Question

Compare the ratios using the models.

2 models. One model has 5 sections and is labeled 4 to 5. The second model has 10 sections and is labeled 9 to 10.

The left model should have
segments shaded.
The right model should have
segments shaded.
So, 4:5
9:10.

Answer 1

To compare the ratios of the two models given, we need to analyze the shaded segments in each.

### Model 1: 4 to 5
- This model has **5 sections**.
- It is labeled **4 to 5**, which means out of the 5 sections, **4 sections are shaded**.

**Shaded segments in Model 1:** 4 sections out of 5
**Ratio:** \( \frac{4}{5} \)

### Model 2: 9 to 10
- This model has **10 sections**.
- It is labeled **9 to 10**, which means **9 sections are shaded out of 10**.

**Shaded segments in Model 2:** 9 sections out of 10
**Ratio:** \( \frac{9}{10} \)

### Comparing the Ratios
To compare \( \frac{4}{5} \) and \( \frac{9}{10} \):

1. **Convert both fractions to the same denominator** (which can be 10 in this case).
- \( \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} \)
- \( \frac{9}{10} \) remains as is.

Now we have:
- Model 1: \( \frac{8}{10} \)
- Model 2: \( \frac{9}{10} \)

### Conclusion
Comparing \( \frac{8}{10} \) and \( \frac{9}{10} \):
- \( \frac{8}{10} < \frac{9}{10} \)

Thus, the shaded portion in Model 1 (with a ratio of 4:5) is less than that in Model 2 (with a ratio of 9:10).

### Summary:
- **Model 1 (4:5)**: 4 out of 5 sections shaded.
- **Model 2 (9:10)**: 9 out of 10 sections shaded.
- The ratios show that Model 1 has a smaller proportion shaded compared to Model 2.