\begin{tabular}{l} BE SURE TO SHOW YOUR WORK, (2 points) proportion. Cirele yes or no, \\ \begin{tabular}{l} 1. \( \frac{8}{9}, \frac{16}{21} \) \\ Solve each proportion. BE SURE TO SHOW YOUR WORK. (4 pts, each) \\ \begin{tabular}{l} 2. \( \frac{1-5}{4}=\frac{3}{2} \) \\ \hline 3. No \\ \hline\( \frac{6 p-2}{7}=\frac{5 p+7}{8} \) \\ \hline\end{tabular} \\ \hline\end{tabular} \\ \hline\end{tabular}

Let's tackle the problem step by step! To check if the proportions are equivalent, we can cross-multiply. 1. For the proportions \( \frac{8}{9} \) and \( \frac{16}{21} \): \[ 8 \times 21 = 168 \quad \text{and} \quad 9 \times 16 = 144 \] Since \( 168 \neq 144 \), the answer is **No**. 2. For the equation \( \frac{1-5}{4}=\frac{3}{2} \): Simplify the left side: \[ \frac{-4}{4} = -1 \] Since \( -1 \neq \frac{3}{2} \), this proportion is **No**. 3. For the equation \( \frac{6p-2}{7}=\frac{5p+7}{8} \): Cross-multiply: \[ 8(6p - 2) = 7(5p + 7) \] This gives: \[ 48p - 16 = 35p + 49 \] Then, collect like terms: \[ 48p - 35p = 49 + 16 \\ 13p = 65 \\ p = 5 \] Now let’s summarize the findings in an engaging way! History loves proportions! Did you know that the concept of proportion dates back to ancient civilizations? The Greeks, particularly, delved deep into proportions and ratios. They believed these mathematical principles were not just for calculations but also tied to the aesthetics of art and architecture, like the famous Golden Ratio! And speaking of real-world applications, proportions are not just for math class! You might use them unknowingly while cooking or baking. If a recipe serves four but you need to serve six, adjusting the ingredient proportions is key! It's like being a math magician in the kitchen!