Question

What are equivalent rational numbers ?

Answer 1

Equivalent rational numbers.

A rational number is a number that can be stated in the form of$\frac{p}{q}$ where $p\mathrm{and}q$ are integer such that $q\ne 0$.

Equivalent rational numbers: Two rational numbers are equivalent if their lowest form or standard form after reduction, is equal.

In any rational number, its numerator and denominator are multiplied or divided by the same integer to give the equivalent rational number.

Let $\frac{a}{b}$ be any rational number, then the equivalent rational number is determined as follow:

$\frac{a}{b}=\frac{a\times m}{b\times m}$or$\frac{a}{b}=\frac{a÷m}{b÷m}$

Where $m$is any integer.

Example:

Let us consider a rational number $\frac{4}{6}$.

The equivalent rational numbers are found as follows:

$$\begin{gathered} \left(i\right)\frac{4}{6}=\frac{4\times 2}{6\times 2}=\frac{8}{12} \\ \left(i\right)\frac{4}{6}=\frac{4÷2}{6÷2}=\frac{2}{3} \end{gathered}$$

Therefore, the equivalent rational numbers of $\frac{4}{6}$are $\frac{8}{12}\mathrm{and}\frac{2}{3}$.

Hence,Two rational numbers are equivalent if their lowest form or standard form after reduction, is equal.