Question

Subtract and simplify:
$\frac{2}{3}-\frac{1}{2}=$

• A. $\frac{5}{6}$
• B. $\frac{1}{3}$
• C. $\frac{1}{6}$

Answer 1

The correct option is C $\frac{1}{6}$

$\frac{2}{3}-\frac{1}{2}$
As these are unlike fractions, we need to convert them into like fractions.

Step 1: Find the LCM of denominators 3 and 6

Multiples of 2: 2, 4, 6, 8, 10, ...
Multiples of 3: 3, 6, 9, 12, 15, ...

6 is the common multiple of 2 and 3. So, LCM of 2 and 3 is 6.

Step 2: Now, we have to convert the denominators of both the fractions into 6 (LCM of 2 and 3) without changing the fraction value.
$\frac{2}{3}=\frac{2\times 2}{3\times 2}=\frac{4}{6}$
$\frac{1}{2}=\frac{1\times 3}{2\times 3}=\frac{3}{6}$


Step 3: Now, subtract the fractions
$\therefore \frac{2}{3}-\frac{1}{2}=\frac{4}{6}-\frac{3}{6}$

$=\frac{4-3}{6}$

$=\frac{1}{6}$