Question

Subtract $\frac{1}{11}$ from $\frac{1}{2}$ and choose the correct answer.

• A. $\frac{9}{22}$
• B. $\frac{7}{22}$
• C. $\frac{13}{22}$
• D. $\frac{2}{11}$

Answer 1

The correct option is A $\frac{9}{22}$

We have to subtract $\frac{1}{11}$ from $\frac{1}{2},$ so we have to find the value of $\frac{1}{2}-\frac{1}{11}.$

As these are unlike fractions, we need to convert them into like fractions.

Step 1: Find the LCM of denominators 2 and 11

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, ...
Multiples of 11: 11, 22, 33, 44, ...

22 is the common multiple of 2 and 11. So, LCM of 2 and 11 is 22.

Step 2: Now, we have to convert the denominators of both the fractions into 22 (LCM of 2 and 11) without changing the fraction value.

$\frac{1}{2}=\frac{1\times 11}{2\times 11}=\frac{11}{22}$
and $\frac{1}{11}=\frac{1\times 2}{11\times 2}=\frac{2}{22}$

$\therefore \frac{1}{2}-\frac{1}{11}=\frac{11}{22}-\frac{2}{22}$
$=\frac{11-2}{22}$
$=\frac{9}{22}$