To determine which proportion correctly describes the relative amounts of each color of blocks, let's first analyze the color distributions in each group.
Group 1:
- Red blocks: 15
- Green blocks: 45
Group 2:
- Red blocks: 30
- Green blocks: 90
Now, let's simplify the ratios for each group:
Group 1 Ratio:
- Ratio of red to green blocks = \( \frac{15}{45} \)
- Simplifying \( \frac{15}{45} \) gives \( \frac{1}{3} \).
Group 2 Ratio:
- Ratio of red to green blocks = \( \frac{30}{90} \)
- Simplifying \( \frac{30}{90} \) gives \( \frac{1}{3} \).
Now let's consider the proposed responses:
- \(\frac{1}{3}\) - This reflects the ratio of red to green for both groups. This is correct.
- \(\frac{15}{45}\) - This is the ratio of red to green for Group 1, simplified, also equals \( \frac{1}{3} \).
- \(\frac{15}{45} = \frac{90}{30}\) - This represents the equality of the ratios for both groups, which is also true (after simplification both sides equal \( \frac{1}{3} \)).
- \(\frac{15}{45} = \frac{30}{90}\) - This shows the equality of the counts, which upon simplification also holds true.
Since all options reflect correct proportions relating to the red and green blocks, every option is valid. However, if you are looking for which one describes the relationship succinctly, \(\frac{1}{3}\) is the simplest representation, as it summarizes the relationship in a single fraction.
Final Answer:
\(\frac{1}{3}\) is the correct proportion describing the relative amounts of each color.
1 answer