Question

Compare the ratios 4:5 and 16:20.

2 models. One model has 5 sections. The second model has 20 sections.

4:5
16:20

Answer 1

To compare the ratios 4:5 and 16:20, we can simplify and analyze them based on their relative values.

**Step 1: Simplify the Ratios**

1. **For 4:5:**
The ratio 4:5 is already in its simplest form.

2. **For 16:20:**
To simplify:
- The greatest common divisor (GCD) of 16 and 20 is 4.
- Dividing both sides by 4:
\[
\frac{16}{4} : \frac{20}{4} = 4:5
\]
Thus, 16:20 simplifies to 4:5.

**Step 2: Comparison**

Since both ratios simplify to 4:5, **they are equivalent ratios**.

**Step 3: Model Representation**

For visualizing the ratios in models:

- **First Model (4:5)**:
Imagine dividing something into 5 parts, where 4 parts represent the first quantity and 1 part the second. This can be visualized as:
- 4 sections of one color (say blue) and 1 section of another (say red).

- **Second Model (16:20)**:
You can divide the same concept further into 20 parts. Here, maintaining the same ratio means:
- 16 sections of the first color (blue) and 4 sections of the second color (red).

Both models reflect the same ratio (4:5) proportionately, even though one has more sections than the other.

**Conclusion:**

The ratios 4:5 and 16:20 are equivalent, and both can be represented in models where the proportion remains consistent regardless of the total number of sections.