Question

Determine if 2.25/10 =? 9/40, or 2.25/12 =? 90/40 is a proportion.
A. 2.25/12 = 90/40
B. 2.25/10 = 9/40
C. None of these sets of ratios is a proportion.
D. 2.5/10 = 90/40

Answer 1

To determine if the given ratios form a proportion, we need to check if the cross products are equal. Two ratios a/b and c/d form a proportion if \( a \cdot d = b \cdot c \).

Let's evaluate the two options given:

### Option A: \( \frac{2.25}{12} \) and \( \frac{90}{40} \)

Cross multiplication:

\[
2.25 \cdot 40 = 90 \cdot 12
\]

Calculating both sides:

Left side:
\[
2.25 \cdot 40 = 90
\]

Right side:
\[
90 \cdot 12 = 1080
\]

Since \( 90 \neq 1080 \), this is **not a proportion**.

### Option B: \( \frac{2.25}{10} \) and \( \frac{9}{40} \)

Cross multiplication:

\[
2.25 \cdot 40 = 9 \cdot 10
\]

Calculating both sides:

Left side:
\[
2.25 \cdot 40 = 90
\]

Right side:
\[
9 \cdot 10 = 90
\]

Since \( 90 = 90 \), this is a **proportion**.

### Option D: \( \frac{2.5}{10} \) and \( \frac{90}{40} \)

Cross multiplication:

\[
2.5 \cdot 40 = 90 \cdot 10
\]

Calculating both sides:

Left side:
\[
2.5 \cdot 40 = 100
\]

Right side:
\[
90 \cdot 10 = 900
\]

Since \( 100 \neq 900 \), this is **not a proportion**.

### Conclusion:

The only set that forms a proportion is option B: \( \frac{2.25}{10} = \frac{9}{40} \).

So the correct answer is:
**B. \( \frac{2.25}{10} = \frac{9}{40} \)**.