# How do you add 1/3 + 5/12 + 4/5?

Apr 29, 2016

$\frac{1}{3} + \frac{5}{12} + \frac{4}{5} = 1 \frac{11}{20}$

#### Explanation:

To add $\frac{1}{3} + \frac{5}{12} + \frac{4}{5}$, firs convert all denominators to Lease Common Denominator (LCD), which is nothing but Least common multiple of $3$, $12$ and $5$. As $3$ is a factor of $12$, their LCD is $12$ and LCD of $12$ and $5$ is $12 \times 5 = 60$ (as nothing is common between them. Hence LCD of $3$, $12$ and $5$ is $60$.

Hence, converting each denominator of $\frac{1}{3} + \frac{5}{12} + \frac{4}{5}$ to LCD,

$\frac{1}{3} + \frac{5}{12} + \frac{4}{5}$ = $\frac{1 \times 20}{3 \times 20} + \frac{5 \times 5}{12 \times 5} + \frac{4 \times 12}{5 \times 12}$

= $\frac{20}{60} + \frac{25}{60} + \frac{48}{60}$

= $\frac{20 + 25 + 48}{60} = \frac{93}{60} = \frac{31 \cancel{93}}{20 \cancel{60}} = \frac{31}{20} = 1 \frac{11}{20}$

(We have divided $93$ and $60$ by $3$ here to simplify.)