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>

Rewrite the division expressions as fractions

\[

$$\begin{aligned} \text{Left Side (LHS)} &= \frac{\frac{10}{3}}{25} = \frac{10}{3 \times 25} = \frac{10}{75} \\ \text{Right Side (RHS)} &= \frac{2}{15} \end{aligned}$$

\]

Apply the cross product property

\[

$$\begin{aligned} 10 \times 15 &= 150 \\ 75 \times 2 &= 150 \end{aligned}$$

\]

Compare the cross products

\[
150 = 150
\]
</reasoning>

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

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Answer:

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<reasoning>

Rewrite the division expressions as fractions

\[

$$\begin{aligned} \text{Left Side (LHS)} &= \frac{\frac{10}{3}}{25} = \frac{10}{3 \times 25} = \frac{10}{75} \\ \text{Right Side (RHS)} &= \frac{2}{15} \end{aligned}$$

\]

Apply the cross product property

\[

$$\begin{aligned} 10 \times 15 &= 150 \\ 75 \times 2 &= 150 \end{aligned}$$

\]

Compare the cross products

\[
150 = 150
\]
</reasoning>

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

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"Mathematics",
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]
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