Question

Add and simplify:
$\frac{1}{3}+\frac{3}{4}+\frac{7}{12}=$

• A. $\frac{3}{5}$
• B. $\frac{4}{5}$
• C. $\frac{5}{3}$

Answer 1

The correct option is C $\frac{5}{3}$

3, 4, and 12 are the denominators of all the three fractions respectively.

Let's convert the unlike fractions into like fractions
Multiples of 3: 3, 6, 9, 12, 15, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, ...
Multiples of 12: 12, 24, 36, 48, ...
LCM (3, 4, 12) = 12

Now we have to convert the denominators in all the 3 fractions into 12 (LCM of 3, 4, and 12)

$\frac{1}{3}=\frac{1\times 4}{3\times 4}=\frac{4}{12}$
$\frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}$
and $\frac{7}{12}$ is already in its twelfth form.

$\therefore \frac{1}{3}+\frac{3}{4}+\frac{7}{12}=\frac{4}{12}+\frac{9}{12}+\frac{7}{12}$

$=\frac{4+9+7}{12}$

$=\frac{20}{12}$

$=\frac{2\times 2\times 5}{2\times 2\times 3}$

$=\frac{5}{3}$