# How do you evaluate 5/6-2/3?

Mar 16, 2018

$\frac{1}{6}$

#### Explanation:

Both fractions must have the same denominators before you can add the numerators:.

$\frac{5}{6} - \frac{2 \times 2}{3 \times 2}$

$= \frac{5}{6} - \frac{4}{6}$

$= \frac{1}{6}$

Mar 16, 2018

$\frac{1}{6}$

#### Explanation:

$\text{before subtracting the fractions we require them to have}$
$\text{a "color(blue)"common denominator}$

$\text{this is achieved by multiplying numerator/denominator}$
$\text{of "2/3" by 2, thus making the denominator 6}$

$\Rightarrow \frac{5}{6} - \left(\frac{2 \times \textcolor{red}{2}}{3 \times \textcolor{red}{2}}\right)$

$= \frac{5}{6} - \frac{4}{6}$

$\text{now subtract the numerators leaving the denominator}$

$= \frac{5 - 4}{6} = \frac{1}{6}$

Mar 16, 2018

Make both numbers have a common denominator of 6, then just subtract to get $\frac{1}{6}$

#### Explanation:

To subtract the numerators (numbers at the top), find a common denominator (number at the bottom), which in this case I'll use 6, since 6 is a common multiple of both 6 and 3

So to convert $\frac{2}{3}$ to $\frac{n}{6}$, where $n$ just stands for some number you want to find, multiply both top and bottom by 2

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

So you replace $\frac{2}{3}$ with $\frac{4}{6}$ in that expression

$\frac{5}{6} - \frac{2}{3} = \frac{5}{6} - \frac{4}{6} = \frac{5 - 4}{6} = \frac{1}{6}$

To get the answer $\frac{1}{6}$