Question

Add and simplify:
$\frac{2}{3}+\frac{5}{6}+\frac{7}{9}=$

• A. $\frac{41}{24}$
• B. $\frac{41}{18}$
• C. $\frac{33}{18}$
• D. $\frac{33}{24}$

Answer 1

The correct option is B $\frac{41}{18}$

3, 6 and 9 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 6: 6, 12, 18, 24, 30, 36, ...
Multiples of 9: 9, 18, 27, 36, ...
LCM (3, 6, 9) = 18

Now we have to convert the denominators in all the 3 fractions into 18 (LCM of 3, 6, and 9)

$\frac{2}{3}=\frac{2\times 6}{3\times 6}=\frac{12}{18}$
$\frac{5}{6}=\frac{5\times 3}{6\times 3}=\frac{15}{18}$
and $\frac{7}{9}=\frac{7\times 2}{9\times 2}=\frac{14}{18}$

$\therefore \frac{2}{3}+\frac{5}{6}+\frac{7}{9}=\frac{12}{18}+\frac{15}{18}+\frac{14}{18}$
$=\frac{12+15+14}{18}$
$=\frac{41}{18}$