Question

use the cross product property to determine whether or not the following equations are proportions:

\\(\frac{10}{3} \div 25 = 2 \div 15\\)

Explanation:

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<reasoning>

Convert ratios to fractional form

\[
\frac{\frac{10}{3}}{25} = \frac{2}{15}
\]

Simplify the complex fraction

\[
\frac{10}{3 \times 25} = \frac{10}{75} = \frac{2}{15}
\]

Verify using cross-multiplication

\[

$$\begin{aligned} 2 \times 15 &= 30 \\ 15 \times 2 &= 30 \\ 30 &= 30 \end{aligned}$$

\]
</reasoning>

<answer>
Yes, the equation is a proportion.
</answer>

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Answer:

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</pre_analysis>

<reasoning>

Convert ratios to fractional form

\[
\frac{\frac{10}{3}}{25} = \frac{2}{15}
\]

Simplify the complex fraction

\[
\frac{10}{3 \times 25} = \frac{10}{75} = \frac{2}{15}
\]

Verify using cross-multiplication

\[

$$\begin{aligned} 2 \times 15 &= 30 \\ 15 \times 2 &= 30 \\ 30 &= 30 \end{aligned}$$

\]
</reasoning>

<answer>
Yes, the equation is a proportion.
</answer>

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]
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