Question
Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios.
Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check the two that apply.
(2 points)
Responses
6:8
6:8
9:12
9:12
4:5
4:5
5:6
Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check the two that apply.
(2 points)
Responses
6:8
6:8
9:12
9:12
4:5
4:5
5:6
Answers
GPT-4o mini
To determine which ratios are equivalent to the ratio of 3 parts silver to 4 parts green (3:4), you can find equivalent ratios by multiplying both parts of the ratio by the same number.
1. **6:8**
- This can be derived from multiplying both parts of 3:4 by 2:
\(3 \times 2 = 6\) and \(4 \times 2 = 8\)
- So, \(3:4\) is equivalent to \(6:8\).
2. **9:12**
- This can be derived from multiplying both parts of 3:4 by 3:
\(3 \times 3 = 9\) and \(4 \times 3 = 12\)
- So, \(3:4\) is equivalent to \(9:12\).
3. **4:5**
- This does not match as you cannot simplify \(3:4\) to get \(4:5\).
4. **5:6**
- This does not match as well as it does not maintain the same proportion as \(3:4\).
The two equivalent ratios are:
- **6:8**
- **9:12**
1. **6:8**
- This can be derived from multiplying both parts of 3:4 by 2:
\(3 \times 2 = 6\) and \(4 \times 2 = 8\)
- So, \(3:4\) is equivalent to \(6:8\).
2. **9:12**
- This can be derived from multiplying both parts of 3:4 by 3:
\(3 \times 3 = 9\) and \(4 \times 3 = 12\)
- So, \(3:4\) is equivalent to \(9:12\).
3. **4:5**
- This does not match as you cannot simplify \(3:4\) to get \(4:5\).
4. **5:6**
- This does not match as well as it does not maintain the same proportion as \(3:4\).
The two equivalent ratios are:
- **6:8**
- **9:12**