Question

Subtract and simplify:
$\frac{3}{4}-\frac{5}{12}=$

• A. $\frac{7}{6}$
• B. $\frac{1}{3}$
• C. $\frac{3}{2}$

Answer 1

The correct option is B $\frac{1}{3}$

$\frac{3}{4}-\frac{5}{12}$
As these are unlike fractions, we need to convert them into like fractions.

Step 1: Find the LCM of denominators 4 and 12.

Multiples of 4: 4, 8, 12, 16, 20, 24, ...
Multiples of 12: 12, 24, 36, 48, ...

12 is the common multiple of 4 and 12. So, LCM of 4 and 12 is 12.

Step 2: Now, we have to convert the denominators of both the fractions into 12 (LCM of 4 and 12) without changing the fraction value.
$\frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}$
$\frac{5}{12}$ is already in its twelfth form.

$\therefore \frac{3}{4}-\frac{5}{12}=\frac{9}{12}-\frac{5}{12}$
$=\frac{9-5}{12}$
$=\frac{4}{12}$
$=\frac{2\times 2}{2\times 2\times 3}$
$=\frac{1}{3}$