Pregunta
Express the following as a ratio in its simplest form: \( \begin{array}{lllll}\text { (1) } 16 \text { to } 12 & \text { (2) } & 27 \text { to } 36 & \text { (3) } & 16 \text { to } 24 \\ \text { (4) } 35 \text { to } 25 & \text { (5) } & 18 \text { to } 15 \text { to } 24 & \text { (6) } & 100 \text { to } 10 \text { to } 10000 \\ \text { (7) } 1,2 \text { to } 0,4 & \text { (8) } & 0,32 \text { to } 0,08 & \text { (9) } & 0,1 \text { to } 0,001 \\ \text { (10) } 2.1 \text { to } 0,7 \text { to } 0,14 & \text { (11) } & 60 \mathrm{~cm} \text { to } 1.2 \mathrm{~m} & \text { (12) } & 8 \mathrm{~kg} \text { to } 800 \mathrm{~g} \text { to } 4000 \mathrm{~g} \\ \text { (13) } 48 \text { seconds to } 1 \text { minute } & & & \end{array} \)
Ask by Nichols Pierce. in South Africa
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
Here are the simplified ratios:
1. 4:3
2. 3:4
3. 2:3
4. 7:5
5. 6:5:8
6. 10:1:1000
7. 3:1
8. 4:1
9. 100:1
10. 15:5:1
11. 1:2
12. 10:1:5
13. 4:5
Solución
Sure! Here are the simplified ratios for each of the given expressions:
1. **16 to 12**
\[
16 : 12 = 4 : 3
\]
2. **27 to 36**
\[
27 : 36 = 3 : 4
\]
3. **16 to 24**
\[
16 : 24 = 2 : 3
\]
4. **35 to 25**
\[
35 : 25 = 7 : 5
\]
5. **18 to 15 to 24**
\[
18 : 15 : 24 = 6 : 5 : 8
\]
6. **100 to 10 to 10,000**
\[
100 : 10 : 10,000 = 10 : 1 : 1,000
\]
7. **1.2 to 0.4**
\[
1.2 : 0.4 = 3 : 1
\]
8. **0.32 to 0.08**
\[
0.32 : 0.08 = 4 : 1
\]
9. **0.1 to 0.001**
\[
0.1 : 0.001 = 100 : 1
\]
10. **2.1 to 0.7 to 0.14**
\[
2.1 : 0.7 : 0.14 = 15 : 5 : 1
\]
11. **60 cm to 1.2 m**
\[
60\,\text{cm} : 1.2\,\text{m} = 60 : 120 = 1 : 2
\]
12. **8 kg to 800 g to 4,000 g**
\[
8\,\text{kg} : 800\,\text{g} : 4,000\,\text{g} = 8,000 : 800 : 4,000 = 10 : 1 : 5
\]
13. **48 seconds to 1 minute**
\[
48\,\text{seconds} : 60\,\text{seconds} = 48 : 60 = 4 : 5
\]
---
**Summary of Simplified Ratios:**
1. \(4 : 3\)
2. \(3 : 4\)
3. \(2 : 3\)
4. \(7 : 5\)
5. \(6 : 5 : 8\)
6. \(10 : 1 : 1000\)
7. \(3 : 1\)
8. \(4 : 1\)
9. \(100 : 1\)
10. \(15 : 5 : 1\)
11. \(1 : 2\)
12. \(10 : 1 : 5\)
13. \(4 : 5\)
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Mind Expander
(1) The ratio \( 16 \text{ to } 12 \) can be simplified by dividing both terms by their greatest common divisor, which is 4. This gives us \( 4 \text{ to } 3 \). (2) For the ratio \( 27 \text{ to } 36 \), we can simplify by dividing both numbers by their greatest common divisor, which is 9. Therefore, it simplifies to \( 3 \text{ to } 4 \).
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