# How do you evaluate 1/3+1/2+2/3?

Jul 15, 2018

color(maroon)(=> 9/6 = 1 1/2

#### Explanation:

$\frac{1}{3} + \frac{1}{2} + \frac{2}{3}$

As there is no common factor between 2 & 3, 2*3 = 6 is the L C M.

$\implies \left(\frac{1}{3}\right) \cdot \left(\frac{2}{2}\right) + \left(\frac{1}{2}\right) \cdot \left(\frac{3}{3}\right) + \left(\frac{2}{3}\right) \cdot \left(\frac{2}{2}\right)$ as 6 is the L C M of 2 & 3.

$\implies \left(\frac{2}{6}\right) + \left(\frac{3}{6}\right) + \left(\frac{4}{6}\right)$

$\implies \frac{2 + 3 + 4}{6}$

$\implies \frac{9}{6}$

$\implies 1 \left({\cancel{3}}^{\textcolor{red}{1}} / {\cancel{6}}^{\textcolor{red}{2}}\right) = 1 \frac{1}{2}$

Jul 15, 2018

See a solution process below:

#### Explanation:

To add fractions they must be over a common denominator.

To change the denominator without changing the value of the fraction we can multiply each fraction by a form of $1$

$\frac{1}{3} = \frac{2}{2} \times \frac{1}{3} = \frac{2 \times 1}{2 \times 3} = \frac{2}{6}$

$\frac{1}{2} = \frac{3}{3} \times \frac{1}{2} = \frac{3 \times 1}{3 \times 2} = \frac{3}{6}$

$\frac{2}{3} = \frac{2}{2} \times \frac{2}{3} = \frac{2 \times 2}{2 \times 3} = \frac{4}{6}$

We can now rewrite the problem and add the fractions as:

$\frac{2}{6} + \frac{3}{6} + \frac{4}{6} = \frac{2 + 3 + 4}{6} = \frac{9}{6}$

We can reduce the fraction as:

$\frac{9}{6} = \frac{3 \times 3}{3 \times 2} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times 3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times 2} = \frac{3}{2}$

If necessary, we can convert this improper fraction into a mixed number:

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

Jul 15, 2018

$\frac{3}{2}$

#### Explanation:

Recall that to add fractions, we must have like denominators. We can start off by adding the fractions with the denominator of $3$ to get

$\frac{3}{3} + \frac{1}{2} = 1 \frac{1}{2}$, or $1.5$.

A more systematic way would be to get a common denominator of $6$, since this is the LCD of the fractions.

To get a denominator of $6$, we can multiply the first by $\frac{2}{2}$, the second by $\frac{3}{3}$, and the third by $\frac{2}{2}$. We now have

$\frac{2}{6} + \frac{3}{6} + \frac{4}{6}$

$\frac{9}{6}$, or $\frac{3}{2}$, or $1 \frac{1}{2}$, or $1.5$.

Hope this helps!

$\frac{3}{2}$

#### Explanation:

$\frac{1}{3} + \frac{1}{2} + \frac{2}{3}$

$= \setminus \frac{1 \setminus \cdot 2 + 1 \setminus \cdot 3 + 2 \setminus \cdot 2}{6}$

$= \setminus \frac{2 + 3 + 4}{6}$

$= \setminus \frac{9}{6}$

$= \setminus \frac{3 \setminus \cdot 3}{3 \setminus \cdot 2}$

$= \frac{3}{2}$