Compare the ratios 4:5 and 16:20.

Question

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.