **Divide both quantities by their greatest common divisor (GCD).** 3. **Express the result as a ratio in the form \( a : b \).** Let's go through each ratio step by step. ### (1) \( 18 \text{ to } 12 \) - GCD of 18 and 12 is 6. - Simplified ratio: \( \frac{18}{6} : \frac{12}{6} = 3 : 2 \) ### (2) \( 24 \text{ to } 32 \) - GCD of 24 and 32 is 8. - Simplified ratio: \( \frac{24}{8} : \frac{32}{8} = 3 : 4 \) ### (3) \( 15 \text{ to } 25 \) - GCD of 15 and 25 is 5. - Simplified ratio: \( \frac{15}{5} : \frac{25}{5} = 3 : 5 \) ### (4) \( 30 \text{ to } 20 \) - GCD of 30 and 20 is 10. - Simplified ratio: \( \frac{30}{10} : \frac{20}{10} = 3 : 2 \) ### (5) \( 9 \text{ to } 15 \text{ to } 21 \) - GCD of 9, 15, and 21 is 3. - Simplified ratio: \( \frac{9}{3} : \frac{15}{3} : \frac{21}{3} = 3 : 5 : 7 \) ### (6) \( 1000 \text{ to } 10 \text{ to } 100 \) - GCD of 1000, 10, and 100 is 10. - Simplified ratio: \( \frac{1000}{10} : \frac{10}{10} : \frac{100}{10} = 100 : 1 : 10 \) ### (7) \( 1.6 \text{ to } 1 \) - Convert to whole numbers: \( 1.6 : 1 = 16 : 10 \) - GCD of 16 and 10 is 2. - Simplified ratio: \( \frac{16}{2} : \frac{10}{2} = 8 : 5 \) ### (8) \( 0.36 \text{ to } 0.06 \) - Convert to whole numbers: \( 0.36 : 0.06 = 36 : 6 \) - GCD of 36 and 6 is 6. - Simplified ratio: \( \frac{36}{6} : \frac{6}{6} = 6 : 1 \) ### (9) \( 0.01 \text{ to } 0.00001 \) - Convert to whole numbers: \( 0.01 : 0.00001 = 1 : 0.001 \) - GCD of 1 and 0.001 is 0.001. - Simplified ratio: \( \frac{1}{0.001} : \frac{0.001}{0.001} = 1000 : 1 \) ### (10) \( 2.4 \text{ to } 0.8 \text{ to } 0.16 \) - Convert to whole numbers: \( 2.4 : 0.8 : 0.16 = 24 : 8 : 1.6 \) - GCD of 24, 8, and 1.6 is 0.8. - Simplified ratio: \( \frac{24}{0.8} : \frac{8}{0.8} : \frac{1.6}{0.8} = 30 : 10 : 2 \) ### (11) \( 1.5 \text{ m} \) - Convert to whole numbers: \( 1.5 : 1 = 15 : 10 \) - GCD of 15 and 10 is 5. - Simplified ratio: \( \frac{15}{5} : \frac{10}{5} = 3 : 2 \) ### (12) \( 6 \text{ kg} \text{ to } 600 \text{ g} \text{ to } 3000 \text{ g} \) - Convert all to grams: \( 6000 : 600 : 3000 \) - GCD of 6000, 600, and 3000 is 600. - Simplified ratio: \( \frac{6000}{600} : \frac{600}{600} : \frac{3000}{600} = 10 : 1 : 5 \) ### (13) \( 48 \text{ seconds to } 1 \text{ minute} \) - Convert to seconds: \( 48 : 60 \) - GCD of 48 and 60 is 12. - Simplified ratio: \( \frac{48}{12} : \frac{60}{12} = 4 : 5 \) ### (14) \( 3 \frac{1}{7} \text{ to } \frac{11}{14} \) - Convert to improper fractions: \( \frac{22}{7} : \frac{11}{14} \) - Cross-multiply to find GCD: \( 22 \times 14 = 308 \) and \( 11 \times 7 = 77 \) - GCD is 11. - Simplified ratio: \( \frac{22}{11} : \frac{11}{11} = 2 : 1 \) ### (15) \( 2 x^{2} y \text{ to } 6 x y^{2} \) - GCD of coefficients: \( 2 \) and \( 6 \) is \( 2 \). - Simplified ratio: \( \frac{2 x^{2} y}{2} : \frac{6 x y^{2}}{2} = x^{2} y : 3 x y^{2} \) ### Summary of Simplified Ratios: 1. \( 3 : 2 \) 2. \( 3 : 4 \) 3. \( 3 : 5 \) 4. \( 3 : 2 \) 5. \( 3 : 5 : 7 \) 6. \( 100 : 1 : 10 \) 7. \( 8 : 5 \) 8. \( 6 : 1 \) 9. \( 1000 : 1 \) 10. \( 30 : 10 : 2 \) 11. \( 3 : 2 \) 12. \( 10 : 1 :