Question

Is the ratio$a:b$always, sometimes, or never equal to the ratio$b:a$? Explain.

Short answer

Ratio$a:b$ is never equal to$b:a$.

Step-by-step solution

Step 1. Given information.

The given ratio is$a:b$ .

Step 2. Concept Used.

A number and its inverse is never equal.

Step 3. Let’s check with the help of an example.

Suppose that,

$\begin{array}{l}a:b=2:1\\ \frac{a}{b}=\frac{2}{1}\end{array}$

Find the inverse of given ratio.

$\begin{array}{l}b:a=1:2\\ \frac{b}{a}=\frac{1}{2}\end{array}$

Here we can see that both the ratios are not same.

Therefore, the ratio$a:b$ is never equal to.$b:a$