Question

Add and choose the correct option:
$\frac{2}{3}+\frac{1}{5}+\frac{6}{15}$

• A. $2\frac{4}{15}$
• B. $15\frac{1}{4}$
• C. $4\frac{1}{15}$
• D. $1\frac{4}{15}$

Answer 1

The correct option is D $1\frac{4}{15}$

3, 5 and 15 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, 18, 21, ...
Multiples of 5: 5, 10, 15, 20, 25, ,,
Multiples of 15: 15, 30, 45, 60, ..
LCM (3, 5, 15) = 15

Now we have to convert the denominators in all the 3 fractions into 15 (LCM of 3, 5, and 15)

$\frac{2}{3}=\frac{2\times 5}{3\times 5}=\frac{10}{15}$
$\frac{1}{5}=\frac{1\times 3}{5\times 3}=\frac{3}{15}$
and $\frac{6}{15}$ is already in its fifteenth form.

$\therefore \frac{2}{3}+\frac{1}{5}+\frac{6}{15}=\frac{10}{15}+\frac{3}{15}+\frac{6}{15}$
$=\frac{10+3+6}{15}$
$=\frac{19}{15}$
$=\frac{15+4}{15}$
$=\frac{15}{15}+\frac{4}{15}$
$=1+\frac{4}{15}$
$=1\frac{4}{15}$