Question

The antecedent and the consequent of a ratio ________ interchanged unless there is a change in the given statements.
(a)Can be
(b)Cannot be
(c)Sometimes
(d)none

Answer 1

Hint: Think of writing ratio $a:b$ in division form. Then, the dividend is known as the antecedent of the ratio and the divisor is the consequent of the ratio. Then, apply the same rule that can be applied to division of two numbers, that is $\dfrac{a}{b} \ne \dfrac{b}{a}$.

Complete step-by-step answer:
Ratio is a comparison of two numbers.
If a ratio is written as, $a:b$, then $a$ and $b$ are known as the terms of ratio.
In ratio, $a:b$, the term $a$ is called the antecedent of the ratio and the term $b$ is called the consequent of the ratio.
The ratio can also be written in division form such as, $\dfrac{a}{b}$, where the dividend is known as the antecedent of the ratio and the divisor is the consequent of the ratio.
Just as, $\dfrac{a}{b} \ne \dfrac{b}{a}$, similarly, $a:b \ne b:a$
Therefore, we can say that, the antecedent and the consequent of a ratio cannot be interchanged unless there is a change in the given statements.
Hence, option B is correct.

Note: When the ratio is written as $a:b$, then $a$ and $b$ are generally in simplest form, that is they do not have any common factor other than 1. Conversion can be done to the simplest form by dividing the greatest common factor between them.