Question

Check if the following pair represent the same rational number:
$\frac{1}{3}$ and $\frac{-3}{9}$

Answer 1

Given: $\frac{1}{3}$ and $\frac{-3}{9}$
$\frac{-3}{9}=\frac{-3}{3\times 3}$ $[\because 9=3\times 3]$

$=\frac{-1}{3}$
Now, two numbers are $\frac{1}{3}$ and $\frac{-1}{3}$

Since both the rational numbers have the same denominator and numerator but they are of opposite signs.

$⟹$ they lie on either side of zero on the number line.
$\therefore$ $\frac{1}{3}\ne \frac{-3}{9}$