Question

Determine if 2.2510=?940
, 2.510=?9040
, or 2.2512=?9040
is a proportion.(1 point)
Responses

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

2.510=9040
Start Fraction 2.5 over 10 End Fraction equals Start Fraction 90 over 40 End Fraction

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

None of these sets of ratios is a proportion.

Answer 1

To determine if any of the given sets of numbers form a proportion, we need to check if the cross products are equal for each pair of ratios.

1. For the first set: \(2.2510 = 940\)
- Expressed as fractions:
\[
\frac{2.25}{10} \quad \text{and} \quad \frac{9}{40}
\]
- Cross products:
\[
2.25 \times 40 \quad \text{and} \quad 10 \times 9
\]
- Calculating:
\[
2.25 \times 40 = 90 \quad \text{and} \quad 10 \times 9 = 90
\]
- Since \(90 = 90\), this set is a proportion.

2. For the second set: \(2.510 = 9040\)
- Expressed as fractions:
\[
\frac{2.5}{10} \quad \text{and} \quad \frac{90}{40}
\]
- Cross products:
\[
2.5 \times 40 \quad \text{and} \quad 10 \times 90
\]
- Calculating:
\[
2.5 \times 40 = 100 \quad \text{and} \quad 10 \times 90 = 900
\]
- Since \(100 \neq 900\), this set is **not** a proportion.

3. For the third set: \(2.2512 = 9040\)
- Expressed as fractions:
\[
\frac{2.25}{12} \quad \text{and} \quad \frac{90}{40}
\]
- Cross products:
\[
2.25 \times 40 \quad \text{and} \quad 12 \times 90
\]
- Calculating:
\[
2.25 \times 40 = 90 \quad \text{and} \quad 12 \times 90 = 1080
\]
- Since \(90 \neq 1080\), this set is **not** a proportion.

In conclusion, only the first set \(2.2510 = 940\) is a proportion.