Question

Evaluate:

$\left|\frac{1}{3}-\frac{1}{5}\right|$

Answer 1

Step 1: Convert all the rational numbers in equivalent form.

Given : $\left|\frac{1}{3}-\frac{1}{5}\right|$

To convert them in equivalent form take LCM of the denominator.

LCM of $3$ and $5$ is $15$.

Now convert both rational numbers in equivalent form with denominator $15$.

$\Rightarrow \frac{1\times 5}{3\times 5}=\frac{5}{15}$ and $\frac{1\times 3}{5\times 3}=\frac{3}{15}$

Step 2: Evaluate $\left|\frac{5}{15}-\frac{3}{15}\right|$

So, $\left|\frac{5}{15}-\frac{3}{15}\right|$

$$\begin{gathered} =\left|\frac{5-3}{15}\right| \\ =\left|\frac{2}{15}\right| \end{gathered}$$

$=\frac{2}{15}$ $\left[\because \left|\pm \mathrm{a}\right|=\mathrm{a}\right]$

Hence, $\left|\frac{1}{3}-\frac{1}{5}\right|=\frac{2}{15}$.