Question

$\left(a\right)$Apply the means-extremes property of proportions to the proportion.

$\frac{e}{f}=\frac{g}{5}$and you get$5e=?$

$\left(b\right)$Apply the property to the proportion$\frac{5}{f}=\frac{g}{e}$ and you get$?=?$

$\left(c\right)$Are the proportions$\frac{e}{f}=\frac{g}{5}$ and$\frac{5}{f}=\frac{g}{e}$ equivalent Why

Short answer

a.The result is,$fg$.

b.The result is,$5e\text{and}gf$.

c.They are equivalent.

Step-by-step solution

Step 1. Given information.

Proportion is given as,

$\frac{e}{f}=\frac{g}{5}$

Step 2. Apply means-extreme property.

End value is extremes,

and middle are means.

Step 3. There is called extreme property as shown below.

$\begin{array}{l}\frac{e}{f}=\frac{g}{5}\\ e\times 5=g\times f\\ 5e=fg\end{array}$

Therefore, the result is,$fg$ .

Step 1. Given information.

Proportion is given as,

$\frac{5}{f}=\frac{g}{e}$

Step 2. Cross multiply each value.

$\begin{array}{l}\frac{5}{f}=\frac{g}{e}\\ 5\times e=g\times f\\ 5e=gf\end{array}$

Therefore, the result is $5e\text{and}gf$.

Step 1. Given information.

Proportions are given as,

$\frac{e}{f}=\frac{g}{5}\text{and}\frac{5}{f}=\frac{g}{e}$

Step 2. Cross multiply each value.

$\begin{array}{l}\frac{e}{f}=\frac{g}{5}\text{and}\frac{5}{f}=\frac{g}{e}\\ e\times 5=g\times f\text{and}5\times e=g\times f\\ e5=gf\text{and}5e=gf\end{array}$

Yes, they are equal.

Therefore, the answer is, they are equivalent.