How do you simplify $\frac{1}{2} + \frac{2}{3} + \frac{3}{4}$ ?

Question

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Answer 1

$\frac{1}{2} + \frac{2}{3} + \frac{3}{4} = \frac{2 3}{1 2} = 1 \frac{1 1}{1 2}$
add them if the denominators are common. Now as LCD of the denominators $2, 3$ and $4$ is $12$
$\frac{1}{2} + \frac{2}{3} + \frac{3}{4} = (\frac{1}{2} \times 1) + (\frac{2}{3} \times 1) + (\frac{3}{4} \times 1)$
$= \frac{1 \times 6}{2 \times 6} + \frac{2 \times 4}{3 \times 4} + \frac{3 \times 3}{4 \times 3}$
$= \frac{6 + 8 + 9}{1 2} = \frac{2 3}{1 2}$

Answer 2

\frac{1}{2} + \frac{2}{3} + \frac{3}{4} = \frac{2 3}{1 2} = 1 \frac{1 1}{1 2}

add them if the denominators are common. Now as LCD of the denominators

2, 3

and

4

is

12

\frac{1}{2} + \frac{2}{3} + \frac{3}{4} = (\frac{1}{2} \times 1) + (\frac{2}{3} \times 1) + (\frac{3}{4} \times 1)

= \frac{1 \times 6}{2 \times 6} + \frac{2 \times 4}{3 \times 4} + \frac{3 \times 3}{4 \times 3}

= \frac{6 + 8 + 9}{1 2} = \frac{2 3}{1 2}