Question

Determine if 2.25/10 =? 9/40
, 2.5/10 =? 90/40
, or 2.25/12 =? 90/40
is a proportion.(1 point)
Responses

None of these sets of ratios is a proportion.
None of these sets of ratios is a proportion.

2.2510=940
Start Fraction 2.25 over 10 End Fraction equals Start Fraction 9 over 40 End Fraction

2.2512=9040
Start Fraction 2.25 over 12 End Fraction equals Start Fraction 90 over 40 End Fraction

2.5/10 = 90/40

Answer 1

To determine if the ratios form a proportion, we need to check if the cross-products are equal for each pair of fractions. A proportion is established if \( \frac{a}{b} = \frac{c}{d} \), which implies that \( a \cdot d = b \cdot c \).

Let's analyze each case:

1. **For \( \frac{2.25}{10} \) and \( \frac{9}{40} \)**:
- Cross-multiplying gives:
\[
2.25 \cdot 40 \quad \text{and} \quad 10 \cdot 9
\]
- Calculate:
\[
2.25 \cdot 40 = 90
\]
\[
10 \cdot 9 = 90
\]
- Since \( 90 = 90 \), this is a proportion.

2. **For \( \frac{2.5}{10} \) and \( \frac{90}{40} \)**:
- Cross-multiplying gives:
\[
2.5 \cdot 40 \quad \text{and} \quad 10 \cdot 90
\]
- Calculate:
\[
2.5 \cdot 40 = 100
\]
\[
10 \cdot 90 = 900
\]
- Since \( 100 \neq 900 \), this is not a proportion.

3. **For \( \frac{2.25}{12} \) and \( \frac{90}{40} \)**:
- Cross-multiplying gives:
\[
2.25 \cdot 40 \quad \text{and} \quad 12 \cdot 90
\]
- Calculate:
\[
2.25 \cdot 40 = 90
\]
\[
12 \cdot 90 = 1080
\]
- Since \( 90 \neq 1080 \), this is not a proportion.

### Summary:
- **Proportion found:** \( \frac{2.25}{10} = \frac{9}{40} \)
- **Not proportions:** \( \frac{2.5}{10} = \frac{90}{40} \), \( \frac{2.25}{12} = \frac{90}{40} \)

Final answer: **None of these sets of ratios is a proportion**, except for the first one. However, since the question was whether any of the sets are a proportion, the solution is:

**2.25/10 = 9/40 is a proportion.**