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

Question

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

UpStudy AI · Accepted Answer

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) $$ 18 	ext{ to } 12 $$
- GCD of 18 and 12 is 6.
- Simplified ratio: $$ \frac{18}{6} : \frac{12}{6} = 3 : 2 $$

### (2) $$ 24 	ext{ to } 32 $$
- GCD of 24 and 32 is 8.
- Simplified ratio: $$ \frac{24}{8} : \frac{32}{8} = 3 : 4 $$

### (3) $$ 15 	ext{ to } 25 $$
- GCD of 15 and 25 is 5.
- Simplified ratio: $$ \frac{15}{5} : \frac{25}{5} = 3 : 5 $$

### (4) $$ 30 	ext{ to } 20 $$
- GCD of 30 and 20 is 10.
- Simplified ratio: $$ \frac{30}{10} : \frac{20}{10} = 3 : 2 $$

### (5) $$ 9 	ext{ to } 15 	ext{ to } 21 $$
- GCD of 9, 15, and 21 is 3.
- Simplified ratio: $$ \frac{9}{3} : \frac{15}{3} : \frac{21}{3} = 3 : 5 : 7 $$

### (6) $$ 1000 	ext{ to } 10 	ext{ to } 100 $$
- GCD of 1000, 10, and 100 is 10.
- Simplified ratio: $$ \frac{1000}{10} : \frac{10}{10} : \frac{100}{10} = 100 : 1 : 10 $$

### (7) $$ 1.6 	ext{ to } 1 $$
- 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) $$ 0.36 	ext{ to } 0.06 $$
- 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) $$ 0.01 	ext{ to } 0.00001 $$
- To eliminate the decimal, multiply both terms by 100000: $$ 1 : 0.00001 	imes 100000 = 1 : 0.1 $$.
- GCD of 1 and 0.1 is 0.1.
- Simplified ratio: $$ \frac{1}{0.1} : \frac{0.1}{0.1} = 10 : 1 $$

### (10) $$ 2.4 	ext{ to } 0.8 	ext{ to } 0.16 $$
- 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) $$ 30 	ext{ cm to } 1.5 	ext{ m} $$
- Convert 1.5 m to cm: $$ 1.5 	ext{ m} = 150 	ext{ cm} $$.
- Ratio: $$ 30 : 150 $$.
- GCD of 30 and 150 is 30.
- Simplified ratio: $$ \frac{30}{30} : \frac{150}{30} = 1 : 5 $$

### (12) $$ 6 	ext{ kg to } 600 	ext{ g to } 3000 	ext{ g} $$
- Convert 6 kg to g: $$ 6 	ext{ kg} = 6000 	ext{ g} $$.
- 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. $$ 10 : 1 : 5 $$
Here are the 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

YERCISE 4 You may use a calculator in this exercise.
Express the following as a ratio in its simplest form:

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