Question

Add and choose the correct option:
$\frac{1}{3}+\frac{1}{6}$

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{6}$

Answer 1

The correct option is B $\frac{1}{2}$

3, and 6 are the denominators of both the fractions respectively.

Let's convert the unlike fractions into like fractions
Multiples of 3: 3, 6, 9, 12, ..
Multiples of 6: 6, 12, 18, 24, ..
LCM (3, 6) = 6

Now we have to convert the denominators in both the fractions into 6 (LCM of 3, 6)
$\frac{1}{3}=\frac{1\times 2}{3\times 2}=\frac{2}{6}$
and $\frac{1}{6}$ is already in its sixth form.

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

Now, prime factorising both the denominator and numerator and cancelling the common factors, we get
$=\frac{1\times 3}{2\times 3}$
$=\frac{1}{2}$