Question

Explain an easy way to show that the proportions$\frac{x}{7}=\frac{2}{3}$and$\frac{x}{2}=\frac{3}{7}$ are not equivalent.

Short answer

The given fractions are not equivalent.

Step-by-step solution

Step 1. Given information.

The given proportions are,

$\frac{x}{7}=\frac{2}{3}and\frac{x}{2}=\frac{3}{7}$

 Step 2. Formula used.

The value of X are different in both proportions.

The given proportions are,$\frac{x}{7}=\frac{2}{3}and\frac{x}{2}=\frac{3}{7}$

For, $\frac{x}{7}=\frac{2}{3}$

Step 3. Using cross multiplication and solving for x.

$\begin{array}{l}3x=14\\ x=\frac{14}{3}\end{array}$

And for,$\frac{x}{2}=\frac{3}{7}$

Step 4. Using cross multiplication and solving for x.

$\begin{array}{l}7x=6\\ x=\frac{6}{7}\end{array}$

Here, we get for different fraction get different value of X.

Therefore, the given fractions are not equivalent.