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

To express the given ratios in their simplest form, we will follow these steps for each ratio: 1. Divide each term of the ratio by the greatest common divisor (GCD) of the terms. 2. If there are more than two terms, find the GCD of all terms and divide each term by that GCD. Let's solve 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) \( 1.6 \text{ to } 1 \) - To eliminate the decimal, multiply both terms by 10: \( 16 : 10 \). - GCD of 16 and 10 is 2. - Simplified ratio: \( \frac{16}{2} : \frac{10}{2} = 8 : 5 \) ### (8) \( 0.36 \text{ to } 0.06 \) - To eliminate the decimal, multiply both terms by 100: \( 36 : 6 \). - GCD of 36 and 6 is 6. - Simplified ratio: \( \frac{36}{6} : \frac{6}{6} = 6 : 1 \) ### (9) \( 0.01 \text{ to } 0.00001 \) - To eliminate the decimal, multiply both terms by 100000: \( 1 : 0.00001 \times 100000 = 1 : 0.1 \). - GCD of 1 and 0.1 is 0.1. - Simplified ratio: \( \frac{1}{0.1} : \frac{0.1}{0.1} = 10 : 1 \) ### (10) \( 2.4 \text{ to } 0.8 \text{ to } 0.16 \) - To eliminate the decimal, multiply all terms by 100: \( 240 : 80 : 16 \). - GCD of 240, 80, and 16 is 16. - Simplified ratio: \( \frac{240}{16} : \frac{80}{16} : \frac{16}{16} = 15 : 5 : 1 \) ### (11) \( 30 \text{ cm to } 1.5 \text{ m} \) - Convert 1.5 m to cm: \( 1.5 \text{ m} = 150 \text{ cm} \). - Ratio: \( 30 : 150 \). - GCD of 30 and 150 is 30. - Simplified ratio: \( \frac{30}{30} : \frac{150}{30} = 1 : 5 \) ### (12) \( 6 \text{ kg to } 600 \text{ g to } 3000 \text{ g} \) - Convert 6 kg to g: \( 6 \text{ kg} = 6000 \text{ g} \). - Ratio: \( 6000 : 600 : 3000 \). - GCD of 6000, 600, and 3000 is 600. - Simplified ratio: \( \frac{6000}{600} : \frac{600}{600} : \frac{3000}{600} = 10 : 1 : 5 \) ### 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. \( 10 : 1 \) 10. \( 15 : 5 : 1 \) 11. \( 1 : 5 \) 12. \( 10 : 1 : 5 \)