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.

A 2-column table has 3 rows. Column 1 is labeled Silver paints (parts) with entries 3, blank, blank. Column 2 is labeled Green paint (parts) with entries 4, blank, blank.

Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check all that apply.
4:5
6:8
5:6
9:12

Answer 1

To determine which ratios are equivalent to the ratio of 3 parts silver to 4 parts green, we can simplify the ratio and check if the given options are equivalent.

The ratio of silver to green can be written as:

\[
\frac{3}{4}
\]

We will check each option to see if it simplifies to \( \frac{3}{4} \):

1. **4:5**
\[
\frac{4}{5} \quad \text{is not equivalent to } \frac{3}{4}
\]

2. **6:8**
Simplifying \( \frac{6}{8} \):
\[
\frac{6 \div 2}{8 \div 2} = \frac{3}{4} \quad \text{(equivalent)}
\]

3. **5:6**
\[
\frac{5}{6} \quad \text{is not equivalent to } \frac{3}{4}
\]

4. **9:12**
Simplifying \( \frac{9}{12} \):
\[
\frac{9 \div 3}{12 \div 3} = \frac{3}{4} \quad \text{(equivalent)}
\]

In conclusion, the ratios equivalent to 3 parts silver to 4 parts green are:
- **6:8**
- **9:12**