Question

Choose the correct symbol to make the following expression true.
$\frac{1}{2}\text{?}\frac{1}{3}$

• A. $<$
• B. $>$
• C. $=$
• D. $\le$

Answer 1

The correct option is B $>$

Let's compare $\frac{1}{2}\text{and}\frac{1}{3}:$

Step 1: Find the LCM of denominators of the given fractions.
i.e. LCM of 2 and 3
2 can be written as $2:2\times 1$
3 can be written as $3:3\times 1$

Taking the factors with highest powers common, we get
$2^1$ from 2 and $3^1$ from 3.

Multiplying them, we get $2^1\times 3=6$ as the required LCM.

Step 2: Now, we multiply $\frac{1}{2}$ and $\frac{1}{3}$ with $3$ and $2$ respectively to make their denominators as $6.$

$\therefore \frac{1}{2}=\frac{1\times 3}{2\times 3}=\frac{3}{6}$

and $\frac{1}{3}=\frac{1\times 2}{3\times 2}=\frac{2}{6}$

When fractions have the same denominator, then the largest fraction is the one with the largest numerator.

So, just compare the numerators 3 and 2.

Since $3>2$
$\therefore \frac{3}{6}>\frac{2}{6}$
$\Rightarrow \frac{1}{2}>\frac{1}{3}$