Question

Which two ratios form a proportion?(1 point)
Responses

4/20
and 2/5
4 over 20 and 2 fifths

20/4
and 2/5
20 fourths and 2 fifths

4/20
and 1/5
4 over 20 and 1 fifth

20/4
and 1/5
20 fourths and 1 fifth

Answer 1

To determine which two ratios form a proportion, we need to check if the cross-products are equal. A proportion is formed when two ratios, \( \frac{a}{b} \) and \( \frac{c}{d} \), satisfy the condition \( a \cdot d = b \cdot c \).

Let's evaluate the provided pairs:

1. **4/20 and 2/5**
- Cross-products: \( 4 \cdot 5 = 20 \) and \( 20 \cdot 2 = 40 \) → Not equal, so not a proportion.

2. **20/4 and 2/5**
- Cross-products: \( 20 \cdot 5 = 100 \) and \( 4 \cdot 2 = 8 \) → Not equal, so not a proportion.

3. **4/20 and 1/5**
- Cross-products: \( 4 \cdot 5 = 20 \) and \( 20 \cdot 1 = 20 \) → Equal, so they form a proportion.

4. **20/4 and 1/5**
- Cross-products: \( 20 \cdot 5 = 100 \) and \( 4 \cdot 1 = 4 \) → Not equal, so not a proportion.

The correct answer is **4/20 and 1/5**. These two ratios form a proportion.