# What is the simplified value of  1/7 + 3/14 + 2/3 + 2/5 + 5/6 ?

Apr 29, 2016

$\frac{1}{7} + \frac{3}{14} + \frac{2}{3} + \frac{2}{5} + \frac{5}{6} = 2 \frac{27}{105}$

#### Explanation:

To add $\frac{1}{7} + \frac{3}{14} + \frac{2}{3} + \frac{2}{5} + \frac{5}{6}$, firs convert all denominators to Lease Common Denominator (LCD), which is nothing but Least common multiple of $7$, $14$, $3$, $5$ and $6$.

LCD of $7$, $14$, $3$, $5$ and $6$ is

$14 \times 6 \times 5 = 420$ (as $7$ is a factor of $14$ and $3$ is a factor of $5$).

Hence, converting each denominator of $\frac{1}{7} + \frac{3}{14} + \frac{2}{3} + \frac{2}{5} + \frac{5}{6}$ to $420$,

$\frac{1}{7} + \frac{3}{14} + \frac{2}{3} + \frac{2}{5} + \frac{5}{6}$

= $\frac{1 \times 60}{7 \times 60} + \frac{3 \times 30}{14 \times 30} + \frac{2 \times 140}{3 \times 140} + \frac{2 \times 84}{5 \times 84} + \frac{5 \times 70}{6 \times 70}$

= $\frac{60}{420} + \frac{90}{420} + \frac{280}{420} + \frac{168}{420} + \frac{350}{420}$

= $\frac{60 + 90 + 280 + 168 + 350}{420}$

= $\frac{948}{420} = \frac{237 \cancel{948}}{105 \cancel{420}} = \frac{237}{105} = 2 \frac{27}{105}$

(We have divided $948$ and $420$ by $4$ here to simplify.)