# What is 1/3+ 3/4+ 1/2?

Mar 29, 2016

$\frac{1}{3} + \frac{3}{4} + \frac{1}{2} = \frac{19}{12}$

#### Explanation:

To add proper fractions, we need to first make their denominator identical. This can be done in one step, but to demonstrate, we will add the fractions one by one.

First, we add $\frac{1}{3}$ and $\frac{3}{4}$. To do so, we need them to have a common denominator. Therefore, we will find a common multiple of 3 and 4. That would be $3 \times 4 = 12$. You can easily verify that $12$ must have both $3$ and $4$ as factors. So,

$\frac{1}{3} + \frac{3}{4} = \frac{1 \times 4}{3 \times 4} + \frac{3 \times 3}{4 \times 3}$

$= \frac{4}{12} + \frac{9}{12}$

$= \frac{4 + 9}{12}$

$= \frac{13}{12}$

Next, we add $\frac{1}{2}$ to $\frac{13}{12}$. Again, we need a common denominator. That would be $2 \times 12 = 24$. You can verify that 24 has both $12$ and $2$ as factors. However, the number $12$ has also both $12$ and $2$ as factors.

It is easier to deal with smaller numbers, so we use 12 instead of 24.

$\frac{13}{12} + \frac{1}{2} = \frac{13}{12} + \frac{1 \times 6}{2 \times 6}$

$= \frac{13}{12} + \frac{6}{12}$

$= \frac{13 + 6}{12}$

$= \frac{19}{12}$

Therefore,

$\frac{1}{3} + \frac{3}{4} + \frac{1}{2} = \frac{19}{12}$