Question

Setting StartFraction 7 over 3 EndFraction equal to which ratio would result in a valid proportion?
StartFraction 9 over 49 EndFraction
StartFraction 18 over 42 EndFraction
StartFraction 42 over 18 EndFraction
StartFraction 49 over 9 EndFraction

Answer 1

To determine which ratio results in a valid proportion when set equal to \( \frac{7}{3} \), we need to check if the cross products of the fractions are equal. A proportion states that two ratios are equal, so if we set \( \frac{7}{3} = \frac{a}{b} \), then we must have:

\[
7b = 3a
\]

Now, let's evaluate each option:

1. **Option 1: \( \frac{9}{49} \)**

\[
7 \cdot 49 \quad \text{and} \quad 3 \cdot 9
\]
\[
343 \quad \text{and} \quad 27
\]
\( 343 \neq 27 \) (not proportional)

2. **Option 2: \( \frac{18}{42} \)**

\[
7 \cdot 42 \quad \text{and} \quad 3 \cdot 18
\]
\[
294 \quad \text{and} \quad 54
\]
\( 294 \neq 54 \) (not proportional)

3. **Option 3: \( \frac{42}{18} \)**

\[
7 \cdot 18 \quad \text{and} \quad 3 \cdot 42
\]
\[
126 \quad \text{and} \quad 126
\]
\( 126 = 126 \) (proportional)

4. **Option 4: \( \frac{49}{9} \)**

\[
7 \cdot 9 \quad \text{and} \quad 3 \cdot 49
\]
\[
63 \quad \text{and} \quad 147
\]
\( 63 \neq 147 \) (not proportional)

Thus, the ratio that results in a valid proportion with \( \frac{7}{3} \) is:

\[
\frac{42}{18}
\]